Welcome back to my channel and welcome if you're new here. My name is Jen I'm a certified weight loss and nutrition coach and I'm on the WWW blue plan today's Monday So that means it's a meal prep day and I have three Absolutely fantastic recipes for you I have breakfast lunch and a really really good snack slash dessert recipe all of my recipes are on my website Which is linked down in the description box below You'll also find the links and discount codes to some of the products that I shared with you today As well as the rest of my favorite things you'll also find my nutrition coaching website I'd love to help you configure your macros one-on-one coaching even group coaching So definitely check that out if you are new to my channel I'd love it if you'd stick around and subscribe and hit the little bell next to it I'd love to have you also give this one a thumbs up if you are here for meal prep And lastly make sure you head on over and check out my Facebook group We'd love to have you join that amazing community as well. So without further ado Let's jump into this week's WWW meal prep for breakfast this week. I'm bringing in holiday all things holiday We are doing a cranberry and orange buttermilk breakfast bake So it's kind of a spin on a pancake bake with all the holiday flavors of cranberry and orange So let me show you what's in breakfast first.  I will link Locanto's website down below with a discount code for you guys They have great products in general, but they have all of the really good sugar alternatives Everything from granulated brown sugar powdered sugar. So definitely check them out and you get a discount So that's linked down below for you. This is just some organic flour Butter. I'm using the melt plant-based butter You'll need vanilla extract and baking powder salt Fresh cranberries and one navel orange. So let's make breakfast. So to get started on our bake We are going to add in one half of a cup of butter. This is exactly half of a cup in here It's actually just a little bit shy, but I'm not really too worried about that So I did let this sit out and become room temperature So we're gonna add that in and then I did zest that orange So we'll add in the zest of the orange. We don't need the juice So just the zest and then I'm just going to take a spoon and we're going to cream this together We're really going to incorporate the orange zest with that butter once your butter and orange zest is nice and creamed together We are going to add an egg and I apologize. I didn't show you that in the beginning You're also going to need one egg So my apologies for that and we're also going to add in our vanilla So about a teaspoon of vanilla and then we are going to cream this together and again You can use a spoon like I am here or you can use a hand mixer whatever your preference is I'm just going to use a spoon and just really really dig in and get this mixed really well once that is mixed together We're going to add in our two cups of all-purpose flour And then we also want a teaspoon of baking powder and then just a pinch of salt So we're going to just add just the tiniest bit of salt and now we're going to combine this together until fully mixed We're now going to add in one cup of monk fruit sweetener give that just another quick mix You are going to have your batter be kind of lumpy and chunky You can see how my batter isn't nice and smooth it will become smooth once we pop in our buttermilk So the next step is to add in one half of a cup of low-fat buttermilk Now stir that until fully combined and then lastly are our cranberries So I ended up adding about another half of a cup of buttermilk It just wasn't quite the right consistency This is kind of what you're looking for more of a batter and then lastly we're going to add two cups of Fresh cranberries and then we're just going to fold those in now. This was almost that entire bag I would say that there was maybe half of a cup of the fresh cranberries left over So our batter is done. Look at how amazing that looks So I went ahead and grabbed out a pretty good size pan about an eight by eight or a nine by nine We are going to spray that really well with non-stick cooking spray We certainly don't want our delicious bake to stick to the pan and then we are going to add in our batter and Smooth it out so it's nice and even and I did just turn my oven on to preheat to 350 degrees So I have my mix in my pan doesn't this look amazing you guys Last step before it goes into oven is take your monk fruit or whatever sweetener you're using You want about a tablespoon or so and we're just going to sprinkle that over the top and when it cooks It'll get that nice Crystalline caramelized sugary top. Oh my goodness. This is going to be Amazing, so I am going to pop this in the oven 350 degrees For about 45 minutes or so or until the pancakes are cooked all the way through look at this you guys This looks so good. You can't really see but there is this crystallization on top from that monk fruit Oh my goodness. I am pretty darn excited for this breakfast So I am going to let this cool slice it into servings and I'll be back to give you points and calories So I went ahead and cut it into eight servings So one of these squares is a serving I'm planning on pairing this with some eggs because eggs are zero points on the blue plan This bake cut into eight servings is seven smart points on all plans.  It is so cranberry orange. It is Incredible so highly highly recommend this recipe. It would be a great great breakfast for the entire family For lunch this week I'm making a teriyaki turkey rice bowl Packs of protein past with veggies and then of course carbs and the rice very very well balanced lunch So let me show you what's in our recipe first We're going to make our homemade teriyaki sauce So I'm going to show you what's in that and then I'll show you what's in the ground turkey portion So first you're going to need some red wine vinegar soy sauce or coconut aminos minced garlic Ground ginger you could use fresh ginger whatever your preference is some sort of brown sugar alternative You guys know I'm obsessed with sucre and gold. I actually buy this off of the net triton website same place I buy my pasta so I'll link that down below for you about a quarter cup of water And then we're probably going to need a couple more tablespoons to make it the right consistency And then you'll need a thickener so cornstarch or arrowroot powder whatever your preference is So that is what is in the homemade teriyaki sauce and then for the ground turkey You're going to need obviously a pound of ground turkey. This is 99 percent We'll need some rice.  So let's put together the teriyaki sauce ingredients It does need to go in to a pan so that it can go on to the stove to warm So to that we are going to add in two tablespoons of sucran or whatever brown sugar alternative that you're using one quarter cup of water One half of a cup of soy sauce or in my case Coconut Aminos we have a couple of teaspoons of minced garlic Maybe a little more than a couple of teaspoons and then we do need to add in one tablespoon of Cornstarch or whatever you're using as your thickener So I have again the arrowroot powder So I'm gonna go ahead and add that and then we also need to add one tablespoon of red wine I'm sorry two tablespoons. Oh My gosh Okay, then so we probably have a little more than two tablespoons of red wine vinegar Oh my gosh how you know I could edit this out, but I'm not going to because this is real life So I'm not too worried about it to be honest with you. I don't know how much that was but you want about two tablespoons I cannot believe that okay moving on. So we are gonna go ahead and add in about a teaspoon of ground Ginger and then we're gonna pop this on the stove until it warms through and the sugar is dissolved So all of my ingredients are here in my saucepan I'm just going to warm them until it thickens up So I did go ahead and add my arrowroot powder directly You can also mix that with a couple tablespoons of water and make a slurry So kind of whatever your preference is but I am just going to stir and heat until my sauce has thickened Right and look at this. Oh my gosh. It's nice and thick. Oh, it looks so good So I'm just gonna set this aside while we put together the rest of the bowl now I'm gonna chop for the bowl. So I have some green onions here. This will actually top the bowl I have three small ones here. We're just gonna pop each vegetable in a bowl a couple carrots here Here I'm going to peel and chop and my onion a bowl for each of them You are I don't know what you've been through why you got scars Since you walked through the door, I've been trying to reach you On my stove I have a really good size skillet and we are going to add a tablespoon of oil Let that kind of warm up for just a couple of seconds and then we're gonna pop in our onions All right, we're gonna go ahead and add in our onions, and we're just going to let those cook until softened Once your onions are soft. We're going to add in one pound of Ground turkey and we are going to let this cook until about 75% of the way cooked through and then we're going to add in broccoli and carrots Once your turkey is cooked all the way through your carrots and your broccoli have started to soften maybe 50% Softened we are going to go ahead and add in the teriyaki sauce that we made earlier And we are going to let this simmer for about five minutes or so We want to make sure all the flavors get combined and my rice is cooking and it should be done And then we're ready to assemble the bowls. All right, everything is ready We have the teriyaki turkey with veggies that smells incredible and then here is my cooked rice So I did half of a cup of cooked rice per bowl There may be some additional rice left over, but I am points wise planning for a half of a cup per bowl So we're going to start by adding rice to all five meal prep bowls This makes five servings and then we'll top it with this delicious turkey teriyaki mixture So i'm going to do one half of a cup of rice. So I have a half of a cup here I'm just going to pop in my rice Add that to the bowl and then we're just going to repeat now I think that's plenty of rice because we're also going to have the turkey mixture So let's build the other four bowls So we have all five bowls of rice half of a cup each now We're just going to divide our mixture evenly over the top I'm just going to start with a spoonful per bowl And I'll just keep going until we've used all of the meat and veggie mixture These look so Good look at that What a huge hearty lunch. I'm I'm really excited for this. So I have my chopped up green onions I'm just going to add them to the top now if you don't like your green onions warmed up Because they will be warmed as we heat this up each day. You can go ahead and add them right before eating But yeah, you guys look at this delicious lunch. So let's go over points and calories So the recipe made a total of five bowls or five servings It is six smart points purple on blue and purple and seven on the green plan Just because there is just the tiniest amount of points for the 99 ground turkey Now if you're on the purple plan and you opt for a zero point rice So you use a brown rice then it would only be one point This whole bowl is one point on the purple plan and the calories will be here on the screen So this is going to be fantastic. It's a well-rounded like I said lunch with the carb protein and veggies Another fun holiday vibe recipe we're going to do some pumpkin energy bites These are going to be nice clean whole food great for on the go I find myself being so busy these days that I'd like to have a really good healthy hearty little snack That's low point and low calorie to take with me.  Yes, please You can really use any one of the lilies chocolate chips regular butterscotch whatever your preference But i'm going to do the white chocolate chips the pumpkin spice ones by the way would be delicious But I can't find those in my area. So white chocolate it is So to start on our pumpkin energy bites, we can do this one of two ways Now the original recipe says to add all of the ingredients to a food processor and pulse it I am not going to do that I'm actually just going to add everything to a bowl Because I want my bites to not be a really like small grained bite I want them to kind of have the whole oats. So whatever your preference is I will link the original recipe on my website So you can make yours either way, but I weighed out one quarter cup of nut butter on my food scale It's just easier than using a measuring cup and then I have two cups of rolled oats I have one half of a cup all my half of cups were dirty So I put it in a one cup, but I have one half of a cup of maple syrup You can also use honey kind of whatever you Prefer and then we are going to add one half of a cup of pumpkin puree My mixture is ready to go. Look at how good that looks. It smells So good and then I have just a quarter sheet pan here with some parchment And what I'm going to do is roll these in to 25 balls. Now. I want about 25 I don't know exactly how to get 25, but I'm going to do my best And then we'll kind of figure our points accordingly But we're going to roll those out set them here on the parchment paper And these actually go into the freezer. I believe to harden and then that's where you can store them Or in the refrigerator to eat them throughout the week. So let's roll out our pumpkin balls So I ended up getting just under 30 bites 29 to be exact So my points are actually going to be a little bit lower So when I share the points and calories with you, I'll let you know what the points are with 25 bites versus 29 And I'm going to pop these in the freezer They say to freeze them and then either store them in the freezer or the refrigerator So I just want to get them nice and frozen so I can show you what the actual finished product looks like And then I'll give you the points and calories. I just pulled the energy balls out of the freezer They are nice and frozen. So you can again store them in the refrigerator or the freezer I think I'm going to keep mine in the fridge because I got 29 bites instead of 25 my points drop So they are only two smart points on both the blue and green plan And one point on the purple plan isn't that great Now if you get 25 bites like the recipe calls for they are three points on blue and green and two on the purple plan But this is an absolute clean ingredient healthy Protein pumpkin energy bite. So I can't wait to have these all week long. Thank you for joining me on this week's meal prep I hope that you are as excited as I am about these three recipes. They're amazing. I can't wait and I'm feeling some fall vibes Even getting into Christmas. I'm so excited for this week's recipes Again, they are all on my website My website is linked down in the description box along with my nutrition coaching website Links and discount codes again to my favorite things and the items I shared with you today and the link to head over and join me on facebook So definitely check out that description box if you love today's video Please give it a big thumbs up and last but not least make sure that you subscribe We'd love to have you. Thank you so much for watching and I'll see you in my next video. Bye


Hi everyone, welcome to this presentation. I'm Takanari Suzuki and today I will talk about what we learned from creating Ospo at Cybertrust Japan. This is a gender. At first I will talk about me and then I will talk a bit about my company Cybertrust Japan. Then I will talk why we need to make Ospo and how was the situation before Ospo. After launching the Ospo, when we make the Ospo, what we learned from the 2D Groups Ospo resources. Then I will talk about what changed after creating Ospo and the future plan and the conclusion. About me, I'm Takanari Suzuki. I'm leading Cybertrust Japan Ospo to open source officer. I'm also an open source engineer. About open source on me, when I was a university student in 1999, I read the Cathedral and the Bowser essay and I learned about open source at that time. And in 2007, I joined Cybertrust Japan. At that time it was a miracle in us. I worked for Miracle ZBX and Miracle Renact as an open source engineer. And currently working also for Miracle Renact development system. This is my company Cybertrust Japan. As you see, there are 3 sections. The left side is original Cybertrust Japan's businesses like authentication or securities. The right one originally came from Miracle Renact. It merged to Cybertrust in 2017. It has Renact and open source business. As you see, there are some logos like Miracle ZBX. It is a system monitoring software. In the bottom, there is embedded Linux distribution EM Linux and cyber Linux distribution Miracle Linux. There is also the IoT section. It's based on the security technology and open source technologies. Currently our company is based on open source and security. We have some open source products. I will talk about how was the situation before the Ospo about open source culture and open source business mind. As I told, the current Cybertrust Japan is the result of the merger of 2 companies Cybertrust Japan and Miracle Renact's open source company. There was some gap in open source mind. We need to keep and extend open source culture and open source business mind because there are some different people coming from different cultures. We need to sometimes explain why we need to contribute to open source or why we need to talk with community people. Sometimes we need to talk such things in our company. Before that, I was in Miracle Renact. In Miracle Renact, it was natural thing to do open source. Actually, I didn't mind so much about why I have to communicate with open source committee or why I have to contribute to open source. But now we need to have some system as a company to communicate with each other to contribute and use open source. As I said, it was natural. Our open source culture was mainly kept by the branched open source engineers. Each developer contributes a source code to each open source software. Actually, it's natural thing and we didn't talk so much about each other as a report. We found some bug in open source software and just contributed. Actually, it's a bit volunteered and not system as a company. We need to build a system as a company to keep it. Some workers and management people thought open source was only about technology and intelligence and compliance and securities. We had a bit of gap in the mind. Open source strategy about joining open source development or events often individually in each section or each engineer decision. Actually, we just did such things because we wanted or we need. Actually, we can cooperate more with each other and we need to do such things. About open source compliance. Some people have enough open source license knowledge but others not. There are some issues. My response to these issues, as I said, I've read Cathedral and Bazaar and especially the magic card run. It's written about open source business and open source community relationships. I already know the open source community and open source business can go together. I need to find or make some model or guide to do such open source system in our company. In 2021, I found the Renax Foundation and 2D Group's OSPA resources. In such 2D Group's OSPA resources, there are many useful guides and resources to apply open source to our company. It also suggests Cathedral and Bazaar as one of the must read books. Actually, I thought this is what I was searching so OSPA is what we need. So we created the OSPA. We launched the OSPA this year, 2022. This is the press release. This is translated June 23. What we learned from 2D Group's OSPA resources. As you see, there are many guides and case studies. In such guides, there is how to make the ecosystem of the community or how to host the open source project or the compliance or also about open source commercial ecosystems. OSPA is covering not only about technology thing or contributing code. Of course, the contributing code is the most important thing I think and it's useful for business, security and compliance. So this is good for us. Also, the many case studies is important. Also, this training module, actually I'm still reading this. I'm not yet finished but it's interesting because there is an open source business strategy course. So if we can share which kind of open source existing and we can know the open source business model common sense so we can talk more easily in our company. So I think it's so good training modules. So OSPA is not only for technology but also for culture, business and compliance and so on. There are stages of OSPA. This is a picture. Often the telegroup introduces this picture and for making OSPA more effective we need to collaborate on open source more strategically not only individually. And by collaborating more we can contribute more strategically or getting more leadership in open source so it will become a benefit for company. So this kind of guide or resources is useful for us. After creating OSPA we defined the five goals of our OSPA. The first one is assisting in development, sharing and implementing open source utilization strategy. This is what I'm doing. These five goals is actually this one. The second goal is working with open source communities to keep and extend effective contribution. The third one is promoting effective use of open source in products and services. It means process development, how to apply open source to our product and services. The fourth one is keeping and extending open source license compliance. The fifth one is promoting open source culture in the company. And this is our OSPA activity field. Actually, the most important thing in open source is contributing and writing code, the open source activity. That is the center part of the box. But actually, for doing that, just doing that is not easy to do, actually making our culture or training or supporting the new developers or collaborating with other sections needed. And actually bridging the open source activity and business strategy is important. Without such thing, it's difficult to continue or getting help or difficult to get in budget. So for doing open source contribution and activities, we need to do these green boxes. Actually, the blue one is what we will get by these activities. So these are our OSPA activity fields. And I mapped the five goals I talked to these activity fields. The first one is the goal about assisting in development, sharing and implementing open source utilization strategy. This one will affect everything about the open source thing in our company. So this is the first thing and it will affect everything in our company. So after writing or making these five goals is what I am doing. And actually still kindly building the strategy. Next one is working with open source community to keep and extend effective contributions. We could keep the contributing to CanalCI and CIP and other open sources. And one member is now CanalCI TSC member and maintainer. And also we assisted to boost open source activity about our open source products. So for example, we started Miracle Renux user meetup and made new wiki for getting more users of Miracle Renux distribution. And also we encouraged the EmRenux team, its EmRenux distribution to attract and gather more interest. And not only joined open source event but actively participated. For example, we were joining the open source event individually or just joined and not being sponsored. But in this year Open Source Summit Europe 2022 we had a session about CanalCI and we sent a developer about CanalCI and the corporate part was accepted. And this event, Open Source Summit Japan we encouraged management people to sponsor the event. And actually we became a goal sponsor of this event and we sent three speakers including me to this event. And also another guy will talk as Open SSF Day. So actually four speakers. And next one is promoting effective use of open source in products and services. As I told, we are now starting Open SSF related team. We are assisted to start that team, improve collaboration with each section. Actually, that Open SSF team originally started in the EmRenux section but actually the open source security is so much important and it's not only about EmRenux system. So now we are involving the many sections and because also we could talk with marketing or some other people we could join the Open Source Security Summit Japan and we could join in the discussion and also we could involve our authentication section. It's originally the previous Cyber Trust Japan section. So someone knows Open Source but not so much so we are involving them to join this Open SSF team because there is a six store project. Six store project is about code signing. So such authentication section team is so much interested in this project so we involve them. And next one is keeping and extending Open Source license compliance. We started internal Open Source license study meeting with legal section so we could also involve the legal section and actually also tomorrow, after tomorrow there is an Open Compliance Summit our legal section member will also go that conference so I think it's going good to involving them. And we also assisted to start cross-bought company S1 team. S1 is also an important thing recently and originally it started at security section and embedded system section but they were working individually in each section so we need to communicate with each other so we could make such cross-company team because of Ospo we could have connection to talk with each other about the next one, the promoting Open Source culture in the company. We could start Open Source contribution assisting project so because we can teach each other for how to contribute Open Source or teaching the experience because by such things new developer can be Open Source contributor more faster so we started such project and also we started internal technical casual meeting we can talk casually about Open Source experience or contributions and Open Source activities became more encouraged by our company so for example we praised active Open Source engineers like the Karnel CI person is now praised because of the person became Karnel CI TSC member and maintainer and also another guy became Python JP chairman so that person also got prize so we are encouraging engineers to do more Open Source activities and also we are encouraging members to join Open Source event and supporting the cost actually because before that each developer went Open Source event by themselves by their money actually because they wanted to go but after we said after we need to support them because that becomes our company profit so we became to support them so this is the progress status of our Ospo activity fields after everything already checked is anyway we need to continue so it's not finished actually we need to continue but in many fields we could do many things making community, bridging the Open Source activity and business strategy or such things and still but there is some boxes we need to do so this is the status future plan actually I wrote future plan but actually this is issues issues to solve future issues so there are some issues because Ospo is actually going well because many sections request ask us to how to join Open Source community or how to do the Open Source activity or also the management people said how to use the Open Source for new business for example actually Open Source SSF is we are trying to concentrate so actually we got many requests from many sections so actually it's going good but in some aspect we need more human resources for expanding Ospo activity in our company so it's a kind of happy problem but still a problem so we need to allocate more Ospo members of us is needed and also the Open Source knowledge gap in our company actually we are doing some supporting project but still there is a gap so we need to keep having such project and adding more training course or using the training course in Relax Foundation or the training modules still thinking about this and also I'm thinking about how our Ospo should be as a company owning the Open Source products and communities like MNACRINACS and EMNACS because you know often the Open Source consuming Open Source is most easily consuming and sometimes we find about we contribute to that Open Source or getting presents in the community but hosting the Open Source products or communities is in opposite side we have to attract people to join our community or attract people to use our product so actually we are now building the communities for MNACRINACS and perhaps also the EMNACS so still we are thinking about how we should be these things are issues to solve so anyway as a conclusion these are conclusions the two groups Ospo documents are fundamental resources for implementing Ospo Cyber Trust Japan is improving OSS contribution by Ospo Cyber Trust Japan Ospo is covering technology, culture, business, compliance and so on so that's all for my presentation thank you so do you have any questions? the mic will come I think that it's a little bit difficult to build Ospo team small organization so do you think Ospo tasks can be outsourced? outsourcing in our company or outside of company you mean? if you can can I speak in Japanese? it's a company that has a little bit of a relationship so it's not a company that has the hope to build Ospo but in the future I would like you to talk about consulting about Ospo business so outside of company of course perhaps some kind of tasks can be outsourced and after we need help from other people because at least for us we are still searching what is good for Ospo so outsourcing is one of the options but I think some essential part is still needed in the company is it okay for your question? thank you for the presentation my question is how did you secure the legal team's involvement do you have someone from legal team working with you in Ospo full time or is it dedicated a certain percentage like they work 10% on Ospo matters and is it the same people in legal department whoever is available at the time if you need help currently part of their time will be used for Ospo but actually not is so much using for Ospo but anyway full time Ospo member is not always best I think because bridging each section is important for Ospo so doing the bigger section work and also Ospo work is good for bridging each section so I think of course actually we have too many things to do so we need more help but still doing both section work I think is better for doing Ospo is it okay? thank you okay okay I see okay thank you


published in November, 2020. This article was authored by Zishan Fatima, Chanda Shafsadi, Aisha Nasheen, and others.


What we are saying, loudly and clearly, is enough, is enough! We want a government that represents all of us not wealthy campaign contributors. We want a campaign finance system that is not corrupt. We want an economy that is not rigged. We want a criminal justice system that is not broken, permanent, that instead of spending trillions of dollars on a war in Iraq that we never should have gotten into, we are going to reinvest in the South Bronx and a community all over the country.


Okay, welcome to the CMC Markets Weekly Charting Analysis. My name is Jasper Lawler, your host for today. The webinar scheduled to last about 30 minutes. Sometimes we'll go over a bit. I'll typically stop the recording, but can always cover some extra questions if you have them. Feel free to ask a question or make a comment anytime. Always more fun if it's interactive, but I'll try to respond as quickly and as best I can. We're just getting through the risk warnings on the screen here. I advise you to take heed of. The talk at the moment is an asset class that I don't always focus on in these webinars, but I'm going to touch on briefly. It's the bond market really, specifically Gilts. It's not one of the most popular products traded in CMC markets, not especially sure why. It's maybe a bit more niche, arguably. Sometimes not as much volatility, but there is a bit at the moment. I typically have them up on my screen down here, just these three main ones. This is our proxy for the German. These are all 10-year bonds, 10-year government bonds, Eurobund, UK Gilts, and the US 10-year Treasury note. As you can see, Bund is kind of flat today. Treasury notes, obviously, we have moved into the US session yet, but pretty flat. Gilts selling off quite a lot for a Monday morning. Let's pull up the chart here and you'll start to see why. I have posted this on the chart forum. This being the daily chart, but it makes a bit more sense if I show you the weekly chart. Here are our highs over here in 2011. We obviously had a big sharp rise in yields there. We've pretty much just reached that old resistance level and formed a fairly classic-looking double top pattern. We've rolled over through the neckline. As of now, we're sitting on about a 61.8% retracement of this rally up. Basically, I've just placed, if I could drop down to the daily chart again, this was good old Brexit the day before and this is the day after. This whole move higher is basically just because the Bank of England had some pretty sour forecasts on what would happen to the UK economy, still does, if we voted to leave the EU. The expectation was that once we did vote to leave the EU, that the Bank of England were going to come in with a bunch of stimulus, possibly involving buying government bonds. That did happen. That happened on August 4th. That's this big move up here. Actually, what happened is we topped out about a week later. That was pretty much the top. Did a little false breakout over here. Tried it again, tried it again. Whatever that is, fifth time of trying, the market realised there was a distinct amount of selling going on here. Overcame the buying and we've rolled over ever since. It's been quite a sharp decline now. When you get a sharp move in any market, it sort of rubs off on risk sentiment a bit. Theoretically, bonds are something you buy as a more conservative investment. If bonds are going down, typically, what you would expect is that equities move higher because they're a riskier investment. People are moving out of safer investments into riskier ones. That's not so much the case at the moment, just because a lot of the reason people have been buying stocks is because, quote, unquote, it's the only game in town. As in, bond yields are so low and our savings account interest is so low that you can't really make money anywhere else. Obviously, with the exception of non-financial assets, properties and plastic cars and fine art and all the rest of it. All those prices are massively pushed higher. We're in bubble territory for a lot of assets, riskier assets because you can't make money in a kind of traditional way in the money markets or in bond markets. That's where we are. As a result, the fact that yields are going higher, yields go inversely to prices. These are prices. Prices going down, yields, interest rates going back up, that makes stocks relatively less attractive. The dividends that you would earn on stocks are still higher than these yields, but the gap is smaller now. Making stocks relatively less attractive than they were just a couple of weeks ago in comparison to bond markets. Let me know if you want a bit more explanation on that. It goes some way to explain why we're seeing a bit of decline in equities and why we've been in a bit of a ... As this decline in bond markets been happening, we haven't seen any massive decline in stocks, but we have seen a bit of a range taking place close to the highs of the year. I'll start with US stocks. This is our weekly chart, always best to typically want to do a bit of your charting on a Sunday or on a Monday. Just get a read on where you think. What color do you expect this week's candle stick to be in the most simple terms? That should form the basis of how you do your trading this week. It's an incredibly simple way to put it, but really that clears up a lot. If you look at this weekly chart, this week is going to be a down week. Obviously you want to be looking for short-term selling opportunities, vice versa if you think this is going to be a green candle this week. You're looking for buys. It's not too straightforward. It often isn't as to which one of those candles it's going to be, because we're basically in a range, as I've mentioned here in a very simple chart forum note, for 1, 2, 3, 4, 5 weeks. We've put a pretty much been capped between this old resistance here and this old resistance here. These are these weekly levels of defining the short-term range. If we drop down to our daily chart and we find a bit of a chart pattern here. We've got this triangle in place which has broken to the downside. First sign of weakness is the breakdown. We've got a reversal of that long-term support as you might expect. Then reverse somewhere in the vicinity of this trend line. Also the breakdown here. Obviously we had this, this is the daily candle. You can see that where it took out the low of that day, that's where we've fallen away from again. A breakdown, a touch of the long-term support, hitting that resistance again. Naturally you would expect maybe another go at this support, but whether that support gives way or not is hard to tell. The evidence would suggest it will. To me it looks like a lot of selling came into the market. Price has reacted. But the big sellers, they don't want to be selling down here. They want to average in. This to me looks like distribution. We're in a bull market, so that could easily be wrong. I should qualify myself there, but that's the way it's looking at the moment. Big sell, consolidation, distribution, people trying to buy the bounce. The people that were selling up here don't want to sell here, but they're selling at that long-term previous resistance. Eventually the market is going to give way to the downside. That's the way it's looking to me. It does look slightly different in the UK because while the US stocks have been down for two weeks, we actually posted an all-time record high on the Fitzy 100. Obviously the pound playing a big role in that. I'm not going to go over all of that again because I'm sure you guys have read that ad nauseam at this point that the weaker pound is helping UK stocks. But there's this short-term chart here, so I want to go over what we were looking at here. This being the daily chart. Obviously the trend lines always go off a bit when you switch between four hours and daily. This happens in every chart package. But that's that trend line. We've got to close down there below that trend line. We're down here. We've moved below this 50-period moving average on the four-hour chart, but of a sign that the short-term trend is turning lower as was the break of that trend line. We've got a breakdown and a bit like US markets. We've got this long-term resistance here, which has then acted as support on the downside. I've put that as the previous peak, but obviously these levels down here significant too. We've had a rebound off there, but that rebound stalled at... Sorry, I'm flipping between time frames a lot. This was the low here, so a bit like that other chart where we had the low, and then we broke down through it. We extended the low and then we came back and tested where we broke down. That also happened to be if you'd drawn your Fibonacci's where we had the 61.8% fib. If Fibonacci's they come in for a lot of criticism, you just say, oh, if you plot enough levels, one of them will work. I tend to just stick with the last two here, the 61.8 and the 78.6, because they have a deeper retracement. The shallower the retracement, the bigger the chance that you're wrong and then it extends lower. Obviously you can miss 50% retracement if you only wait for these two, but by its nature, if you're waiting for the bigger pullback, if you're cutting your losses, if the market makes a new high and it's no longer going to downtrend up here, that distance between 61.8 and the highs is obviously smaller than if you're using a 50 or a 38. That's what we've got here. Obviously the market's in a bull market, so there's a slight tendency to try and push higher, but it's only made it as far as that daily low and the 61.8, and this 50 period on the four hour kind of playing its part in this selloff as well. Moving average is it's really a personal preference thing. How quick or slow do you want your moving average to kind of reflect the change in the trend? You can use a 50 hour moving average on the four hour or even on the hourly chart as a change in the short-term trend, or you could use equally a five or a ten day moving average. They are basically the same thing, it's just a matter of how you're looking at them. I mean I say the same thing, they can capture the same thing. So this to me is a confirmation of that judgment from the other, from the US 30 chart that we've taken out some lows here. We've pulled back and it looks like we're angling for another push lower. And one target to look out for is this low down here, which lines up quite nicely with this 61.8. Mine says 100, just because of the way I've used the fibs, it says minus, but you know that's more like the 161.8% fib extension. So again we're pushing into this longer-term resistance turn support, so obviously it can hold, but a break, you know I don't think there's too much stopping us from getting down to these kinds of levels, maybe even this big daily low down here, which would basically put us in that sort of 6800 type vicinity. Let's have a switch across to Germany. The range is even more clear cuts in this Germany 30 chart. Again this is a weekly chart and arguably we were still part of the trend during these three candles. It's not entirely fair, but we haven't gone anywhere outside of those three candles. So one, two, three, four, five, six, seven, eight, nine, 10, 11, 12, until our 13th week of trading in a range in the Germany 30s. So you know, there's not a trend taking place to adjust your trading accordingly. On the shorter term, you'd expect coming up into these levels, you know maybe to get another reaction again, and if not there, you'd expect up at the top of the range equally. Down at this low is a bit close to the middle of the range for my tastes, but these lows down here, down to this low, down to this low, still pretty much part of the range, and you could expect some sort of reaction there. Worth looking at how the momentum is really compressed. So depending on which trend line we get a break from, looks like it could be the upper line that breaks, which would suggest a push higher. That would obviously go counter to what's happening in the other markets, but we've not seen such kind of an obvious kind of break down in the German market. It's just been trading sideways. Over to the FX market. Plenty of ranges happening at the moment. So Euro, obviously the most clear cut advantage. This is just a short term range that I kind of zoomed in on here. Signs that this last week was quite a nice trend in the Euro. This could easily continue, but we've come into an oversold area just about, and we're coming into this daily swing low down here. So already getting a bit of reaction before getting to that area. But I would say this trend line and then obviously that big Brexit spike low, being the kind of two areas you want to look for the lowest risk possibilities when it comes to a reversal, higher back into the range. But being open to the idea that actually maybe this trend continues to the downside. What evidence do we have that's happening? Just that there's been some lower highs being put in on the weekly chart. You know, the fact that we just keep edging slightly lower. And the lows, you know, that was quite a big volatility breakdown there. So if you're calling that, the kind of range that we've been looking at, kind of equivalent looking range that we were looking at in the stock markets, we've seen a breakout of that range. And this is big support down here, but that's the kind of volatility you need to sustain a break lower. So I think the mentality here is, you know, looking out for these two support areas to work, looking for some reaction off there. And then, you know, trading that breakout to the push high on the short term, or looking for pullbacks, a touch of that support, if I may as well go down to the short timeframe, kind of say what I'm talking about here, three hours.  But obviously, if we don't get that to that, we stall again around 110, which is a big psychological level, which is kind of where we are at the moment. If 110 proves a bit of a barium, we start pushing down. Yeah, I think that will most likely happen, we'll get down to one of these areas. But if we again, we fail at 110. It's a good sign that the downtrend is is picking up some momentum, and we're actually not going to hold the support. So it's one of those where, yep, there's a support, we want to look to buy for it. But, you know, you can just chuck your limit order to buy in there. That's certainly a way many people can do it and you can make money. But you know, an alternative, if you have the time to look at the charts is to wait for some sort of reaction and trade the break or the pullback from that break. Stirling obviously was coming in for some early selling today. Again, difficult difficult chart to be trading, but a bit of a kind of triangle pattern, showing itself here from that extreme low thing is this low. I mean, it's all in our charts is actually not bad, because it's it's basically drawn from 120. So our charts actually a bit below 120. If you were to assume that the low was 120 on that day, actually, this trendline works slightly better. Yet it's, yeah, so it's calling that low 120 up to there. And you can see that we're we've kind of edge below it. And now we're tracking back down again. So, you know, hasn't been heavy selling obviously a good dose of uncertainty. No one's really sure if we deserve to push sterling below 121, particularly the Bank of England. Do they really have the ability to cut rates again? You know, I think that's pretty debatable, given the current economic scenario, particularly if inflation is rising, we'll get a better idea of that tomorrow when CPI comes out for the US and the UK. Obviously, you know, the the other reason to push sterling lower is as a US rate rise. But you know, I think that's that's already factored in with sterling at 120. I mean, to justify moves much lower, it's it's it's the political uncertainty in the UK. And it's the prospect of another rate cut. I don't I don't see the Fed getting aggressive enough to really justify the sterling down at these levels. We've known that the Fed's been keying up for a rate rise this whole year. So I don't I think that's it's hard to justify moves lower, basically from the dollar side, unless US data really starts to ramp up. And next year, suddenly we're expecting, you know, rate rises every couple of months. But that doesn't really look to be the case at this point. I got a question on Dolly Yen. I'll get to that right now, Richard, if that's all right. Typically, just cover those three major pairs. If there's any other currencies, anyone wants me to have a look at just give me a shout or happily do so. So it's here, Richard and everyone else. This is our this is our daily chart. I'm sure you've all got something very similar on there. We have that triangle pattern. We've broken the the top line of that triangle pattern. And we've run into this little super simple technical analysis at this point. We had a triangle, we got a breakout from the triangle, but we've stalled at, you know, this this resistance area at the 104, which was one of the peaks that we used for the triangle pattern. So that will often happen. To me, the pullback has been minimal that that that's pretty much a bearish engulfing candlestick there. I mean, ideally, you want to see a bit of a kind of pop above the high to make a higher high to but the body engulfs that previous body. That's a bearish pattern at a resistance and it failed the next week pretty much. We've pushed back into those resistance areas at plus 104. We haven't had the close above that peak yet.  Sometimes the these internal trend lines work quite well. That seems to be defining the trend. So to my mind, I don't think the price is going to pull back much further than this rising trend line. Or the again, I've got this the 50 period average moving average on the four hour chart going, you know, which has kind of worked quite well here. You know, I think I don't think the price should if it's going to break 104 30 in the short term should go much lower than here. You know, if we do get another pullback to 103 again, then it just I think the breakout maybe is less likely.  I mean, I say yours. In my case, I'm looking at this as being a 104 30 possible breakout here just because we haven't had much of a pullback yet. And we've got that breakout that triangle pattern where the projection should be higher. So kind of base case, you know, expecting that longer term push higher. You know, so this first support doesn't work. Then you obviously, you know, you reassess and look at the next support below that 103, then I think that probably changes the picture somewhat.  Should we get through there? You know, the range being not so much the triangle, obviously, but more like this sort of 100 to 104 time range. I hope that makes sense. So we've got a few minutes left just to go over the commodities here. Something before I do get to the commodities and probably worth mentioning, obviously the main economic event this week, probably you'd be the European Central Bank, I say probably just because they're not likely to actually do anything. But we are, we do have, we have had Eurozone inflation today, you know, rising inflation, increasingly a bit of a concern. And that we did have those rumors a week or two ago that the ECB had been discussing tapering their QE program. So if you get that QE tapering alongside the Bank of Japan, potentially tapering their program, focusing just on yields rather than the number of assets they're buying, higher inflation in the UK, arguably preventing the Bank of England from doing more. And the Fed raising rates is all a picture of central banks pulling back a bit. So that would definitely be one to want to look for central banks pulling back, you know, when they've been one of the major forces behind the low yields that have made stocks more attractive than that would be, that would probably be a bearish sign for the market if we get some extra indication from them that they have in fact been considering tapering. They'll get questioned on it. I would imagine that Merrill Gregory will probably give quite a straight answer to say that they weren't actually considering tapering. What people are actually the general market consensus at the moment is that they're going to extend the life of their bond purchase program. And they're going to have to make a decision on that sooner rather than later because the end of the program is March. But I would say it's probably not going to be this month. You know, it's more likely to be December when they offer some sort of idea on that. Nonetheless, the fact that we had that big sell off in the Euro did certainly combine with more hawkish talk with the Fed, but obviously happened in the week pre this ECB meeting as well. Anyway, so now I will go to oil firstly. So again, again, just looking at a long term level, you know, this is like the highs of the year. We got a couple of false breaks on the day and we pulled down. We had three days of declines. So then if you do go down to the short time frame that I had on using this peak, we dropped back from the 61.8. You know, if you are struggling to get hold of the if you use the if you use the peak up here, we haven't actually got to we came just shy of the 61.8 level there. So maybe some room, you know, if we are looking for this long term level to hold, maybe some scope for market to roll over again up here. But at the moment, it's looking relatively strong.  Generally, the support levels holding quite well. So people who've been buying into this support, this little short term drift down seems to have seems to have kind of ended. So just look maybe for anything up here because we are we are basically at a long term resistance. Obviously, we're in it, we're in an uptrend, but just keep, you know, keep an eye on that resistance holding. So we've got that bold line in itself, just draw that from the old highs and those two fibs as possible areas that the the market could roll over from. You know, so it's in this sort of zone we need to look out for up through there and it looks like the trend should should continue. Gold again, iron up a long term level. This time on this time it's support. It's the 1250. We had a hefty sell off in gold. The week before last. So now we're back down at this spike low and it's also the 1250 round number doesn't seem to be much of a bounce. But at the moment, you know, you can see on the short level that people keep the 1250 keeps getting defended. You know, this is it right here. You know, this is the first rebound that we got after after spiking low spiking lower than 1250. We never quite got above that spike high here. We did get above these highs. So you know, the fact that the the highs keep kind of drifting lower doesn't give me massive confidence. But the moment we're still seeing every time we get down somewhere in there, people buying up in this 78.6 worked on the one occasion. I think that was when we had a non thumb. No, it was kind of quite remember what's causing that large volatile day. But nonetheless, 1250 a big key area for gold. To me, the fact that we're the highs keep kind of drifting lower doesn't give me a lot of confidence is going to hold. So I'm not necessarily looking for that level to hold much longer. And I think we probably get another push down to this one 1208. You know, should that level give way, you know, look for the short term pullbacks to to to to ride that down here. There really isn't too much in the way of support between 1250 and sort of 1210. This is potentially $40 extra on the downside here. So yeah, I think that's that's it. I've not seen. Okay, Euro sterling, I will go over that. And we've got a few, few seconds left on the official recording, but I'll extend that a little bit. Obviously, you know, Euro sterling, more more being driven by by the pound than the Euro side of things at the moment, because the Euro had quite a decent sell off last week. But you're not really seeing that particularly reflected in Euro sterling, because you know, the sell off in the pound was just that much more dramatic. So a good pair to trade when you're trying to kind of avoid trading, you know, just the dollar and what the Fed are going to do this much more story on on the weakness in UK politics and the uncertainty. Obviously, today, if you read my morning note and Michael's morning note, been, you know, there's, there's lots of kind of political strife at the moment. Chancellor Philip Hammond apparently trying to urge us to, you know, to pay the into the EU budget and just to maintain that the EU passporting rights and put immigration on the back burner. Obviously, the people that were favoring Brexit, not such a fan of that idea. So there's a bit of a tussle going on inside government creates uncertainty. And you know, the pound is the is the whipping boy for that. So trend is clearly higher. But obviously, this the 90 level. And you know, the old time, not the old time. So the multi year high back at what was actually at 90, basically 91. It's a key levels that we're kind of kind of looking at here. But it's similar to the the sterling chart in that, you know, with that, you know, crazy sell off day that we had hard to kind of really pinpoint what levels to use. Now, if you use 92, because you know, again, who lots of in the FX market, it's not a centralized exchange. No one, you know, there's different interpretations as to what the high actually was. If you use 92 as a conservative high, then we're kind of pushing into a potential triangle top roundabout here. But I I wouldn't necessarily be too confident about selling into this pair just at the moment.  So the obvious support number one would be down here at the kind of the bottom of this range that we've been since that big, that big buy up day. And if that gives away, then I think we're just looking at, you know, the the resistance pre that day. So they're two, two, two levels to look at there. Now, if we do get a breakthrough, this triangle, I'm getting a bit of a breakout. So then start looking for maybe pullbacks from the from the breakout. I hope that helps. Okay, well, good luck with trading this week, everyone. Yeah, watch out for the ECB midweek. We've got a lot of inflation data coming out for those trading the currencies. And, you know, keep an eye on this bond market sell off, particularly in the gilts. Because if that continues that could also could also weigh on equities, those those higher yields, reducing the attractiveness of stock markets and whenever there's a sharp sell off, that rattles investors a bit. So that'd be a reason for stocks to not to do so well. Thanks again, Jeff Lawler Sony out


to thank all the organizers for the invitation. Thank you for the nice introduction. And then just the one thing is like, if you post the question in the chart and I happen to miss it, please feel free to speak up. I would be happy to address any of the questions. Today I would like to talk about the joint work with Frank Caragari and the Vaseline Dimitriv on the observations of the erosmetic holnomicity theorems. And so I would like to first talk about the first application that some of you may already heard one of us speaking on the unbounded denominator conjecture. Then I would like to use that as an opportunity to kind of motivate the so-called erosmetic holnomicity theorem. And then I'll give another application to periodic data values. So let me start from the unbounded denominator conjecture situation is so we consider finite index subgroups. And there's a special type called the principal congruence subgroup, which are the elements congruence to the identity matrix mod n. And so this helps us to like see two types of subgroups. One is the so-called congruence one, namely those ones can be defined using congruence conditions. And the other ones, we call them non congruence subgroups. And the question is like, could we just distinguish these two types of subgroups other than just this definition? And it goes back to the work of Art King, Schrodinger, where they're proposing the conference in 1968. And they said that conjecturally one could study the free coefficients of the module forms was level to the finite index subgroup gamma and try to distinguish whether gamma is congruence or not congruence. And to set up some mutations, and I would like to require a classical example goes back to the work of Klein and the three. And so we start from the lambda function, namely it's like the Hobson module of like, in the curve with a level two full level two structure, and it could be concretely write down as this Q expansion. The formula that doesn't really matter for us, what's important is lambda over 16 is a Q expansion. I forgot to write that Q equals to here Q equals to pi i e to the pi i tau. So the important thing is like this lambda function as a Q expansion has Z coefficient and the more over is like, it doesn't have constant term and the leading term for Q it has coefficients one. So this is the important thing for us about like lambda over 16. And so we could study like finite index subgroups of gamma two, which coming from like coverings of like C minus two points. So like one easy covering was coming from like the like n's power map.  And the work of Klein three, they said that this group gamma n is congruence if and the only if n divides eight. So one could actually do a computation in this special case by just like compute what are the possible like, sorry, what one can do like concrete computation to see which ones are congruence or not. But for the purpose of today's talk, I would like to mention the observation here is like, if we take the ace roots, another thing that we use from the formula above is if we take the ace roots, it's still have integer coefficients. But if we take, for instance, the third root, then we can actually compute the free coefficient and see that we have denominators show up and the denominators here show up as three. So that's why like we do see if we just like take all the facts and try to make observations, we see that the relation whether like a subgroup, a finite index subgroup in this particular case being congruence or not is related to when we look at the three coefficients of the option module, whether it has denominators or not. And more generally, we don't need to talk about the way zero module for when we can talk about module forms of with K and the devil gamma. And for today's talk, we do not, we allow ourselves to have module forms, which has like, which is metamorphic at the cuffs. And when we talk about Q expansion, of course, we could talk about Q expansion at all the cuffs, but like just the four simplicity for today's talk or just the night and go also like compatible with the literature will usually here just take the Q expansion at the cuffs, i infinity. And also, as we'll see from the proof is like, usually the Q expansion, since we are not meromorphously at the cuffs, it will start from some like n zero, but like taking the situation that n equals to assuming it's holomorphic at one cuffs will still give us the essential case of the conjecture. And the other cases can be easily reduced to the essential case. So usually when we talk about module forms as homomorphic functions, we have real coefficients to be complex numbers. But actually, indeed, we could study like just the module forms with three coefficients over a cube bar, it's because like all these module curves can be defined over a cube bar. And the entire space of module forms is been spanned by module forms defined over cube bar. So that's why, okay, so I think I made a couple of reduction steps as night for today's talk, we talk about no module forms, we are not meromorphic at all the cuffs, but night for simplicity, we assume it's homomorphic at one cuffs. And we only consider module forms was coefficient is like in cube bar. And this already sees helps us to see like all the module forms like with with respect to say one, like finite index comma. And now we are actually at the point that we could formulate the conjecture. Conjecture set the following so we can observe two things, given a module form was like Q expansion at i infinity inside with coefficient three coefficients in cube bar. And the two things are equivalent. One is that so it doesn't essentially doesn't have the knowledge or it has bounded a denominator naming that we can use an integer to clean up all the denominators of the three coefficients, which if you use, okay, let me actually flip a couple of slides back and go back to the example of like the third root of lambda, although I did not write out all the coefficients. But from the first couple of things, it seems that at least for this example, it's like the power of three is getting larger and larger when we do this kind of third roots situation. So that's in first case is like we don't allow the denominator to get larger and larger. So we study these module forms. And the second part is saying that these module form is equivalent to say that the level of the module form is actually congruent by the level it meets the largest possible gamma such that F satisfy the transition law for the module form. And the conjecture of the theorem says that these two things are the same. So let me first make a remark about like congruent, why congruent module form has like bounded denominators that comes from the situation is like when we have congruence like that, oh, we have the classical hex theory, which decompose all the homomorphic module forms into summation of hack Eigen forms. And we also know that the non for the normalize hack Eigen forms, all the three coefficients are algebra integers. And hence like for congruent module forms, we can we first reduce to the homomorphic case and decomposing to hack Eigen forms. Now we have things which satisfy condition one. So that is like relatively classical, and which also motivates the conjecture in the still the same paper of Archie and Schrodinger, they did some computations and they expect the situation to be true for like all the like just for non congruence once the module forms are not congruence. And this is like proof that in the reading the work of Frank Karagalli-Batling images and myself. Okay, so to motivate the title, the title of the talk says like the Arithmetic-Connomistic theorem.  Okay, so the idea of proof is like it's standard that people can reduce the theorem, the proof of the theorem to the weight zero case. And then we're going to fix an N, which is the least common multiple of all the curves with of gamma. And now it's like we have with zero case, namely that we look at all the module functions, namely these are like rational functions with restricted pole because we only allow pole at infinity. And so basically it's like rational functions over the module curves defined by the level of gamma. So that's why it's a finite dimension of extra space if we view it as a dimension as a vector space over the J9 or like for synthesis they will study it's over the like them the line. And that is fine as far as we take the intersection of our group with like gamma that this doesn't change like the think topic. Okay, so this is one thing it's like we know that at least for the congruent situation. So actually more precisely here it is, it's like the number in here, which is the least common multiple of the cusp width is called the Woffat level. And in the work of Woffat, he proved that if we have a congruent module form, so like condition one says bounded denominator, so like assumption two says congruent. So for by the work of Woffat, he proved that if we have a congruent, if we know our plurium module form has level which is congruent, and we know that the like least common multiple of the cusp width is in, then he proved that this group gamma, or like this module form must be kind of of level, the group gamma must contain gamma and the module form must have level gamma n. And that's why we can actually consider the dimension in this case, just by the index of the group gamma n inside sl2z. Sorry, my typo here, it's kind of switched the order of the index. And then in this case, we can compute it's like asymptotically n cubed. So in this case, we know like everything about what is the dimension of the vector space. Now we're going to go for the part one is like we have a module form with zero, and we know that the Fourier coefficients has z bar coefficients. And then we want to actually give an upper bound of the dimension of the entire vector space. And this is like where the like L diversity theorem or the Arithmetical Naomi theorem plays in. So basically it's like, I think in the next couple of slides, I'm going to explain like why such a theorem would actually give us a certain like dimension bound. So these terms will give us a dimension bound, which related to certain things that we can compute explicitly. And then with some inputs from Navierian theory, we'll be able to actually get an upper bound, which is not too far away from the first one. Because it's like, there's two parts I would like to explain is like, of course, we are expected to have a dimension bound, which is at least n cubed, because it's like we already see from the classical Hex theory, it's like everything true is containing one. So that's why like we definitely expect to have a dimension which is at least n cubed. And then here is like we get the dimension which is not the desired n cubed, but not too far away from it. And the final contradiction, if you are interested, like you could read our paper, I'll explain later, but the essential contradiction come from, let me just be brief here, the contradiction coming from that, like the log n doesn't really matter. If we had one counterexample, one could use kind of like replace tau by tau over p to construct a new counterexample. By counterexample, we mean that a model formed with like Z bar coefficients, but it is not congruent, whose level is not congruent. So using this trick, we can actually produce too many counterexamples, so that like by too many, it's kind of it's violating the upper bound n cubed log n that we have as like with that angle to infinity. That's why like we get a contradiction. So in short, it's like the Woffort kind of computation is like from his work classical, and then we have some extra input from like a non-congruence module form saying that we don't need the like very sharp upper bound. We have some kind of like rooms that we can preach, namely that n cubed times any power of log would be suffice for the things to work, and then we just need certain type of like good enough upper bound, and that is where we are going to use the so-called arithmetic polynomial theorem. Okay, so before I move on talking about like arithmetic polynomial theorem, I would like to talk about a very special case of it first. So go back to the classical situation is like, I hope that kind of it doesn't seem a little bit out of nowhere because it's like we're studying like module form with full coefficient to be algebra integers. So that's why here we have like a power series with integer coefficients. And then the easiest case we could say something is like when the convergence radius is strictly greater than one, then like from calculus, the like or you could sense defense and do like Cauchy integration formula, that's what we know that the coefficients a m must be strictly smaller than n as n goes to infinity, and hence the only integer which has absolute value strictly smaller than one is zero. So that's why it's a polynomial. And of course, it's like from the arithmetic point of view, the Archimedeum place is not kind of something special from like all the other periodic places. That's why we could just like have like a static version, which we are now considering convergence radius at all other primes. And but here we put a restriction thing that we only want like finally many of them to be to could have possibility to be strictly smaller than one. And those are more generally in the broader work situation, they talk about the convergence radius of meromorphic they don't require like on a disk the function to be holomorphic meromorphic is good enough and the conclusion is a rational function. So these are the like classical work where people study power series and conclude that it's a rational function. And in our case, it's like we are not really going to be able to kind of use these type of rationality criterion because somehow like, if you actually try to think about what's the possible convergence radius we could say about our like module form, it's not large enough. So that's why like we can go a little bit further, which goes back to the work of event j when he was working on this so-called L diversity criterion. So the difference between the previous one and this one we still talking about like power series with Z coefficient. But like what if the convergence radius is too small is we can actually just look for maps from the unit disk to see where C has coordinate x. So instead of just looking at the disk around just the disk around zero and the try to pick the largest possible disk, we say that we allow ourselves to study maps from a disk to see. And here the derivative actually is like the thing that we replace the convergence radius in the previous baby case. And of course it's like this number like if you pick the largest possible one, it should be larger than the convergence radius that we talked before. And so similarly there's a static version. And if we require this map to be injective, it gets some like rationality criterion goes back to the work of Prodiapo trenders. And what's more important is the proof is effective. So here's the thing is like in the work of like event j he did not just prove that the function f is algebra. He also proved that like he can use the function phi or if you use like more places just like all these kind of uniformization from unit disk maps, and you use all these maps to actually give a like upper bound explicitly upper bound on the average versus degree of the function. So that's the important part for us. And I would like to use module forms. So we'll see a version of this quite here and later. Now let me just summarize what is important is like we replace convergence radius by these kind of maps from the disk to the coordinate. And just let's look at the example of module forms and the four simplicity, we just study those ones with cusp voice device to that's why we can write as like the bracket q and restrict ourselves to the coefficient because the general case can also be reduced to this case. And the record like what is important for us is like lambda over 16 is q plus higher powers and the z coefficients, which means that if we have a power series with z coefficients in q, we can write it as a power series with z coefficients in x where x is lambda over 16. Okay, so now we have a power series in x, it has z coefficients. Up here, we know it's a rational function on a curve which admit the finite run fine covering to the lambda line. So it's algebra over q lambda. So like the even if we can find a nice five, which I'm going to extend like how it's kind of like the first statement of the theorem is not enough. What we need is like we need an upper bound of the algebraic degree. It's the same as saying here we can actually can bound the degree of like this night. So we have a like z coefficient module form f it lies on some like module curve, and we can actually bound the degree of this module curve over p1. And by using the kind of the actually effective upper bound from the algebraic degree coming from the theorem. Unfortunately, that the previous kind of like in the theorem in Andrews book doesn't give us a good enough bound. So that's why we're going to do the following refinements. Okay, so I'm going to expand a little bit of the notation later because this is just for the purpose that we would like to incorporate the cusp of ways to be not necessarily to that we need to do something else. And I would like to just the first to display the theorem. It says like, let me just the emphasis on the part that we have a five here. So we have a five such that's like two conditions. One is like the free coefficient has z coefficient. The other is like when we kind of pull back to find it has a holomorphic function. So this is the kind of essentially also kind of we put the end. So feel free to think about the situation when n equals to one. Like as kind of it gives you the main part, like the main idea of the theorem is like, we have the z coefficient part. And then we also have like, when we pull back by a max five, it gives something which is holomorphic. And then overall, we'll have a dimension bound, which is essentially using the function five. It's like we want the derivative to be as large as possible because it's like, this is like what we replace the convergence radius. And we also want the function five to not grow too quickly. Because if you think about like, you would like to use like Cauchy integration theorem to like prove something which is similar to the baby case, then we would like to use like the Cauchy integration formula to get some upper bounds of like the absolute value, which we know it's an integer. That's why it's at least the one from the lower bound, if not zero. And that's why when we use this kind of integration theorem in complex analysis, we would like to control the size of the function five that we use to pull back f. Okay, now go back to a little bit of the technical detail here, is that we have, so in general, we won't be able to talk about cusp with equals to two case, then we have like t equals to q to the one over n. And also it's like instead of working with lambda over 16, we work with the answer of it. And those then so you use the familiar you that we seen before is like take the answers of it. And so what is fine, fine comes from the following is that we want to map essentially it's like, we want to avoid the single add we want to avoid the cusp because cusps is where that we do not know how to expand our module forms over the cusps. And like the, like, complex analysis speaking, like, if these are the single add we probably won't be able to expand our power series over them. So we would like to avoid the cusps and but we want the derivative to be as large as possible to have a like small dimension bound here. So that's why the natural thing that if we know which points we want to avoid the natural thing that's when what do is take the universal covering the universal covering is the one which gives the largest possible like derivative. And but like in order to control the top part. I mean so we just shrink it a little bit so that we are not integrate on like, we need to pick a small close disk inside the open disk. And that's all. Okay, so I hope it's like, let's put this way is, what is this strength sense is like I still only use some explanation about like why condition one to host for all our module forms with like all five level and and also like have Z coefficients, although the Z coefficients part is kind of relatively obvious here. And the choice is just the like the choice that we make for the fight here is to hope that we have a dimension which is not too big. And the more concretes speaking, that's the situation. So, so the Z part gives the condition one of the serum and the wolf of the devil. So here's there's the one cost that I intentionally did not mention, which is the cost plus zero is because if let me go back to the previous slide is like, we do rule out all the like answers, but we did not rule out the cost for zero. And we say we take the universal coverage. So why is it good for us? That is because our assumption the wolf of the devil guarantees that the local monogamy at all these kinds of weights zero module form there are like rational functions on the big module curve. And we'll have kind of local they just looks like take the at worse to take the answer. That's why when we take the lambda map by the answer, it already solved the kind of local finite monogamy. That's why we can actually extend our function over the zero plus. So that's why it's like zero is different from the other ones. And this like, we're looking like take answer is the purpose to solve the local singularity so that we can actually extend it over. Okay, then like, if one just follow the previous thing and just do the explicit computation, which I'm not going to give more details, during the explicit computation from the previous formula, when really gets the n cube log n bind by some inputs also from the Navina series. I would like to mention that also in the reasons work communicated to us by like boss and the shops, they can give an alternative. Actually, they give two alternative proofs our serum with the constant e here replaced by two. So for our for this application, it doesn't matter which constant we have here because in the end of the all we want is just the like a capital O of n cube log n. But for the Okay, then put this way is like, not for this application, we don't care about the coefficients. And hopefully some future applications will be able to see sometimes like having certain improvements would be like better. And that's why I would like to talk about a kind of like, I'll put it as a simplified version of what we can prove for the arithmetic connomicity theorem, which would also give us like the other application, periodic data values. So let me first explain this theorem. And so this is essentially not similar to the previous theorem. Let me first point out what's in the previous theorem. So we said that we could replace e by two. So we have this integration, just take them that equals to zero case. So we have the integration here. And we also have the derivative here. Okay, so there's like two or three other things pops out here. One is lambda. The other is not RP. The last one is Sigma. The not RP part that you can feel free to ignore it because it's just the same that we want to just the easiest possible analytic version, where we have like the periodic convergence radius in the conditions three here, we want to have the periodic convergence radius to be at least RP. So that's just like an easy like analytic version. Actually, more generally, we could instead of talking about convergence radius, we could also try to do these like entry type of maps. But for simplicity, that's just a stick always like periodic convergence radius. And the lambda parts, which probably will show up in the last couple of stands, and that this is kind of give us a continuous way to like see a lot of like different erasmatic polynomial theorems. So the important part is the Sigma. So let's look at the condition one here. The condition one here is like previously in the previous application of the unbounded denominator case, we have like z coefficients, or you could do like z to the one over m to make it the analytic version. That's completely fine. But like sometimes we'll have a denominator which of form like we take the square bracket here means the least common multiple of one up to n to some integer power. So in the later application, so there's two parts of the story. One thing is like when a typical example I could give here is like think about the function fx equals to log one minus x. Okay, so the for the function of log one minus x, you'll see that if not to have z coefficients and the like power series, the Taylor expansion, you will have like one over n. So you have n show up on the denominator. The log x is kind of like commonly studied object in like do fentanyl geometry. So we would like to take that into account. And then this, so that's where the Sigma comes in. And also it's really, let me also say a little bit of the kind of the name of the theorem. The theorem is still like when we consider all the functions with some control on the denominators of the power series. And then the condition two and three could think about it as like we have certain type of convergence radius at all the places. And so here we only say p divides n because for the others we can truly bounded by one. And then we're going to give a dimension upper bound of the vector space spanned by all these functions. And the whole normal velocity coming from is like unlike the situation when we do not have denominator. So when we have a function f with z power, sorry, with z coefficients, you raise to any power, you still have a z coefficients power series. And it's kind of converge on the same disk for like all kinds of conditions. But unfortunately, once we put into this denominator condition, we will not be able to just raise to the power. If I say f square, then unfortunately, I won't say that it's have like denominator of this type one up to n to the Sigma. So that's why it's no longer an algebraicity theorem. And we also know that log one minus x is not an algebra function. And the but what is the kind of operation that one can do without like increase the denominator and having the same kind of convergence property that's taking derivative and that it's been the whole normalcy. It's like instead of using f, f square powers of f to span a vector space of large dimension and talking about the algebraic degree, here we're talking about f, the derivative of f, higher powers of derivative like the iterative derivatives of f. So that will expand like a vector space with functions all satisfy those like trivially satisfy all the conditions if our f satisfy the condition. And then the conclusion would be that the differential module which given by like f derivative like iterative derivative of f will be a finite dimensional vector space. In other words, it's like f would satisfy a differential equation of finite order and we give an upper bound of the order of the differential equation. So that's the difference between like the waste denominator and without denominator case is like we're like go beyond the situation of the algebraic theorem and we talk about the so-called arithmetic polynomial theory. And so here is like I'm going to give you an example of like a difference polaroid that one could do like by choosing a different lambda. But first I would like to actually explain what is the denominator comes from. And does that come from that we can think about the baby case of the broader work of power series that we talked about before. In the situation where we have just the finite many primes show up on the denominator, the proof can actually come in from a product formula. But unfortunately it's like when we have just the q coefficients instead of z to the 1 over n coefficients, then like we cannot just directly exchange the summation because exchange the summation is not holds when we have actually like infinitely many things that we have to take care of. And that's why there's kind of a so-called tau invariance introduced in the book of NG where which essentially measures the difference when you do the exchange of limit and the product formula thing that one could prove the baby case for z to the 1 over n. And the generalization of the previous situation is like so let me not flip back the slides but saying rapport is previously we said if we have the summation of log rv strictly positive that like when we are in the just the finite many denominator case we have something as a polynomial. Now if we have infinitely many primes show up on the denominator, then the generalization we should do is like the summation of the radius strictly greater than the tau function here and then the conclusion that it is a polynomial. So this is let me just flip back this is related to the denominator because the first two turn is just the summation of like generalizations of convergence radius and then minus sigma in this case one can actually compute sigma is exactly the tau invariance that using like nj's definition. So like it says it's like if like we definitely wanted the denominator to be positive in order to have a meaningful dimension model. So back to our case is let me just restate what's the situation that we use it's like we have ventral functions and we have like the tau invariance is smaller than sigma we have the convergence radius and we have like for simplicity here we just like manipulate the arc medium space with a generalization of the radius then the conclusion is like we could have such a dimension bound. So to compare to the previous case when we have the integration bound so previously we have the integration of the log source of this function but unfortunately we have a coefficient two there and then in this case if the superman is not too big then the coefficient that we could put here is one. So here is just the kind of you can choose the lambda in the previous theorem like wisely so that you could get like basically a family of dimension bound and it depends on what type of problem that we try to solve some cases like different them that will give like better bounds all the other case. Okay so okay good let me just summarize it's like basically what is our input is like for each place we want to have certain type of like generalization of the convergence radius and depends on like how good the function is and then we can actually cook up a dimension bound in terms of all these uniformizations and I would like to talk about so in the book of nj on g functions given that he already introduced the like tau invariant he also had the version of the bound of the dimension just the bound is like not as good as the one that we present here. Okay so I would like to actually give the second application of today for the previous theorems about like the like zeta values. Let me just so quickly go through like the classical situation is that we have the Riemann zeta function we consider the zeta values and then conjectually we expect that all these are outrageously independent over q and there are previous results for zeta 2 and zeta 3 and we will not be able to say anything about the classical zeta value 5 but in the periodic situation life is a little bit easier so the periodic zeta value can be defined as like the limit like so remove the p part and take the limit of like the zeta value once we take the limit in the periodic sense um so the limit exists so based on like commerce congruence condition on the Bernoulli numbers or the other thing one could think about are these are like constants of like periodic isonstein series as like periodic isonstein series can also be achieved by like interpreted like the like classical isonstein series and in the work of frank carugari in truzon 5 he proves that the like true adic and the three adic zeta value as three are not rational using the over convergent isonstein series and using the dimension bound that i just showed earlier that were able to prove that the true adic zeta value at five is not rational so the definition gives us like a numbering set q2 and what we can do is to prove that this numbering set q2 is actually a numbering set q2 not rather than a rational number okay so i would like to report a little bit from like frank's work about like what is the like isonstein series and how did he actually set up things to use the over convergence okay so as i said like these like periodic zeta values can be actually realized as like the constant term of a periodic module form with weight in this case negative 2k and the we can pair it with a classical module form to make it into something of weight zero and also for x not two it's a rational curve and then it has a hapsen module so we have the product of a weight 2k and the weight negative 2k module forms will get something weight zero we can write it as a power series like in terms of the hapsen module of this module curve and we will like to actually study this power series so what do we know about okay so we're going to study this power series and apply our like a mathematical number here and uh sorry there's a typo here is that um we are going to since we're going to talk about like the periodic data value at five which means we are going to take the case that k equals to two for k equals to two so this is a weight minus four module form this is a weight four module form then one can actually run the argument a monogamy typo computation to see that actually indeed is like these functions so four is related to the 2k here so these functions are all linear independent like the smallest kind of degree of differential equations that such function was scientifically done like degree five differential operator so these things are not any independent so we at least have a lower bound of the space that we are going to study if we assume for contradiction that the periodic data value is rational so what about the radius so the radius is like since it's a like weight negative 2k module form so we see that the denominator it will have n to the 2k plus one and the classical one is essentially like z coefficients and the half sum module is also z coefficients so when we put things together is that we know that derivative doesn't change convergence radius so we can just think about f so it has like the periodic convergence radius to be at least one for all the primes and the and the here is the extra like over convergence comes in is like in this case we can have more about the true added convergence radius we could have a true added convergence radius to be 2 to the 12 which is like the one on the disk union all the super singular locus and then so so the denominator comes from 2k plus one so the tau sorry the sigma in this case is actually 2k plus one and then for the phi is so we want to have something such that the log the summation of the log of the radius is strictly greater than five and the so if we take just the take the log of like this one okay 12 log 2 and it is indeed strictly greater than five and so which means is like we want to have our like arc media radius to be also not too small and the one of the large ones is that we can take the just the q coordinate q coordinate gives us something such that the derivative is one but unfortunately if you just take the super large disk there we will not be able to have something such that the supremo phi is small so like the formula says let me just flip back a little bit so the formulas here says is like we already have like the 12 log 2 which is very big and our sigma is equals to five so we want to kind of find the like a region not necessarily just inside it we would like to find a region inside the q coordinate disk such that this one is not too small so that we still have this one positive and this one is not too large things is kind of a very concrete like Hobson module one can actually study like its gross behavior and we were able to actually let me not give details about like what is the precise choice I mean as there are kind of multiple choice one can make is like so one could actually just like choose the super origin to avoid those places where like the function phi gets too large and then we get a dimension bound from our serum to be at most the six so let me just summarize it's like we use the like periodic over convergence to have a larger radius we use the q expansion some part of the q expansion and our Hanami city serum to give them a dimension bound to be at most the six and on the other hand we do have like six functions if we assume for contradiction that this is the rational number that gives us contradiction because all these six functions are linearly independent so what goes wrong the conclusion is like ah we just should not have like f here like so when it's okay when it's rational that's not fine but we should not just have the function f here because it should not have two coefficients it should just never exist in this like um vector space that we study about like convergence radius blah blah blah these type of things okay so and then so as the conclusion that this like periodic data values it's just irrational um okay since I only have three minutes left I would just like to display the slides about the little hint about like how I actually prove the arithmetic Hanami's t-series and this is inspired by the work of boss previous work of boss shambhala and also reading the work of boss shams that we try to revisit the slope method like you know earlier work of boss tried to just to manipulate things to see what type of to get uh I will put it this way like a uniform the proof of the arithmetic Hanami's theorem um in our paper we proved like the serums using like Siegel Neymar and here is like using the slope method we could have like at least so far a uniform bound which sees different chlorase and the upshot is like we construct a z module which is essentially just that the function f along with like some polynomials these are the way that we construct auxiliary polynomials with high vanishing order and now here I'm finally at the moment to expand lambda lambda is like so this is the module is something that we know that we're going to study and in order to apply the slope method we need to make it into an omission module and the lambda here is just the the different choice of norm that we put here so given different choice of norm since it's a different omission module we get different estimates in this kind of slope inequality about the arithmetic degree of the omission module and also the height of the function which is coming from like take the ans coefficient map from these filtrations filtered by the vanishing order and so then like once one set up the slope kind of method when just the estimates all these terms when estimate the arithmetic degree and also the height bound and the putting things together we get our whole normicity bound which is something depends on lambda and then we just choose the suitable lambda for each question in order to get a good upper bound so let me just stop here thank you very much for your attention