It is time for you to make huge changes in 2024 to put you ahead of 95% of the people out there and enable you to be a new person, a changed person by the end of the year. There are no courses that you can take, trainings that you can do, new experiences that are gonna be better than moving abroad in terms of having drastic life-changing effects on your life. Now, don't keep scrolling if you're like, I don't wanna hear about that. Hear me out as to the actual reasons why I think that this is one of the best things that you can do to change and improve your life. If you don't know us, we are a family of six that have moved from the US to New Zealand and we've been here for eight years and I've been sharing my experience on this channel about that, so go ahead and watch that. Also, if you're thinking about moving to New Zealand, I have a free masterclass to get you started on how to go about doing that. Today, let's talk about how to make your life in 2024 the most amazing year yet. There is not that many things that can change your life drastically. Improve yourself as a person. Give you a perspective that you can't even imagine that you needed and just give you a worldwide network like moving abroad. Let's start with some of the objections that people have about moving abroad besides being hard and move and I don't wanna quit my job and it's all risky and all these things, but listen to me. Let's just talk about it at its core.  You cannot grow without doing hard things, without trying new things, putting yourself out there out of your comfort zone, growth does not happen in comfort. So let's kinda bring us back into what we actually value as a person. So if you're happy with being comfortable, this video isn't for you. If you are looking to grow and to prove in 2024, listen up. The first thing that I want you to do is think about the reasons why you don't want to move abroad. What are the reasons? And then look at the underlying value that you are placing on those reasons. So for example, a lot of people think that it's bad to move your kids around. It's bad to leave your family for a time. It is bad to leave your job and it's not gonna be good for your overall career and whatever. So listen to these values. Where did they come from? They came from society. Society gave you these values. Now, if you agree with them, you're good to go. But I challenge you to look at what the values you're agreeing to and make sure that they line up to what you actually think. In addition to values, people have a lot of fears. They have a fear of trying something new. What if I go through this huge effort?  First of all, I have worked with hundreds and hundreds of clients and I've never experienced this. I have had people that have gone abroad and then come home and said they didn't like it but loved the learning that came with that. They had to know. You don't wanna get to 85 years old and have regrets because you never tried it because you were too scared. It's been 84 years. Don't make decisions out of fear. Make good, solid decisions based on what you value and what you think is important in life and what will push you forward in growth in the future. And you don't wanna do it because it seems like a lot of work and you don't wanna have to deal with all your stuff and sell everything. You know what? Anything that's worthwhile is a lot of work. And anybody that tells you different is trying to sell you something. Okay, so the first challenge I have for you is your values.  You're valuing something. Just let's hope that it's yours. Now, the second thing that we need to talk about is that moving abroad doesn't have to be permanent. I have this conversation, I would say weekly for sure weekly with people because they feel like this is so overwhelming. They've spent years coming to this decision. Now, they're in the process of getting their visa and getting a job and finding a house and selling their house and selling their stuff. And they're like, I'm never doing this again. Like this is permanent, okay? Let me tell you, do not think that. I know it can be confusing because a lot of times your visa will say permanent resident, right? But the mindset that I want you to have is that it is permanent, it's just a permanent option for you. It's an amazing option for you. It's an amazing option for your kids like universities are cheaper or they wanna live abroad, they can do that and you have set that up for them. But you don't need to feel like it's permanent because I think that that's what keeps most people from doing it and is where a lot of the hesitation comes. I have a bad feeling about this. Decide, hey, I'm gonna move abroad with my family for two years, for five years, for 10 years. But don't decide that that's for sure what you're gonna do, just let it be. In 2024, this is what I'm gonna do. I'm gonna go for this, I'm gonna try this and I'm gonna have no idea how long I'm gonna stay and I have the option of going home and I have the option of staying here and I have the option of going back and forth as much as I want because we live in a global society. We can now work from anywhere in a lot of jobs and so it gives you options.   It's good for you to have at least done it and knowing that information. It doesn't happen a lot because generally people are way more surprised at how much they love something than not liking something, but it does happen.   It represents what you value. It represents a society that you feel good about living in, that it's run by people that you can get behind. Just don't have too many expectations, you guys. Stop making all of your decisions about your future, about a situation that you've never been into because it just feels better to have some understanding and to have made a decision. Don't just say, I'm willing to step out in growth this year and I'm gonna apply and I'm gonna try this and we'll see how it goes and I'm not putting any limits on it. And I'm telling you it is the most freeing experience. So number one, figure out what you value. Number two, it doesn't need to be permanent. And number three, it forces you to deal with your stuff. Now this is a big one and I'm not just talking about the stuff in your garage and in your basement. I'm talking about your relationships with what you think about your job. It forces you to think about what you want for your kids. It forces you to deal with your actual stuff.  So the biggest problem that I have actually is that I can't remember that I don't have that anymore. Sometimes I go in to bake something and I'm like, I try, I'm looking forever for a pan and I'm like, oh, I must have sold that on my second move. But I'm telling you it is the best feeling. The best feeling to just kind of weed out all the crap that you don't need because you accumulate a lot.  I came with a suitcase and now I had a whole house. And so it's not that hard to sell and it's not a process. And I'm actually a professional at this now. So if you need some assistance, just message me because I know exactly how to do it and it's not actually stressful. So you need to be dealing with the stuff in your life and it is good for you. It forces you. And so you're already, before you've even arrived into the new country that you're going to, you've grown. You've decided on relationships, wants to keep, wants to end.  Hey, we don't do that here. There is most people don't like that you're moving. And so it forces you to really be honest about what you value and why you're doing something. And that's so good for you. So good for you mentally.  If you live under the expectation of other people those relationships can go very poorly in the future because you have become bitter because you're doing what they want to do not what you want to do. And I'm not saying all of your decisions need to be selfish, okay? I'm saying that your decisions need to line up with what you value and that you have a limited time here and you're not waiting until you're 65 to do it. The next thing that you will really gain from moving abroad is experiential learning. This is the most effective type of learning being immersed in something and learning about it through being there and in process and in actual experience. It's not watching it on Netflix. It's not reading about it. It's not taking a course on it. This does not give you experiential learning. Experiential learning is so much more in depth, gives you such perspective and can really change the way that you think about things and what you value just from having that experience. And so whether you move abroad or not, I encourage you to focus on doing things that are experiential learning. Like even if you go to another state or you try something that's totally uncomfortable for you like salsa dancing or some other new hobby but experiential learning is so critical in growth and just it helps you open your mind and helps you actually, and this is one of the key benefits is when you continue to work with others, put yourself in different situations, you have a lot more confidence. You have a lot more insight and you can handle it because you've just moved to another culture and been successful, integrated into a new school and your kids were successful. That is huge learning for them. That is learning that they cannot get by reading in a book and watching Netflix or watching all the short form video. So we've talked about the importance of doing what you value that it doesn't have to be permanent, that it's great to have to deal with your stuff and that experiential learning is the best.  Have an adventure, travel and see things. It's all up to you in the level that's comfortable for you, okay? The global network that you will attain, the lifelong friendships that you will make is like none other when you're moving abroad and you will love it and you will meet amazing people that will teach you things that you cannot learn anywhere else. So get out there this year and make a difference. Choose growth, choose opportunity, I'm here for you. Let me know how I can help. Have it below with what your adventure is gonna be this year cause I wanna know.


Fast forward. Thanks for joining us as we broadcast from the JSA TV newsroom live to LinkedIn and YouTube. You got it. Hey, Dino, we are here to bring you all the latest and greatest from the world of data centers and telecoms straight from the pages of the telecom news blog, which is what you can get to if you scan over my shoulder. That's correct. I'm Dean Perrine, executive vice president at JSA and joining me as always is the lovely my friend, my mentor, my boss, Jamie Scato-Cataya, founder and CEO of JSA. Thank you. Thank you. And yes, hello out there. Or should I say Aloha? That's for all of you guys recently returning home from PTC in Honolulu. I know you're missing the Aloha love. Well, I wasn't there this year, sadly. But our top brass, right? Dean, we sent them out. And all I hear is it was a huge, huge success with record-breaking attendance. And I especially wish I could have joined that K&N Rooftop party.  Beautiful pictures from there. It did sound like a blast. And Jamie, I don't know. Did you see all the pictures from that? Everyone looked a little sun-kissed. I was very jealous of that. That's what we did. Everyone had that glow. I know. I couldn't make it this year. But fortunately, JSA still had it covered with our crack events team and JSA TV broadcasters. I got to watch all of those. They were awesome. So make sure that you check out the JSA TV YouTube channel for tons of interviews from PTC. We managed to catch lots of great moments and insights that you don't want to miss out on. And you know what? For me, one of those big pieces of news coming out of PTC was the announcement of PTC's new partnership with Columbia Business School Executive Education, which they got together to develop the new top talent leadership development program. So really exciting. Very cool there. Yeah, absolutely. Very, very, very cool. And it kicks off next year in Hawaii with 30 executive participants. And I can't wait to see how that goes. Justine, we will be staying tuned. All right, big congratulations also to the winners from this year's PTC Awards, including our JSA clients. We've got Svala for Outstanding Data Center. You go, guys. Zenlayer for Outstanding Enterprise Solutions of the Year. And Master's Challenger Winner, Divesh Gupta of Console Connect. And CEO of the Year, Markel Finger Console Connect. Yeah, boy, those are some big ins. You know, it is award season, which is always kind of fun. When you're making these announcements, I'm always thinking like best picture and all that stuff. Anyway, the list is stellar, and it's awesome to see so many JSA clients winning some awards. Yeah, absolutely. And to celebrate, I think I'm going to have some pineapple with my lunch today. Honor of all my PTC colleagues around Dean. Maybe you can do a little hula dance or get a grass guard around. I don't know. Say goodbye to PTC, or no. You know, Jamie, that's probably not a good idea. We do that.   But I'm going to reserve. I'm going to reserve the hula dancing for PTC in person. Probably for the best. Yeah, yeah. So for all of you who are going to PTC next year, maybe you'll get your opportunity to see me dance in a skirt. And hopefully it'll be a hula skirt. In my mind, there are hordes of people just shrieking as they run from the loo. All the more pokey for me. So that's it. And spam. Oh, that's right. OK, never mind. I changed my mind. All right. Well, we better get to the news before you change back. So ready to jump in with the first segment of today's show, my friend? Yes. Let's get into it with the Movers and Shakers from the past month. Courtesy of JSA's Fast Forward. Here is your Movers and Shakers news. From new hires to award wins and events and publishing news. But it is mostly hiring announcements this time around. So let's kick it off with publishing first. Light River announced a new study that's all about interoperable networking. Along with partner OpenZR Plus, Light River tested optical transceiver modules with a number of vendors to prove that they can easily integrate with existing infrastructure. Very, very important. So check out their new white paper to learn more about that. Well done. Well done, Dean. OK, our next mover and shaker is T5 data centers. We love those guys. They made a leadership change by adding David Miller as their new EVP of Sales and Marketing. So congratulations, David. He comes with plenty of experience in both sales and data network engineering. So great fit for T5. Yeah, lots of stuff going on over there at T5. And good people too. I love them. There are other new VP appointments around the industry as well with Jim Brinkzma joining Light River as their SVP of software solutions. Jim is a longtime SAS expert. You could say he was sassy. He's been sassy for a while. So Light River is betting on him to lead them into continuing to innovate in the optical networking space. And we can't leave out Involta, our friends there. They also did some great hiring. They announced Gabriel Urru as their senior director of product and also Big Juan announcing Bret Lindsay as CEO. Congratulations. Yeah, and we should say that this move coincides with some other big announcements from Involta, including an expansion into Green Bay and the launch of their new secure power co-location offering. So lots happening over at Involta. Definitely one to watch. Yeah, they are like the overachievers of 2024 already. And it's only number one. All right, so the next up is collaboration and innovation. And here we go. Oh, wait, that was you. Sorry. That's OK. That's OK. And swish, collaboration and innovation. Here we go. And now we're here to the collaboration and innovation segment where we break down new partnerships, new products, new services, and new sustainability initiatives. So Jamie, take it away. Ooh, big, big, high barger set. OK, let's go. We start off with Lantana, LED, who supplies lightning for data halls all over the country. And they recently unveiled two new product lines designed to meet the very demanding needs of data centers. The first one called Ellucent, and the second one, Neotarik. Both specifically designed with data centers in mind. Very cool. I'm glad I didn't have to pronounce some of those words this time around, Jay. And speaking of cool products, there's a new AI service being used by SaskTel, the primary telecom provider for all of Saskatchewan in Canada. It's a virtual agent for mobile customers called Lumbot, created by software company Aleppo. Aleppo is very proud of Lumbot as it's highly adaptive and fine tuned for understanding language. Jamie, we are truly living in the future, and I am truly thrilled that I got through that announcement with all of those words. We really are. And our clients are right there on the bleeding edge of this technology. It's incredible. So with that, let's go ahead and switch gears to some facility construction news right now. It's a city filled with great places, but of course now Vancouver, another great spot to see the Spencer building at the city's Harbor Center recently announced a brand new meet me room called MMR5. It's part of a large effort to renovate the building into a cutting edge connectivity hub. Unfortunately yet, no word on whether there will be great snacks in the room at this time. We will get back to you with that very important data. Because who doesn't love snacks, am I right? Over here. Let's get the word out here. Over in Oklahoma City, Toniquin's Edge X Data Center is undergoing some new upgrades. They're preparing the facility for new demands, including AI workloads. When all is said and done, they're hoping to add up to 12 megawatts more power to their data center. And we say all the power to you. Oh, that's good to mind. All right. How can I follow up? I don't know. All right, Lynx Nova recently marked their 10-year anniversary as Northern Virginia's only multi-site IXP to celebrate the added a brand new capability. Guys, here we are. Microsoft Desire Peering Service. Now all peering partners at Lynx Nova can access network solutions specifically designed for tools like Microsoft 365, Microsoft Teams, and Dynamics 365. Happy birthday, Lynx Nova. Happy birthday, indeed. And there is a new kind of energy meter in town for data centers. And energy is a big thing right now. LeGrand's Starline brand unveiled the M70 Critical Power Monitor this month. And it's set to be the new standard for data center busway power monitoring around the globe. The M70 can measure up to six current transformers at once. And I'm not talking about Optimus Prime. I'm going to wait to get to that one, Jamie. I could not wait to get to that one. Good job, Dean. Good job. Walking friends, and as I am talking with my friend. But our friends over at 1623 front, and by the way, I don't use that word lightly. Really awesome people there. They are powering up. They recently deployed three new generators at their Omaha facility. Adding three megawatts of power. This was the first bit of news out of 1623 Farnam since naming Bill Severin as president and CEO. Congrats, Bill. We see you. Congratulations, Bill. Bill has been in leadership there since 2019 as an operating partner. So he's now at the helm, making sure everything's got enough juice. He's juicing it up. So that's the last of our collaboration and innovation news for the month. All right, excellent. Now, Dean, let's talk deals and big wins. Okay, guys, welcome to deals and big wins. This section of our program is all about mergers, acquisitions, expansions, and projects. Go ahead, Dino. I would love to. Okay, here we go. Legrand's made a big move with their acquisition of ZPE Systems, a California-based IT services company specializing in remote management of network IT equipment. Adding ZPE Systems is advantageous for, advantageous for Legrand as ZPE service delivery for edge environments will complement Legrand's line of cabinets, PDU switches, and fiber. Interesting. Also, two of the biggest names in digital infrastructure announced a new deal this past month. Guys, get ready. American Tower and IBM teaming up, y'all. American Tower, set to include IBM hybrid cloud platform to all of its access, edge, data center, ecosystem. Big news, guys. It's also leveraging 5G and AI at the edge. AI at the edge. Jamie, I think we're gonna need to get used to hearing about AI this year. What do you think? I'm thinking that's like the topic of 2024. I agree. Plus, plus, plus. Yeah, our new future. All right. Okay, here's another one, by the way, guys. DotPoints recently announcing their new partnership with Virtuous AI. The company makes custom AI models, which DotPoints plans to use for tackling challenges in data delivery, storage, and processing. Talk about a smart move. Sounds like a smart move, Jay, but more big partnership news coming from in the form of Connect-Based joining, we love Connect-Based, by the way. Connect-Based joining forces with carbon technologies that's QAR, B-O-N technologies. The new alliance will combine Connect-Based's customer network with carbon's lattice SAS orchestration software. This is hot on the heels of their previous acquisition of Master Stream, a pricing and quoting platform for telecom companies. Connect-Based cannot stay out of the news right now. No, no. Awesome. All right, let's go ahead and check in on the New York Hudson Valley area, right? Where Archtop Fiber has been busy bridging the digital divide. You know we love these stories. They've acquired three regional carriers there in the last five months, including most recently Warwick Valley Telephone. Congratulations, guys. This new addition will be rebranded as WVT Fiber and Archtop has already begun to deploy the fiber needed to deliver high-speed internet access to their newly acquired end users. It's a great story all around. Yeah, Archtop has no joke. They are getting it done out there in the Hudson Valley. So congrats to them. Over here in the Midwest, LightEdge started the year by expanding into Minneapolis. They acquired 76,000 square feet of 3.6 megawatt data center space to mark their 12th facility and their first in Minnesota. That's one way to ring in the new year. Congrats to our friends over there at LightEdge. Meanwhile, by the way, Ben with IG leaving their heart in San Francisco. On purpose with their new expanded network into the Bay Area this month, they announced a new project that will install the first Marine cable in the San Francisco Bay in over 20 years, two decades, guys. So that's really cool. Wow, true story, Jay. My grandfather used to play. I left my heart in San Francisco on the organ they had in their family room when I was a kid. Oh my God. That's so weird. Oh, I love that. Yeah, no, I miss my grandfather. But anyway, back to this. Powerhouse data centers stayed true to their name this month by announcing not one, but two new expansion projects. The first one is right in data center alley with a new site in Northern Virginia called Powerhouse95. The second big expansion is their first one outside of Virginia. This one is called Powerhouse Reno. It's located in Nevada in case you didn't pick up on that one. Reno, yeah. No, I love their names. Powerhouse95, I feel like I'm gonna get jolted just by saying it. Really good, great, strong names. Anyway, and I think that's it for deals and big wins of the month. That's right, Jay, giddy up, we did it. All right, well, there is plenty more news coming up this month, including lots from Metro Connect USA taking place in Fort Lauderdale on February 26th, 27th and 28th as well as Mobile World Congress, guys. Get your Barcelona in February 26th through the 29th. Yep, and I will be on site doing some JSA TV live from Metro Connect, so we're looking forward to that very much. So make sure that you just follow JSA social media feeds to catch all the interviews from that event. But Jamie, we're beginning to wrap up here, but something big's going on around here too, right? Something weird, something we're not actually talking about in the fast forward today.   Next week should be a big one for us. Yeah, I'm gonna have to use the bathroom after this. So giddy about what it is that we're gonna talk about. For any help with the response we want. Okay, anyway, thanks for watching everyone and happy networking to you and we'll see you next time. Yeah, as always, happy networking.


Dave Wood from Caltrans District 3 is it correct all right and tell me who you your title Dave Wood Donner Pass Area Superintendent Caltrans all right Dave Wood thanks for joining us today up there at Donner Pass tell me a little bit about what you're seeing right now up there well we have a tremendous amount of water in every form we have snow stacked up 40 50 feet high in storage areas that's slowly melting we have standing water at the side of the road we have overwell overwumped rivers and drains and behind me you have old Donner Pass road which is the old highway and we have a snowblower out there trying to clear out about four feet of water as there's a school down the road that's endangered okay so the Donner trail school okay so a combination of the rain that's been coming down and the snow that's melting as a result of the rain is causing this flooding is that right absolutely we have record setting amounts of snowfall in January and now we're getting tremendous amount of rain it's like standing in the shower out here and it can possibly melt the snowpack very quickly right now below six thousand feet it looks like spring time the snow is almost gone wow and so I'm assuming that besides the location that you're at the highways in general going up and over the pass are a problem as well with the rain well we have enough pitch on the the freeway here that it runs to the sides but there's places where it just overwhelms the drain it keeps going down stream there's enough standing water on the road it's actually possible to hike the plane going uphill or down okay so obviously with the trucks and the other cars I would think that the key advice here would be for people to slow down right absolutely the number one thing you could do to be safe up here is slow down after that be prepared know what you're getting yourself into weather wise by checking the weather go to caltransquickmaps.com you can check the traffic there and any restrictions such as chains or cables necessary and and turn off anything any device or anything that's going to distract you because you need to be paying attention to conditions it's pretty fierce we're in the middle of the wilderness out here and Mother Nature's in full force absolutely and I understand and tell me if you know anything about it I heard you guys have a new a new app I'm sorry a new application for your phone yes that's the caltrans quick map I was talking about that's downloadable to mobile devices you just can't go anywhere in California anymore without checking quick maps first all right sounds good and so in the next let's say the next 12 to 24 hours what are you guys expecting up there we're expecting to four and a half inches of rain that will turn into snow Thursday afternoon into Friday and it's safer for us to have it turn into snow but we're already stacked up snow 25 feet in places on the summit we're running out of places to put it at least the snow gives us more time to deal with the water and the runoff if we get all rain and it starts melting the rest of the snow back right and your camera person there is showing me the snow packed up along the side can you have him or her show me what's going on behind you well we have a snowblower in the background they were blowing water out of a drain to try and get it off the roadway the schools down the road from us here and snowblower is very effective as a water pump and we just have to clear this drain out make sure it's running in capacity to get the water off of this road yeah hey good work up there keep up the great work thanks for the great advice and one thing before I let you go I love the cowboy hat I want one well thank you me too available online I think it was 32 bucks delivered between the cowboy hat and the mustache everybody absolutely no that's a great idea so people can actually buy one of those things are they safe I'm sorry I can't hear you cuz it's traffic so are do they actually protect absolutely it's a safety rated hat I wouldn't wear it otherwise get out that's fantastic hey Dave Dave Wood up there at Donner Pass thanks so much


There have been numerous times over the course of the last couple of years when Elizabeth Warren has disappointed me. Obviously, we all knew that she showed that she isn't very courageous politically when she refused to endorse Bernie Sanders. She did not go out to Standing Rock when water protectors were being brutalized by militarized police and on TYT when she was asked about some members of the Democratic Party being more centrist, more conservative, more corporatist, specifically when she was talking about Joe Manchin she offered up a spirited defense of Joe Manchin, who basically is just a Democrat in name only. He is functionally a Republican, so I've been frustrated with Elizabeth Warren and I've stated before that she lacks political courage because she's not willing to take on her own party. Now when you contrast her with someone like Tulsi Gabbard who endorsed Bernie, who went to Standing Rock, who is fighting against her own party, it's easy to see that Elizabeth Warren does not have any political courage whatsoever. She has essentially been spineless and I don't like to say that because it seems really harsh, but for the most part she hasn't been willing to take a stand if for whatever reason that would make her fall out of favor with the party or would offend elites, specifically Democratic Party elites. However, Joe Biden announced and she actually came out with a pretty strong criticism of him that it made me smile because she is slowly but surely working to earn my respect back and I wanted to share this with you guys because I thought it was great. Our disagreement is a matter of public record. At a time when the biggest financial institutions in this country were trying to put the squeeze on millions of hardworking families who were in bankruptcy because of medical problems, job losses, divorce and death in the family, there was nobody to stand up for them. I got in that fight because they just didn't have any and Joe Biden was on the side of the credit card companies. It's all a matter of public record. That was short but sweet and it's effective because just that statement really tells you everything that you need to know about Joe Biden. He had the opportunity to take a stand for the American people but who did he side with? The credit card companies. And I like how she's kind of preemptively disarming the people who argue that you shouldn't attack other Democrats and the way that she's disarming them is essentially by saying look the disagreements that I have with Joe Biden are a matter of public record so this isn't an attack. I'm just stating what I've already said and there are already people saying that if you have a criticism of another Democrat running for president you should bite your tongue. Like for example George Takai put out a tweet saying you know I pledge to not criticize any Democrat because that could bring down the eventual nominee and make them weaker against Donald Trump. That is such a mealy-mouthed way to look at politics. You're essentially asking progressives to unilaterally disarm because we know that the media, the establishment corporate Democrats will relentlessly attack progressives. So really what you're asking is for us to not criticize other politicians but we're not going to do that. That's what primaries are about. You vet the candidates, you criticize them and then whoever wins wins but if you don't actually vet these candidates if you don't criticize them for their record for substantive reasons you're denying voters the chance to know about these candidates. We need the electorate to be informed going into the voting booth so they're able to make an educated decision and not just vote for Joe Biden because of name recognition because of nostalgia for Obama. People need to know that as Elizabeth Warren points out he stood with the credit card companies. Now what she's talking about here in particular is a bill from 2005 and as Rachel Fraser of the Hill reports in 2005 Biden voted for the Bankruptcy Abuse Prevention and Consumer Protection Act. Critics have said the law enabled credit card companies to target people seeking bankruptcy protection and this is a bill that was sponsored by Chuck Grassley and signed into law by President George W. Bush. If that doesn't speak to how terrible Joe Biden's record is then I don't think anything else will but we don't even need just this one example. He voted for the Iraq War, he voted for NAFTA, he voted to repeal Glass-Steagall. Joe Biden has essentially reliably been on the wrong side of every single issue so for us to not point that out for people like Elizabeth Warren to not point that out is preposterous. If you're choosing to not criticize these candidates you're making them weaker going up against Donald Trump because would you rather them criticize someone like Joe Biden for this now and give him time to come up with a response or would you rather this manifest during the 2020 general election if Biden wins god forbid but if he wins and then Trump does his fake populism thing and then this comes back to bite Biden in the ass wouldn't you want voters to know about this now so ultimately they pick the best candidate I mean I don't get that but I don't necessarily see as much pushback against Warren criticizing Biden here as I initially expected and I think it's because the establishment for the most part they feel safer with Elizabeth Warren and they don't necessarily view her as the threat that she really is yet because she's not polling at you know top three or even top four but in the event she starts to move up in the event she were in Bernie's position I think that they would have criticized her for speaking out against Biden like this so kudos to her I'm glad that she decided to speak up we can't self-censor under the guise of not wanting to weaken a candidate during a primary so I'm glad that Warren is kind of bucking a party orthodoxy here and she's criticizing him because if you sided with the credit card companies then um sorry that's a pretty big mark against you and that's just an objective fact don't blame us for pointing out what Joe Biden did blame Joe Biden for having a garbage record in the first place you could support the humanist report at patreon.com slash humanist report but trust me I'd have way more supporters at patreon if that was my podcast sad


Hi everyone, Joe for Jaspy's casebreaks.com coming at you with a hangar box 2018 2019 chronicles basketball hangar box number 26 chance to win our final $1,700 spot that break is coming up next if you're watching live First things first though, let's do the break itself. So let's randomize those names randomize those teams together Wait for it six and a one seven times. There's the timestamp right there seven times one two three four five Six and seven and final time after seven we've got Ryan down to Ryan and Now let's assign you a team after seven times mr. Mike's the A in the house to one two three four five six and a one and a one seven the final time Pelicans down to wizards remember this is 2018-19. So we're looking for Donchich Dallas Mavericks and we're looking for Trey young Lana Hawks among others among others. There's the first half of the list right there Steven P Hawks for you and there's the second half of the list right there Or where does Dallas is up there? Oh, wow Steve has both the Hawks and the Mavs in this All right, no trade window and in these little giveaway filler mini breaks, whatever we want to call them Because we want to get to the good stuff. We want to get to This we want to get to that. All right. There it is. There's the NT case right behind it That'll do this for this will be in a separate video Cougar watch out. No top gun on the on the TV folks BBC America Although you might you might have a different if you're in different time zone. You might have a different movie Pull up Cougar pull up Maverick, what are you doing? You are low on fuel Matt Unbelievable Like mr. Mike's ad he said earlier. He's he's writing checks his body can't cash There's a Luca Donchich right there and a Marvin Bagley Dallas Mavericks even P Deandre Aten Sons that's not too bad I think he was having a pretty solid season before they hit the pause button On the season sons Zach Paul with Phoenix. So there you go. All right, so that's the break Now let's give away that final spot. Let's grab everyone's names here fresh list new dice new die new die Hard 10 five and a five. Good luck one two three four five six seven eight nine And 10th and final time after 10 A very big. Thank you to all of those people right here from numbers two down to 30 for giving this a shot I really appreciate you getting in and the name on top is going to be adam cuperman. There you go adam Congrats to you. Hey, thanks to everyone else for getting in really appreciated. I'm joe for jasby's case breaks.com We'll see you next time. Bye


So, you want to solve the topological string on the compact kalabiao and so I will address a couple of questions which are different and to the local case and so on. So we want to solve the topological string on compact kalabiao three-fold and I would also call this M and what I mean by that so it's now maybe more specific is the string partition function so it's the closed string partition function. So this will depend on certain kalab parameters and it will depend on the string coupling and we all know it's a sort of perturbative expansion and then there will be a class kappa let's say an h2mz and there will be a sum over the genus g equals 0 to infinity and then there are so this is a generating function like 2g so this is gs 2g minus 2 and then there are numbers that we want to know so let's say r so they are labeled by this club kappa let's put it up and then g and then there is a parameter which counts let's call this q kappa so this counts the class kappa so it's a generating function basically for all these numbers and these numbers are chromofitten invariance and we would like to know them and the the t this t parameter is hidden here so t is something like the volume of a curve so you have you have b field and you have so it's some some of the complex volume of the the volume of the curve complexified is the b field and you write it in this combination and then the q kappa is something like e to the t kappa and so in this way you get you get this scalar volumes in so this other calor parameter now in some sense this is a perturbative expansion you have to think whether it makes sense or whether there are better forms of it and so on but what I can give you today is basically is an attempt to give you this function for elliptically fibered Calabi out in a more or less close form in that I expand in the base of the elliptic vibration so for every fixed class in the base I give you a close form and and so that's the aim of the talk so of course there's a certain motivation so of course I said already the soft chromofitten series soft GV series or at least the counting problem of it and it would also solve this was already in Martin's talks it solves maybe DT on PT series because this invariance are related and then what is more interesting for me and where I get some structure out it also solves a BPS counting problem in five dimensions 5d and this BPS counting problem basically is you look at the 5d Poincare group and then you you see that there's the little group of the 5d Lawrence group so there's the little group and this is SU2 left times SU2 right and now there is certainly a mass to get this Poincare representation there's a mass and you sort of want to calculate something which which depends here on the right spin and the left spin and the mass and so what you what you want to do you want to take a trace of the Hilbert space of this BPS states and then you have various choices of instance first I will sort of don't resolve the right spin so I write something like just J R like this and then you write a parameter for the left spin and then you write something which measures the I mean some measures the energy but since they are BPS states this energy is fixed by a charge lattice and this charge lattice turns out to be this common so then this is where the kappa class comes in and so at the end you get something which which you can write and this was done by Gopal Kumar and Wafa you can write it while also by necrossof independently somehow and so you can write it as as a sum over let's say the genus which is positive and then there is an e kappa g and then this parameter y appears here so it's something like something that we also saw in Martin's talk already and then there's a 2g and then you have this e to the t kappa that measures basically this q so this this measures the mass and then they are fixed by this kappa class and this kappa lies in the lattice and this is because they are BPS states but then there is actually a very interesting formula that is implied by that which I'm really use in the following and that formula I mean again it goes back to Narain Taylor and then was made more general by Gopal Kumar and Wafa so this formula looks like this is basically involves this quantities here so these are BPS indices and they are they can be be in Z so note that if you sort of resolve this this right spin so maybe resolve J right and then you get this this minus one gets a U and then you get on the right hand side things which have depend on J left and J right and not just on the genus and on be on kappa and these are actually in N and that's something sometimes interesting so this is more this is more like a real counting problem this is like a index counting problem and for you can actually do both in the cases that I will discuss I only restrict myself to the index counting problem because the formulas are simpler but you can certainly do both with very similar formalism that you will see so so then you get here well M from one to infinity and then you get a sum over G from zero to infinity and then you get a sum over this kappa that we already had and and then you get this I G kappa and then you get G SM over 2 and then 2 G minus 2 and then you get again this e to the M T kappa okay so this formula is sort of slightly bizarre and it has been used the fact that it's slightly bizarre because if it is a perturbative expansion then at all rational and numbers of GS it has actually poles that's that's pretty bizarre so so let me say note the poles so this come from genus zero because then this is minus one and so note the poles at so this poles of course will play a role so if they are rational then we get the poles and that's that's already I mean this is one of the starting point of this non-perturbative completion that Marcus and his friends are studying so there is also true for the compact case and for the non-compact case but now let me say generally that so let me not arise this formula for a second so so I raised already formula which maybe you would have protested so why should you have protested so let me write this formula again so let's write it like GS 2 G minus and then write just FT like this so this is better for this propose and you see this things are Kayla line bundle so they live in the Kayla line bundle I mean this comes from special geometry like we heard in the talk of beloved so this is like a section of L 2 G minus 2 so then if you think this is a good object you have a problem because this comes in all powers of the exponential if you make a killer transformation you get you get a problem and I will come to this point later but you can you can remedy this you can say okay I take GS and I take a I take a period of that now the period works the spirit transforms in the inverse line bundle so then this formula certainly makes sense but then it's not anymore has any good modeler properties because the period is some complicated object that can transform very complicated and in some sense the reason that in the local case you have this is one you have a global section here makes this formula work if you apply it I mean for instance this wave function thing in the local case this has a beautiful application but in the global case this thing is very much spoiled this property so so this would be only in the local case and this is a huge difference for this for the things for the global case but let me now come to the to the geometries that I want to consider and this geometry is have very much to do with the talk that you hear by Martin Cole so so it except that I'm not looking at elliptic surfaces but I'm looking at elliptic three-folds so so let me sort of make this small remark so basically local Calabiao they are always sort of say of the type you take a total space so M what is my Calabiao is basically the total space of the anti-canonical line bundle over some base so what I want to do is so this is this and then and then this can be solved in many ways so what I want to do today is basically to change the setting slightly but not so much so we make a Calabiao three-fold which is compact so this is clearly non-compact because you have this non-compact line bundle but the only thing that I want to do is I want to exchange this compact this non-compact line bundle by an elliptic fiber so then you have this situation and M is compact and that is not at all very out outlandish when you look at the history of Calabiao so for instance if you take the degree 18 constraint in let's say nine weighted projective space so maybe we should just put it down okay so then you have this Calabiao so this is one of the earliest thing is a degree 18 hypersurface in this projective space weighted projective space so it's six nine six one one and now if you write this down you can immediately see that you get an equation which has this elliptic structure because you call this coordinate y you call this coordinate x and this coordinate you call you and then of course it's already elliptic so it goes y squared and then you have I don't know I don't care about the coefficient at the moment you have x to the three because it's degree 18 and then you get something like a x y z and then you have a product of this use let me call them you you prime for the second and then you get a z to the six so the c to the six you don't see that because this has a singularity you need to blow up parameter and this is the c to the six and then we have a b phi i from 1 to r u i 6 and then you get a polynomial pb u of m and this I write down because now you can see so this is the constraint so this is basically the constraint for this particular Calabiao but you can replace this base so if this is in this case the base is actually p2 but you can certainly do this for any base so that's a very simple yeah so this can this guy has exactly the same situation and then Martin Colts talk it has it has a co-dimension one has only codera fibers e1 and then at higher co-dimension there are more singular fibers but the important point that in co-dimension one is only e1 codera fibers and and then you can calculate the discriminant it has some cusps and so on so it's a complicated thing but I will basically make a prediction for the gram of fitness theory on this space which I think Martin also tried to solve it it's not so easy and then he resorted to the surfaces again and okay anyway so so then but I wanted to give you this algebraic form this is basically like a b-model expression to see what how it connects to the local case because if you take this PB 0 and use this depends on you and M and you set it to 0 well it's actually like UV this is actually the mirror curve so it sort of has a so this is the mirror curve and it's a spectral curve of a matrix model and it has many many nice properties and and you can also see how you achieve this you how do you achieve this so basically you say x e this is the class of the fiber so you take it 8b to the 8 to the 6 so the a is this the b is this and then you you send this to 0 but you keep somehow b fix and then you get you get this so I should say this depends on b and then it well I mean this is this this m a mass parameters but then it also depends on you and you are basically the same you only you have an Italian map between them so basically there's a you is you to the 1 6 so this is an Italian map so that's the way you get you get this local geometries but now let me change gears a little bit and say the same thing from the from the point of view of the a model so for the a model of course I given you the geometry it's basically it's an elliptic vibration over b and then you can use you can use service spectral series spectral sequence in order to get all the topology from the base if the fibers are not so singular so so the question was already asked so today similar like in the talk of Martin we take once we have one section and only Kodaira I1 fibers in Kodim one and then everything is actually given by this spectral sequence so so now we use Larry's spectral sequence to get the top the topological data the topology of M just from B so that's a easy exercises and it works very nicely so so let me introduce some notations so it doesn't pay to keep this formula but so so basically now we introduce some classes so we introduce the class of the fiber which I call T and I call this exponential saying Q and then so this is this is the now we go to the homology so what what do we have so we have we have a curve class I call this curve class e for elliptic fiber so this is the class of the fiber and if you if you want to calculate the scalar parameter you just take what I said before the B and the and the omega the symplectic form and integrated over this curve class so this is this volume and then you have dual devices and this dual devices I also need name for them and then you have the class beta these are classes in the base so these are these are in H2 BZ and then I have here I have well the dual devices go a little bit higher so here the dual devices I should already have a DE and I put a tilde here so this is actually the class of e which is the class of the section and then it's shifted by the canonical class of the basis so this is just follows from the geometry of this and here I have classes which I call DK so maybe I call this also K so there might be K of them and that is just the so here we have of course we have of course e so we have a projection map from e to B here and then this I call B and then this one also to say pull back from the base so this is DK and this these are living on the base so these are these classes and and now you can calculate all the intersection numbers just based on these classes and and and the intersection numbers of the base so that's a easy thing but I need it for some later work so let me just say that okay so you now calculate DE squared so this was this class here and this one just gives this just gives the integration of the second churn class so so if I say C that C K is always the churn class of the base and if it's not the churn class of the base I write the manifold okay so this is the churn class of the base and then we have then we have D we have let's say D E times D K so this is now intersected with this base classes once and this is the C one of the base times D DK so this DK is is this guy so this is a divisor on the base and this number I will call 12 8 sorry 8 K so this is the definition of what AK is and then you have intersection of DE DJ DK and this ones are just given by intersection of the base so this is intersection of the base so this is just over the base and you take the DJ DI and you integrate it over the base so this gives all the intersection numbers and the one which is three times things of the basis of course 0 because it's a vibration okay so then you can get more so you can basically get a C 2 of M so now this is in the total space times DE and you calculate it and it's so this is like a Hirz-Pochriemann rock formula and it's like this and you can also calculate this one on this other types of devices and it gives 12 AK this what I introduced this AK and then the Euler number is actually minus 60 times C 1 squared of the base so for instance in this case this is this famous Euler number 450 minus 450 is the second example that Candela's ever looked at this is this case okay so then for a reason I mean for to see the exhibit the model the modularity I have to make a little change in the so this is the this is the basis of the classes and the curves for the Morricone so this was the Morricone and I make a little change from that and and define DE so this was also why they are tilted before DE I shift again with this canonical pullback of the canonical class of the base and then that will lead to so if the QK where e to the 2 pi I TK and this shifts this classes of the base by so they were before TK and now they are get shifted like this this tau and and then why do I make this change of the base I basically make this change of the base because I didn't like this coupling so I like this coupling I don't like this coupling sort of which which which mixes the fiber and the base in a way that I don't like so basically now in this new base so the key property key property is that in a new base so if I use this guys then these guys are actually zero and by the way this case don't change so they are just the same okay so now I can start start stating the main a serum and then I try to prove the serum and and this has very nice so to say inside in the wave function transformation of the top compact topological string and and I also need this formula so let me make the claim so what is the claim so now so we of course our goal is to expand the string partition function and now I expand it in a particular way so you have the fiber class you have this base classes that are defined and you have the string coupling and now you decide so to say to to expand it in terms of the base classes as I said so and you you pull out beta equals zero which is special it's not Jacobi form but the other will be Jacobi form that's why you pull it out and then you have the rest is a very systematic expansion so it's a b in h m z and then it's z b tau g s and then it's q b so and basically the whole thing that I want to explain you today is why are these guys Jacobi forms and how you can calculate them and how you can eventually solve the problem so that that's the point so this these guys are the main characters in the rest of the talk so what are the what are the properties so I give you a list of properties of this of this z b t g s and so let's start with property one so they have basically three properties and I'm able to prove some of these properties so let's start with property one so so what is this so um so the set b tau g s are Jacobi forms in fact they are meromorphic Jacobi forms not weak so these guys have poles which the poles come basically from here so they are meromorphic Jacobi forms and these meromorphic Jacobi forms they have a weight and they have an index and the weight of this guy I call in general k and it's zero that's very good and the index is actually I call it m and it depends on the base class of course and it's one half times um times the class b times b minus the canonical class so one cb and if you know a little bit of algebraic geometry especially the genus of the curve in the base minus one so that's the index and and then this is not completely true it's up to a up to a multiplier system which is however very trivial so the multiplier system comes because this quantity is not completely sl2z invariant so the multiplier system comes because um if you make the s transformation on this q beta then you will find that this is actually depends on the parity of this curve so basically it is a minus one to the c1 times beta times q beta and if you make the t transformation on it then it has a similar factor so it's minus one c1b times q beta so so this this is a multiplier system which so so the so the set bs have to spill out these factors to make this expression invariant okay so then um the poles are yeah i will talk about the poles but the poles are basically imposed from that so they are they are basically over q and that means they are the torsion point of the elliptic argument so one of the most important thing of course which physically is that you basically identify z with z g with z which is the elliptic argument of the weak jacobi form that's the most important point in in this so so i i don't know how much i should say about jacobi forms so it's a pleasure to talk about them but many people know them or many people don't get too much out of it but let me say one very trivial very trivial thing so so jacobi forms so basically what is it it's a map from the upper half plane times c into c and well that's here in the upper half plane lifts what we call the elliptic argument sorry the modular argument so it's the modular argument and here lives what we call the elliptic argument and this is the one which is going to identify this the string coupling and so they are they can be holomorphic maromorphic whatever and now they have of course transformation properties so you say gamma is a matrix a b c d in sl2z and then you can make the following you have the following transformation properties so basically that's the defining transformation property is modularity and modularity and and quasi periodicity and the modularity says okay the modularity says that if you uh say this is this normal transformation ct plus d so it's the projective transformation and it says that if you uh now plug in here and you take the t of gamma and then there's also a z of gamma which is just z of c tau plus d and you put here the set of gamma then this thing is basically invariant up to uh a phase and this phase is related to the index of this guy so that is the m so it's related to the index and then it is um it is um m and then the c comes up this is the c really from here and then is c squared and then it's over c tau plus d and and then as i said it's invariant otherwise so it's just the phase and then the so this is the modularity and the quasi periodicity says if you if you it's it's sort of say a model it gives a reason to call this the elliptic argument because elliptic curve of course you can shift by one and you can shift by tau and it should not be invariant again up to a phase so that makes this an elliptic argument so if you take c plus mu plus lambda tau then again it's basically the same up to a phase um so it's e to the minus two pi m and then lambda tau plus a two lambda z and by the way here i forgot something important which nobody seemed to have realized so here is a factor of ct plus d to the k and that gives the weight and that is the other thing that that comes in okay so they so what i the index comes in here so the index is only coming as a phase okay and then of course i should say that you know jacobi forms anyway so many things are the wire stress forms the jacobi form the tether functions are jacobi forms with vector value jacobi forms they are jacobi forms so there are lots of jacobi forms that you know but the well i mean the jacobi forms have an expansion if you expand them in z then you get then you get the quasi modular forms you get the eisenstein series e2 e4 e6 and so on so um i guess that's all what i want to say about jacobi forms um but now well at least at the general jacobi form so now let me sort of uh come to the property two so the property two is the following the property two is that the set b are not arbitrary jacobi forms but they are jacobi forms of a very particular type they have the dedicated eta function raised to 12 times c1 times b and then they have a numerator phi b tau of z and this one is a weak jacobi form so this is a very strong statement as it turns out jacobi form and there's also is sort of in the title then finally and then the denominator is um something which goes from l to 1 to b2 so this is the uh numbers of the classes in the base and then it's an s from 1 to bl so bl is the l's component of this vector b that gives the uh a class of the base and then we have tau s z so i haven't told you what this guy is but in order to tell you this i have to go say a little bit more about the structural theorem of jacobi forms so there is a very important theorem of eichle it's okay so this uh theorem says basically the weak jacobi forms are finitely generated and freely from by the eisenstein series e4 the eisensteins and i call this actually q and then e6 and then um and then two other arguments so this this arguments have just wait no index and then there are then there are things which have uh index and that is uh sometimes called gamma minus phi one so this is this is the notation this is k and this is m here this is always like this k and m so this has k minus one and index m and um and then it's the and i said you know jacobi forms of course the jacobi the the teta functions they have a multiply system but there's one teta function which goes into itself and there's teta one and so this this can be used to build a jacobi form and you have to square it and then you take eta to the six and you see this has sort of say weight um this has weight one this has weight three then you have minus minus two and then to the question that it was already asked you can sort of um have two interesting expansions so let me write this like this um x one so there is a product expansion which is sort of nice um and useful actually um so this of course just comes from the jacobi triple product identity and is given like this and now to this other question so you can write this in terms of um expansion in z and then this expansion coefficients will be actually um out of the ring of um of quasi-modular form so this is spanned by e2 e4 and e6 so here is a is like this and then it goes with order z squared uh sorry this is order this is i'm i'm i'm off in the order so this is um this is just set to the four and so it's only it's only even so for instance if you want to do uh open strings of course you knifely would say you have to do uh odd jacobi forms they're even jacobi forms they're odd jacobi forms but you certainly get here only powers which are even in z and that means even in gs anyway so this is the this is the story and now you see why i picked this denominator and that's why i left this formula basically this denominator is precisely to reproduce this poles at the portion point because you see this guy goes with gs with that so it has poles and i sort of multiply here by s to get in this multi covering that generates this torsion points at the rational i i put this i put here this power of this a so it's basically to reproduce this torsion points and this is this i set this uh this is another generator so there's another generator so the other generator is called b by and it has weight zero and index one so b people write like zero one and this is well maybe i just be brief and don't well so it's one half of the elliptic jingles of k three that i suppose everybody knows that is actually so you take k one two two three four and then you take a ratio of theta functions so this is theta at the argument tau and z equals zero that's why you don't take the one and then um so it's anyway has weight zero because you have this nice ratio and then the weight comes from this tether so this is k t and then here is the full argument and you square both of them and that's that's the elliptic so this is these are the other jacobi tether functions so this is generated by these things and um and this is already extremely powerful the statement in the sense that so let's go back to b is equal to p2 well now i tell you for degree zero all five are degrees the only thing is that i have to fix a ring whose dimension you can easily determine because i have told you the dimension of the z at the index and the weight of that don't sucky has given you the index and the weight of this and of course this is classic and so then i i just can build an object which has the right index and the right and and the weight and it will be let's say z1 well let me just so just z1 is as i said phi one over error to the 18 and then it will be just a tau z and this is the only thing that i need to give you and this this one is very primitive so it's minus q over 48 and then 31 q cubed and then 113 p so this has has a weight 12 16 no index in this case because the formulas work out and this gives already infinite number of predictions for higher genes and so you can iterate this process and then since the ring is not so small at some point you would still run out of boundary condition but for instance it is easy to do it for b equals 6 in this case that's okay so you get a lot of lot of predictions and i can sort of convert them in bps invariants give you integer numbers and sort of this were the things that that well you can also write it as thomas and thomas invariants and so on so let me come to the property three so the property three is also very nice so the property three says that once the index is negative or smaller than actually smaller equal than zero so there's a property three property three and the claim is if is smaller equals zero then um then um the phi beta are completely fixed fixed by the vanishing by the known vanishing i g beta so these are the bps indices and basically you know that that if g is greater so this this happens if g is basically too great is too big so this happens if there's a little bit depends on the on the base but it basically goes with the base degree so if b is bigger than this number then then this thing will be zero and you can show that if the index is negative then this grows very small a small this room of a weak jacobi forms and then this this conditions solves it completely so this particular solves the m string the e string the refined m string the refined e string things which have singular fibers and so on so this this observation because all these things precisely the things that soto and these people classified they were rigid in the base so they they they rely on a negative self in the section curve then this is negative the index because of the formula i gave you and then you can solve it so this solves a lot of series but these are local series so this is not so it's the old thing for some reason the global series are really really much harder but they are more trivial more non-trivial than the usual local series that we look at for reason that i now explain so let me sort of in the last minutes try to say you some interesting aspects of the proof of it yes yeah yeah that's what i'm saying so they they are not doing this very good but that's why we now work with them so um so let me let me say some interesting aspects of the proof so i mean the i mean property one is certainly the most important one so let me try to make you understand property one because it's very simple so property one so you know that this um i mean first you have to establish modularity but i don't want to go into the details basically there is a there's a formalism which is comes from the from the from the derived categories so basically in this case there's a four-year mochi kernel so in homological mirror symmetry if you have an elliptic vibration you have a you have a certain property of the four-year mochi kernel so basically what people always well let me just sort of draw you one diagram so that you get that if you want to look it up you can see it so there's two projections you take m times m and you take two projections to the base and then there is this four-year mochi kernel this is the only thing that you have to know so this is uh is tether so this is the ruse-criminant and then it's e times m minus m times e and then um and then you subtract on the also c one of the base and then when you have this object then you can say that in the so this is basically homological mirror symmetry you have your you have the the a-brains but uh and then you know that the s transformation on f and anything in f in the a-brains can be written out in terms of this four-year mochi kernel so that's i mean that's uh so you take some pullback of this and then you take some left action on this map and then you take f and you take this this four-year mochi kernel sorry i should throw it like this and then you you have p and for for some reason we also tensor it also always with um so this has to do with my shift of basis um wow so the upshot is when you have this formula and you know these classes then you can write down an s transformation matrix entirely in terms of the of the intersection of the intersection of this thing this works basically for four-fold three-fold uh k three whatever so everything that has a mirror symmetry so basically then the s matrix i just give the s matrix so the s matrix will be something like one minus one uh and then um 0 0 0 0 0 so this is basically the s this is the the block which is the s and then the other thing so to say here's a block which have a k and then there is a block which has a c k j so basically i i write this like x not x k uh f not um sorry i introduce also a t x t and then i have f uh not f t and f k so this is basically is the the series period then this is the one which talks to the tau this is the one which talks to the base classes and these are the dual periods uh in the same and um and it's a bit ugly so x k so this um yeah maybe you're writing a matrix so then this one is a k as i said and then it has here 0 0 and then it has this intersection matrix on the base i k and then it's minus one and 0 0 0 0 and it has a j and that is um a that is a no 0 then is c 1 squared and 0 0 0 and then minus a j and so there's all the section number so the point is you can establish and you can also do this by just looking at the analytic continuation of the periods this is just a homological mirror symmetry argument if you are powerful and want to analyze the system of um let's say where you have 10 model i two from the fiber eight from nine from the base then you could also do this by analytic continuation but but the but the mathematicians give you a very nice answer and this answer is basically due to bridgeland he does this for case reason and other people like yaw and company have done it for higher dimensional cases and we can i mean they did it sort of wrong so then we have to do it again but the but it's anyway standard and then there's the s transformation the s transformation is even simpler so the s so the t transformation the t transformation you just tensor by you just tensor f not just by this line bundle so then so t would be t of f not you just tensor this by a certain line bundle and that's what we know as the b-field shift so that's and again we do a little bit shift by this class so anyway this matrix will be look similar all in the intersection numbers the only thing that now you have one one zero one and then other other classical intersection so why i'm saying this so i'm saying this because to show you that if you have a partition function and you have the symmetry then you would expect it to be modular because after all this these are the these are the space-time generators of the space-time duality and if you have an object on the calabria it should better be modular i mean this is what string theory tells you and and now i want to make the one important point before i finish so the one important point is so if you look at witton's wave function transformation property i already alluded to this a little bit then so you have so witton says okay we have this e to the g equals zero to infinity and then we have this what i wrote already before the only difference is he now calls this the wave function and then he goes into geometric quantization of h2r so then you do geometric quantization of h3mr and you want that this so to say doesn't depend on the polarization and since the polarization is given by the change of the complex structure you get a differential equation in this complex structure and this looks like a heat equation and it looks like this there's so it's because so let me say a couple of things so basically he said he sets this like this h bar and then he has an h bar squared and then he has an alpha beta gamma so this is originally how how he writes it beta so this is a bar index and this is a gamma and then this guy annihilates this wave function so this is the is the infinitesimal statement for the fact that this wave function should not depend on the polarization and since the polarization is induced on which complex structure you use there is a is a differential with respect to this complex structure this is a complex structure okay and then you see and many people have looked at this including bcuv and you say this this cannot be right well it cannot be right for two reasons and let me sort of give you the trivial reason so first of all well it is right but people thought it was not right and i should tell you why it is right after all so basically let me give you first one make a make a small remark so i said already that this is bizarre because here you have no invariance right you shouldn't take this rather you should take x naught some period you can take any period but this period should be so that it cancels the scalar transformation otherwise this object makes no sense in the beginning i mean because it's not invariant under scalar transformation so and if you do that and you look at this transformation you will see that x naught actually goes under st transformation because this is x naught it goes to x naught c tau plus d so if this goes transforms like this then this guys have to compensate that and if they compensate that then this guys must must be modular forms of a certain weight so it follows it follows that the fg are as a function of tau so this holds all in the limit of the base expansion are are forms modular forms of a certain weight and the weight you can it's just the weight is just given by this index 2g minus 2 and now comes the second thing that is very important but now this guy is almost quasi periodic because of the gopa comma waffa formula so you know already that z goes to z plus one is actually in okay transformation of this is because of the bps formula so if this is a correct transformation and you have this property you can see easily that you also have also have to have to shift by tau that's trivial you just write it down this expansion you shift this by by this amount and then you use that as an invariant and you have to see that this is actually not just a shift but it has to also be shifted by tau must be also possible so this implies this implies quasi periodicity so so this is very trivial in some sense so but you have to see the following i mean you don't really change the polarization because you you you you just rotate the a matrices changing the polarization means changing the b periods and the a periods you don't do this so if you would change the b periods then you would actually change the polarization and the whole thing becomes very intriguing so then it's not so easy to say what is the invariant of it but here we got lucky because because we have this monodromes that just change so to say the a period a periods not the b periods so the full power of this whole thing that i may be saying would be for the quintic when you have this transformation but you also change the polarization then it will be very very powerful even for this case i believe and then there was a second point that i should really finish quickly as i said i mean this this quantity look at this at g equals zero so in so at the at the lowest order in h so a lowest order of h bar this thing is simply wrong because if you pull this down then you get something so now i i sort of absorb this i mean i sort of introduce a new parameter like this uh well this was is the h so just a power counting parameter so now i take the derivative of respect be with h and look in the lowest order in h bar then of course this gives an anti-holomorphic derivative of f naught which is the pre-potential and it gives something here from which is not vanishing because this one is a holomorphic derivative so then everybody says i mean like like bachatsky and digraph and people who talked about the osv conjecture they all say forget about the genus zero part this thing has to be modified and and they modify it simply by say by by excluding all the consequences of it at genus zero and genus one actually genus one is also a problem so precisely the cases where you have this killing field on the world sheet are a problem so i'm saying this is not what you should do so what you actually should do there is a even in the old literature on special dramedy by stromenger there is a unholomorphic pre-potential and this has very much to do also with the talk of of bill uh so there is an unholomorphic pre-potential and this unholomorphic pre-potential has the property that the triple couplings are not given by this but they are given by the covariant derivatives of that um so it's the covariant derivative let's call this unholomorphic pre-potential s and you see since this contained uh i mean this one is is is more trivial but they they start containing the crystal symbols of the connection so they are not holomorphic so if this going to be holomorphic which of course is true in conformal field theory because you fix three points on the sphere there's no degeneration that is holomorphic but this one will be not holomorphic i mean this would not work if this is holomorphic so take this non-holomorphic so the so the point that i'm making is this thing works if you take this old definition of stromenger put a non-holomorphic pre- potential but then you can ask do you know that object and it turns out you know it it is precisely the propagator of bcov so um whether in bcov series are propagators and what i'm what i call s is actually s so that's why i'm called propagator so i i take the bar of the of the propagator of bcov and then i uh take a factor of the caler factor to make it to give it the right caler weight so this is the caler factor so this has well this had for instance as minus two and then uh i wanted to have i know it has two so i wanted to have it minus two one and this has clearly two two this factor so there i make it to a right weight and this thing is actually fulfills it and now you can think what is then this equation is it really fulfilled or not if you take the different uh definition and it turns out is fulfilled and it's very beautiful it's basically fulfilled by this ramanujan identity for modular form so you take well i mean it's so to say convenient to write this as a matrix of propagators which is um well you change the coordinate but it's basically two s s i s i so there are three types of propagators in bcov and so there's uh this is a change of matrix and then you have immediately a property of this big propagators which actually we have found in the paper with marcos and grim and some people uh in malin vise i guess and this is like c k m n and then it's the propagator again m i propagator n j and you see this is precisely when you when you complex conjugate is precisely what you need is precisely if you take this s as the propagator you're precisely fulfill this equation and and why i'm saying this i'm saying this because from this equation if it's correct then you can uh then you can get also the index so you just calculate it and use the properties of this in terms of the topological numbers and then you get the index so the other properties i mean the property three is easy to establish the property two is not so easy to establish also part of the the thing that the paper is not out and uh but um yeah maybe here should finish


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