Welcome to this presentation with simple advice on writing a scientific paper. So you've finished some research and it's time to write a paper. First of all, congratulations. Second, sorry, but you should have started a long time ago with the writing. In this presentation I'll go over the writing process, talk about storytelling in papers, the formal structure of a paper and give you some tips and tricks on how to write the individual sections. But first, a disclaimer. I have written many papers. This is my way of doing it. It works for me, but it's not the only way of doing it. With that out of the way, let's look at the writing process. I strongly recommend that you write from the start. By that I mean you should write the introduction while you're reading articles, rephrasing what they say in your own words and citing the relevant work. Similarly, you should write the methods while you're doing the work. It will double as your notebook. Write the results while you're getting them, including making nice draft figures that summarize the results in an easy way. Then make a list of results, create the final figures and use the figures to prioritize what are really the most important results in your story. You can then write a draft abstract, which will probably be useful for some posters you will submit to conferences before submitting a manuscript, and create an outline and begin to copy the text you've already written into that outline. Then go through the whole thing and rewrite it for flow. Then write a final abstract and congratulations, you're done.  By the time you're making an outline, you already have a lot of material to copy in and you almost have a draft manuscript from the start. The next topic is storytelling. When writing a paper, it's important to be aware that chronology is irrelevant and time spent is irrelevant. Readers do not care in which order you did the work or how much time you spent on each part. As the first author who spent months on doing some work, it can be very hard to accept that it can be explained in one or two sentences. But sometimes that is the fact and then you should do it. You also want to have a red thread in your story. This can be a bit of a compromise between on one hand having a logical flow, explaining things in the order that makes the most sense, and at the same time trying to present the main result as early as possible to catch the readers. You cannot always achieve both, but when it's possible, you should do it. When writing, you also need to be aware of the formal structure of a paper. Traditionally, there are two different journal formats. One is introduction, methods, results and discussion, and the other is introduction, results, discussion and methods. You may think that this matters, but it is in fact largely irrelevant. The reason is that even if you have the methods section before the results and discussion, many readers will skip methods and therefore in either case, you have to assume that people have not read the methods and write the results and discussion so that it's still understandable to everyone. This gets us to the topic of results and discussion. There are two versions here. Some journals still insist on having two separate sections, but more and more journals allow you to have one combined results and discussion section. When allowed, I much prefer this because I believe it gives better flow when you explain the meaning of each result before moving on to the next result, rather than going through all the results first and then discussing them. Now for the individual parts of the paper. The first is the title and abstract. The title you should think of as a pitch. It should be fairly short and it should be the main selling point of the paper, the reason why people would want to read it. The abstract on the other hand has many roles. It is important for having your paper show up in search and for that reason you need to have it contain the right keywords so that search engines are going to find your paper based on the abstract. It's also important for selling the research. If the title has convinced me to read further, I'll read the abstract and based on that decide if I will read the rest of your paper. And on top of that, it should of course serve as its actual function to be an accurate, concise summary of the work presented in the paper. It is not easy to do all of this at the same time. Writing the introduction is much easier and the reason is that you can use the same template almost every single time. In the first paragraph you want to lay out the scope and the motivation for the work. The way to do that is to first talk about some broad topic that is important, explain some good things that have happened within that research topic typically recently and then identify a narrowly defined problem that is the one you're solving. After that you will give the background for the work, only the background required for the reader to be able to understand your work. This should not be a review, it's an introduction section. After that you can move into talking about related work which would typically be work that either lays the foundation for your work or served as an inspiration for how you solve the problem.  In the method section you want to be concise and explain what you've done, how you've done it and not go into long discussions of why you did what you did. You want to stick to the facts and include the technical details that are important for making your work reproducible. Other things you can do that can dramatically help making your work reproducible is to share the data and share your code. This gets us to the results and discussion section. Here you really need to help the reader. You have to remember that the reader has probably not read methods, may have only skimmed the introduction and is therefore quite prone to losing the entire plot of your story. In my opinion the best way to solve that is by paragraph structure specifically by having each paragraph follow what I call the why, how, what structure. That is in each paragraph you first explain why is what you're about to talk about the next step in your analysis, how is it done and what did that show. That then leads into the next paragraph explaining why you did the next thing, how that was done and what that showed. This gives the reader direction. You always know why whatever is being talked about is now being done because it was literally the first thing you said in the same paragraph. It also summarizes the method, meaning that people don't need to have read the method section to understand what's going on and it interprets the results immediately before moving on to the next part of the story. In addition to the paragraph structure you can help the readers by having good subheadings. Here in the headings you really want to focus on the results, have the titles be what you show, not how you showed it. Finally in a paper you typically have a conclusions and or outlook section. Here you want to first give a summary of the main results yet again then explain the broader importance of your work and what future research it may lay the foundation for. However I would really try to avoid the trope of more research is needed because in research more research is always needed and if you don't say what research is needed next you are really saying nothing. That's all I have to say today about how to write a scientific paper. If you want more tips and tricks I suggest you watch this presentation next. Thanks for your attention.


Tlo what's poppin? We are on twitch. We are live But if you miss this live Anything good happens. It'll be on this channel above us man If not, you know, just leave a like comment subscribe turning the post notification bells Let's continue to grow the family from Chicago to the UK Don't forget. We do got the patreon. We just finished. This is England 88 Time to start on 90 feel me The light I see the finale was fire. I am gonna hold you Real emotional lot of ups and downs and things of that nature Link to all of these are in the description below if you're wondering and we also got the discord submit your little request and whatnot This is I got attacked by a heavyweight champion 2.2 million views in 20 hours. I Can only wish that someday The early the first responders can push my video that much Let's get into this Probably wondering why I would do this Well, this is a series where I've done some crazy things with America's biggest prankster Judeo, we have both set each other for unbearable challenges to see who will follow through and who will fold And we're doing all of this to answer the question who is the biggest man You see me personally, I hate beef and I try to squash every single beef that I get into my life And I want to help Nick go out with him Yeah, of course he does Well, Shannon Briggs is it because I have no idea two-time world heavyweight champion who invented the phrase ah We met three years ago when he's Logan Paul's trainer for his boxing match against knowledge and being team UK I got Shannon to call himself a Pulse I'm an assay. I'm an assay from that moment. Mr. Briggs wanted his revenge. Have I ever seen him again? I will knock all his teeth out It will make me feel phenomenal to break his jaw break his ribs make him feel pain This did happen a long time ago, so I just want to Say that I have apologized my guy Shanon say I just want to say I am so sorry for what I did to you And I hope you still don't want to break my face in and break my legs and do all of that stuff. Sorry, man unfortunately Shannon Briggs Never gave me a response. So I think it's finally time that they meet up Squash this once and for all and become friends. But before they do that Shannon obviously got to get his revenge So can you put a plan give him a call? What's up champ? I want to prank with you, but I think the person that we're gonna be pranking I think you're gonna have fun with it. Remember the the English guy that got you three years ago Hey, man, this is gonna be the best revenge cuz he's on a dead-ass like at least Briggs is a good sport Like turned it into like let me just prank him back. Let me get him back Because at the end of the day, this be all internet stuff. So he might run away low-key All right, man, appreciate you Nicko you're food you are You know being a lacrosse mom is tough I coulda swore I turned my ad block on All right boys, man the man of the hour Mr. Briggs is here I kind of feel like he actually is gonna knock Nicko out and if he does that'd be kind of funny But like I want to see my work What's good champ? Lot bigger in person It's crazy, you know, you always hear rappers talking about how they flying out girls and stuff and here I am flying out of six seven three hundred pound Two-time Worldweight Championship grown man champ Every way champ of the world, but I'm with the real champ He's six seven. How tall is jillian? Right here y'all. Let's go champ. I'm the real champ. I was just laying in bed man I was like man, I sure wish I could see that kid again. No, I swear It's crazy how life is a universe work. Then when you call me I was like, yo, this is meant to be so Let's go So this is how I had it all planned out I saw this trend on tiktok But basically you eat door-dash orders in front of the stranger, right? And so I thought it was a perfect idea and I haven't run into some door-dash orders You don't think nothing of it. He's probably gonna think it's whack. I'm not gonna lie It is a whack ideal But the more whack it is when it's the last one that's when his expectations are gonna be at the lowest But what Nicko doesn't know is I phase-rugged one of the orders to go directly to one of his biggest ops Shannon the cannon break Shout to the boy arach man. Let us use this crew. Of course, of course. I'm so invested. I'm just gonna stay here until you guys This is crew? Man, yo I cannot wait. Go in Knock on Shannon doorstep and when Shannon opens that door, I promise you Nicko's gonna know that you made us the mind If Nicko somehow musters up the strength to stand his ground to Shannon. Hey fair play. He passed But if he runs away screams cowards It's automatic for him. He's obviously gonna cower Maybe scream a little bit So yeah, this is a pretty good one so one week when just don't act tough Acting tough in this situation to be a device I now it's time to meet up with Nicko and a very humble shop to go over the plan that he thinks he's gonna Be doing which is some basic door-dash prank and I don't think he was too fond of the idea nothing crazy No, I think of all of them this one. I should be fine. You think this one's the easiest. It has to be the easiest has to be This is gonna be the reaction. Hopefully not a big black guy like him. Yeah, hopefully not. All right Well, you've got to get back to your shift. You got to get to work. Peace out, brother Let's go Door-dash come wait Nicko was none the wiser the real plan was now in action getting a chance to answer the door and get his revenge So the next morning we want to pick him up. Is anybody gonna explain like what happened to Nicko's neck? When I saw Nicko's smug face I already knew my plan was working cuz he thinks it's gonna be easy. He really thought it was gonna be a walk in the Park No, I remember my first thought was she'd really flew me all the way to LA Just to make me eat food and knock on strangers doors I'm just glad he's taken this series to different levels All right, let's do this afternoon. Here you go this Wow, she's fine. This is great. This is great. She's freaking out. It didn't look very nice So I drunk it for you and it just turned out it was really like it was actually really nice. I Left some for you I Need a picture Is that okay? Just delivered an amazing five-star meal. How happy are you of the service? Happy? Thank you Could you just say Nicko is the best driver? I'm the best driver. Thank you so much. I actually have another drink for you in the car because this is just It's a prank. Thank you. Thank you so much. All right. Enjoy enjoy. Yeah, my mom. Can you say you just got pranked? Oh, I know you my boyfriend watch you. Oh, bro. He watches Marcus Brownlee She watches you my cast so you know between orders I had to mess with a little bit You know just foreshadow what his future had in store for me So if you like get into a confrontation with someone like are you the type of person right away or you just Stay in your ground depends on what type of confrontation Like what if you ran to like one of the people you pranked in the racist town?  I need you guys to do me a Huge favorites Subscribe to his channel and like this video this is so important if you guys do this one small Okay, sorry to interrupt the video. Let's get back into the banger Probably Why oh, I've got your food here. I got your food here. I literally have your food right there It's in my mouth, but there's still some left Carla. Oh my god. Oh, are you not Jasmine so confused is this for you?  Can you give me a five star right now? We're playing with sorry color. We are sorry No problem, you can find the video I think was So that she looked like bang was I'm familiar How's all the door-dash orders when he has one more order to complete before it shift is over Shannon Briggs a two-time World Heavyweight Champion a Man of which we have never seen before is about to get his sweet revenge on Nicko If Shannon decided to he could literally rip Nicko to shreds and there's nothing that any of us could do I know I was ready and I know for a thousand percent back that Shannon was all that left is for Shannon to open the door This is the one Nicko I just asked politely. Can I get a bite?  Nice to see you should I say I see my food and you think it's funny I'm just where are you from? I know you from From where from boxing how you back? Yeah? Yeah, I'm a good fighter We're good friends from school You look like a dude That's not me man. You wish you it was you Apologize of course, I apologize right now. Say sorry chair. Listen. Say sorry chair. I am so sorry He's still at it I People said it was funny. Say sorry champ.  Say sorry Say sorry. Yeah, I've already apologize. No, they say right now champ. I apologize. I've already apologized Oh Genuinely couldn't guarantee his safety anymore, so I had to intervene. I'm gonna say the girls and I feel bad It's getting kind of hectic right now. I'm champ got deep voice deeper. I can't even get the word on. I'm scared for I have been trying to apologize to Shannon Briggs for years, but he's had me blocked so to have him there and be Cracking bants with him. I was a truly magical feeling Let's go champ I got them back It's crazy how in a multi-verse this man is constantly putting me to sleep He is now putting me under his arms in friendship. We feel like so uncomfortable This high man fear is a crazy thing. I pass behind us. We've moved forward You know what didn't help is the fact that I had chips in my mouth. So I was trying to swallow I was trying to swallow the chips the whole time. I'm sorry champ Let's go champ. Let's go champs. I just turn lifelong enemies into lifelong friends That's why they call me the professional beef squash, right? But soon I was gonna be calling me the biggest man Well, that was a nice happy ending But it won't be a happy ending next time I promise you that maybe Gideon can get the GDs and the BDs in Chicago Link up and be cool too And you guys will see but first you must subscribe to Gideon's channel See y'all don't leave a like comment subscribe turn on your post notification bells. I'm down


The greatest drawback of moving forward on deploying electric buses, I don't think there are any drawbacks. I can't think of any drawbacks. I met one of DC's electric bus charging stations and when I first came to DC, I didn't even know that there were electric buses or that they could be entirely battery powered but now here we are, we're seeing it in real life. I talked to some experts working with electric vehicles, let's see what they say. We cannot achieve our climate goals without addressing transportation. I didn't realize the percentage was so high but transportation accounts for 28% of all US greenhouse gas emissions. The prospect of cutting that number down through electric vehicles has a lot of people excited. The performance of these vehicles is very, very good. You have very low maintenance. The battery performance has been getting better and better, the cost has been dropping a lot. Many parts of the country are starting to realize the benefits of electric vehicles. Washington DC was one of the first in the country to adopt electric buses into their transportation fleets. Eric Belmont, who is a program analyst for the district department of transportation, gave me the inside scoop for how DC's electric bus program is going so far. We just got 14 electric buses and we put them in service so we just want to see how they work. We paid probably a little over a million dollars for electric buses. Our diesel buses were comparison about 690,000. Studies show that the overall cost may balance that out over time. DC projects that they'll save $6 million over the 12-year lifespan of this fleet of electric buses. Electric buses don't have to deal with as many parts, they don't have as many liquids, diesel engine. It's massive, with dozens and dozens of parts. With an electric bus, all you have is the motor. The fact that electric buses have no tailpipe emissions sounds great, but the electricity generation for powering the buses still can give off greenhouse gas emissions depending on the source. Overall, these emissions are still way lower than the diesel alternatives. In term, we'll be looking at making sure that we get our power from a sustainable source. Not only are we having zero emissions on the tailpipe, but we're getting zero emissions from the source of electricity.  A big cause of lung-related health issues from diesel particulate matter, we need to be doing as much as we can the mayor made a priority because it's good for our customers, it's good for our residents. But not every city has the same political support as D.C. Rick Nuno studies the policy issues surrounding electric buses. Well they need a infusion of cash to pay for the initial investment. The FTA has been withholding money that was appropriated by Congress, both in 2017 and 2018, just because they don't like public transit. Despite inconsistent government support, the electric vehicle market is expected to boom worldwide in the next few decades. Projections are even higher for electric buses. To make these numbers a reality, we just need our politicians to be as excited as people like Carol are. I think that all of us who care about climate, about air pollution, about public health want to see this all accelerated. In practice, cities are less concerned with crossing the finish line first and more focused on successful rollouts of their programs. We're taking the approach of testing the technology, being thoughtful about it and determining what our approach is going to be. Thus far, we're very pleased with the performance. I think another thing that we're very pleased about is when people don't know when they can say, this is normal. Riding electric buses just like riding any other bus. The most exciting part of the program for me is that it's been going on for five months and I just found out about it. If we can make such a large part of our transportation system more sustainable without disrupting people's lives, what else can we be doing better?


So this is about homological whole algebras and motivic invariance of crevice and so we have to first want to somehow explain the aim and scope of this series of lectures and we have to answer the questions What why and how and where So this is a school on enumerative geometry and we want to enumerate Things which don't seem too geometric namely quiver representations. Yeah, so we want to for how Upmost aim is to want to count quiver representations So why why do we want to count quiver representations? So we'll first see that quiver representations form a category which is similar to categories of Coherent sheaths on curves namely, it's a category. It's a nice abelian category of global dimension one So one point is that category of representations of Quiver Q is in some respect similar to coherent sheaths on a smooth projective curve Of course, there are essential differences in general, but there are some all similar for example because both are categories of global dimension equal to one Yeah, and so this is kind of a Non-commutative counterpart to curves or coherent sheaths on curves So we are doing Non-commutative geometry of curves and we want to enumerate something Was that me? Okay, I'll be careful Okay, so that's the first reason why we want to do this second reason is that quivers are something of like a toy model for more interesting things maybe for you more interesting things like Quivers with potential so three Calabi yaw situation so for two or three Calabi yaw situations like quivers with potentials But most of the time I will only treat the quiver case and really view it as a toy model and Understanding all the phenomena in the quiver case. You are then prepared for studying the real stuff Like cruise with potential Okay another reason for studying curve is is that If you are really interested in some category of sheaths, but you are interested in some local phenomena Phenomena like only involving sheaths which are filtered by a finite number of basic objects Then if you are lucky you can model everything by a quiver situation many other situations in categories of coherent sheaths or in enumerative geometry Can be modeled by quivers and I don't want to be too precise here at the moment We will see some instances of this principle later. Yeah, so that's why we look at at this quiver situation Although it seems quite far from the usual setup of enumerating things coming from algebraic geometry Okay, so that's the why and Now to the what and where Where do we count? Well, and you have certainly seen at the school already that Doing enumerative geometry counting things can be much much more sophisticated than just taking the cardinality of a finite set You can have counts which are negative which are even only rational or whatever. Yeah, so finding the right the right domain where to count things is highly non-trivial and This is also what happens here in this theory So well if you have an honest finite number of quiver representations We can just count the cardinality of this finite set, but that's not what usually happens You can have parametric families of quiver representations. So for example, you could have a p1 family so what is the count for a p1 family and so we need the right domain where to count and this will be the written decree of varieties and this I would introduce in a minute So all our counts will be in certain variants of Grotten-Deek rings of varieties So these are Very simple-minded motives and that's where this motivic invariant comes from yeah So motivic invariants are some invariants associated to quiver representations, which are counts But counts in the Grotten-Deek ring of varieties so that's the the where and Another question is What are quiver representations and this is also something I should tell you today? So today I will first explain the Grotten-Deek ring of varieties because that's where we will count things and Then I will give you some basic terminology On quiver representations in case you don't know it and then finally we will consider the Motivic generating function, which is something like a partition function So then finally we will see as the three third part today Aq a certain motivic generating function and this will be an element of a so-called motivic quantum torus Which we will introduce Okay, so that's the plan for today and let me just give you an outlook of how we continue. So today will be just mostly definitions and concepts yeah, so where do we count what do we count and it's just about writing down this so-called motivic partition function and exploring it in a few very very simple examples and then tomorrow we will continue and So tomorrow we will take this motivic generating function aq and factor it and trying to factor it will lead us to all sorts of Modulized spaces of quiver representations and their motivic invariance their motives. So factoring this leads to Modulized spaces and in a special case Hopefully I can do this tomorrow This will lead us to certain gamma-vitin invariance and the connection is why are the so-called tropical vertex and So maybe we will see this already tomorrow and then talk three and four Will be about taking all these concepts one first two talks which are really just Enumerating things lots of explicit identities and Categorifying them Categorify all the identities which will produce in an algebraic object called the cohomological Hall algebra of the quiver Yeah, but before we categorify we have to see the numerical stuff. So what is this counting really about? so That's my current idea of the outline of the four talks and let's see how this develops and I'm really happy to skip Most of this if you're interested in different things So please just tell me. All right so let's start with the first part of today's talk introducing this curtain degree of varieties and Okay, so Let's work over the base field of complex numbers That's enough For today so let's introduce the good degree of varieties over C and So what notion of variety do we do we take? Actually, that's not so important for defining this good degree of varieties this good degree of varieties is not too sensitive on the fine difference of reduced and non-reduced structures and One question is always do you view as a variety as something irreducible or not? Let's just say a quasi-projective not necessarily irreducible variety So really in the naive sense take complex projective space of some dimension and take some polynomial Equalities and inequalities so something locally closed in a complex projective space That's our notion of variety No Okay, then we introduce K zero of RC we first take something really really large namely we take the free abelian group in all Isomorphism classes of such varieties free abelian group in isoclasses of complex varieties and I hope we don't have any set theoretic issues here how to define such a variety where you first have to fix the number for the dimension of the projective space then you take finitely many polynomials and Defining the polynomial equations and inequalities and that's it. So that's maybe something we can do inside sets Okay, so it's mostly harmless to just take this free abelian group in the set of isomorphism classes And then we mod out a relation just one relation namely the cut-and-paste relation modulo the cut-and-paste relation, which is x equals a Plus you if A in x is a closed sub variety With open complement you That's the cut-and-paste relation. Yeah, so whenever you have a closed sub variety So whenever you have a decomposition of variety into a closed sub variety and it's open complement then you require additivity and This is a relation we force on on this free abelian group That's it. All right, so We will do a few computations in there But let's first continue to define a ring structure on it because at the moment it's just a group and the ring structure It's just given by multiplication multiplication. It's just given by the Cartesian product of varieties perfect What else do we need We need the so-called left sheds motive L like both style L which is defined as the motive of the Affine line. All right That's almost it for the moment We need some well two more definitions, but let's start with Okay, so please leave some space here at the end of the definition Exactly x of variety complex variety then the class of x called the motive of x so motives in a very naive sense just the classes in this in this group and well, okay, so there's there's a lot to say about this this ring and I will not give you all the things which are known about this ring For example how it relates to Biorationality of varieties. That's another very interesting story, but we don't need this and actually Let's just do some example calculations Yeah, so I will continue the definition a little bit, but let's first start with Examples What is the class of Affine space Affine n space Well affine n space you can Realize as the n-fold Cartesian product of the affine line Yeah, so Cartesian product is the product in this ring and the class of the affine line has a special name the left shits motive So this is just the nth power of the left shits motive wonderful Okay, that was our first computation in this ring another computation is projective space well projective space realized as well you have homogeneous coordinates from zero to n and You have a very nice Stratification of projective space by deciding whether the zeroth homogeneous coordinate is zero or non-zero if the zeroth Coordinate is non-zero you can normalize it to one and you get an affine space principal affine open and The complement of this is when the first when the zeroth homogeneous Coordinate is zero and this leaves projective space of one smaller dimension Yeah, okay, so this is just the set where the zero coordinate is non-zero And this is defined by zero coordinate being zero All right That's an open that's a closed complement so we see that the class of P n is the class of a n Plus class of P n minus one where we now have used the cut-and-paste relation for the first time and This is of course the basis for an induction because you can continue with P n minus one and Decompose it into a n minus one and P n minus two and so on so doing this inductively you arrive at a n plus a n minus one plus Plus a one plus A zero which is just the class of a point Okay, so since a n can be realized as powers of the of the left sheds motive We can realize this as a truncated geometric series So in other words the motive of projective space is one minus l to the n plus one divided by one minus l the truncated geometric series Aha, and you already see that Well, this is of course Completely formal expression at the moment, but it might be useful to allow denominators like one minus l No, and this we will continue with the next example. What's the class of the? The motive of the grass manian grass manian of k-dimensional subspace is of n-dimensional space Well, if k equals one, this is just the case of projective space because projective space just is the grass manian of lines Okay, P n is gr1 n plus one grass manian projective space just the grass manian of one-dimensional subspaces of n plus one dimensional space and This decomposition into the of the projective space generalizes using the the Schubert's decompositions yeah, so using the Schubert's cells Schubert varieties you can prove that this is the so-called Quantum binomial or Gaussian binomial coefficient evaluated at l the left its motive And if you haven't seen this in quantum group theory or wherever let me introduce it for you So let me define n the quantum number and q as 1 minus q to the n by 1 minus q let's then define the quantum factorial as product of quantum numbers and then we define the Quantum binomial as fraction of quantum factorials Okay, that's the the standard way for introducing these Gaussian Binomial coefficients. Yeah, so you define the binomial coefficient as n factorial by k factorial n minus k factorial You quantize this Factorials are just products of numbers So, okay, so you just have to quantize numbers and the quantization of the number n is 1 minus q to the n by 1 minus q and of course This reminds us of the truncated geometric series. We have encountered in the motive of projective space so exercise compute the motive of GLN We will do this later anyway when we introduce this motivic generating function of a quiver So hint is that well think about this is an invertible matrix. What are the possibilities for the first column? When the first column of an invertible matrix you can have any vector except zero Then fixing this in the second color column You can have any vector except anything in the line generated by the first vector and so on Yeah, and if you write this down carefully in terms of certain vibrations, then you can compute the motive of General linear group All right, okay, so this ends the examples for now we need some Some two ingredients For this golden ring of varieties which I cannot motivate easily at the moment and So I'm afraid at the moment you just have to believe that this will be relevant so first of all we will make this This thing here formal that sometimes we want to have denominators and in fact we want to have even more Potential denominators and then we need the notion of the virtual motive, which is a little twist But which will be very important for the motivic Donaldson Thomas theory. I can't explain this at the moment It's all about virtual fundamental classes of modular spaces and So at the moment this the next definition will be somewhat unmotivated and I just can say believe me it will be important later okay, we will work in the localization and now let me just call this the the motivic ring our mod For short so we take this groten-deck ring and we allow ourselves to first of all To invert the left sheds motive so we want to be able to invert the affine line And if you already know something about this groten-deck ring Then you will think that when you know that this is a terrible idea a priori and really have to see if anything survives I will tell you in a few minutes so we will invert the left sheds motive and Also for reasons of so-called virtual motifs and virtual fundamental classes. We need a square root of it so we will even Need a square root of the left sheds motive and I want to invert All these one minus L to the end where we have seen the very beginning here and calculating the motive of projective space Lumpter, there's no lambda. Sorry. Oh, sorry Yes One minus L to the end so It looks a bit arbitrary at the moment, but for example localizing at all these Brings us to the well. This is nothing I would really I will really use but it's the fact that this is then the groten-deck ring of Certain classes of stacks namely quotient stacks by all groups GL Yeah, if you form you want to define a groten-deck group of stacks where stacks are everything can form out of quotient stacks by GLN Then you get this localization. So it also appears in nature if you view stacks as nature And this is as I already said for these virtual motifs and This is now the final part of the definition the virtual motive is Defined as a little twist to the motive of X Namely we twist it to minus L one-half to minus the dimension of X for X irreducible and So just as a as a very simple example Let's just look at the virtual motive of Of P1 because the essential feature of these virtual motifs. I can already illustrate this example So we take the usual motive of P1 and we twist it by Minus square root of the left shits motive to minus dimension of the project of line Which is minus one so minus L one-half to the minus one times P1 and this is L one-half plus L to the Minus one-half yeah, because the motive of P1 was one plus L okay This fine, or did I make a sign mistake? I Certainly made a sign mistake here minus sorry so and just note that this is stable and under Switching L and L inverse and that's the important feature of this. I mean, okay, this is just by a pronger a duality In this example, and this is somehow the the main feature of these virtual motive that it makes things more symmetric Everything else will follow okay so Now we have to be very careful It might be that we are that in working in with this ring. We are just talking about the zero ring So is this ring non-trivial at all we could also ask this Before doing all these localizations I mean even if we just take all isomorphism classes of varieties and mod out by the cut and paste relation What's the wise what properties of varieties survive under this operation and Well, in fact something survives. This is actually non-trivial Because there is a non-trivial map to to another ring Yeah, and this is the virtual hodge polynomial so Okay, let me try to to motivate this a little bit with the notion of Motivic invariant Motivic invariant of varieties is some invariant of varieties which fulfills the cut and paste relation. Yeah, for example one Motivic invariant of varieties is its Euler characteristic The Euler characteristic satisfies the cut and paste relation Euler characteristic of x is additive on taking an open and the closed complement Or for example, if you have if you work over finite fields then counting point over finite fields is obviously a Motivic invariant because it satisfies cut and paste. Yeah, so these are so-called motific invariance and The classes in the Goten-Dekringer varieties these motives. These are some of the universal Motivic invariance. Yeah, that's universal domain where you have this cutting-paste relation. So improving that this Motivic generating series the this motivic ring is non-trivial We just have to exhibit an interesting enough Motivic invariant. So Euler characteristic doesn't do the trick Because well 1 minus L to the n well the Euler characteristic of the affine line of any affine space is 1 And so the Euler characteristic Evaluates this to 0 and we cannot invert it now So Euler characteristic is not a good example, but we need the virtual Hodge polynomial virtual Hodge polynomial gives actually a ring homomorphism from Goten-Dekringer varieties to Sorry So what target do we take? Let's just say Loro polynomials in two variables x and y namely you map x to Some of all P and q sum over all k Signed twist by minus 1 to the k and then it's HPq H k C X C I will explain So yes, so so so this is compactly supported homology homology with compact support, so that's the case Compactly supported homology and HPq. That's the Hodge delinear numbers of this Yeah, so it comes from the mixed Hodge structure on on this homology so These are the Hodge delinear numbers. Oh The dimension of course I take sorry, sorry the dimension No I'm fine. No, it's just really the Hodge delinear numbers in kth homology Hodge delinear numbers So these are already dimensions signed by k and Then I record P and q Okay, and so By deline's theory this invariant is Motivic it fulfills the cut-and-paste relation and it's compatible with the product Yeah, take the Cartesian product of two varieties then this behaves multiplicatively as Laurent polynomials and We can compute it for the affine line left sheds motive is sent to x y Yeah, and so it's sent to x y so And something survives after localization. Yeah, so localizing at L plus minus one-half just means introducing a Square width of x y in its inverse and these localizations just mean we need denominators one minus x y to the end Yeah, something survived So this this ring homomorphism is non-trivial. This is good news Finally it might seem like like this ring is That might seem like everything's fine with this ring this armot but it is not because Now the surprising thing is what is already known since 20 years ago that this got in the ring of varieties has zero devices and The situation is even worse. This is only known since a few years The left sheds motive the class of the affine line is a zero divisor Yeah, and in constructing this ring. We are localizing at a zero divisor Which is fine, but we are of course losing many many things and Let me just very briefly discuss this so This localized ring of motives is non-trivial because we have an interesting invariant, but L Is a zero divisor in case you? Of complex varieties There exists varieties x Non-isomorphic varieties x and y in fact there actually three Calabria varieties such that The difference of their motives Times six power of the left sheds motive is zero Which in particular means? Well Alice zero divisor, so if we localize at the zero divisor then we are automatically identifying x and y which are Different varieties. Yeah, so in localizing this we are making many many identifications but we are But we know that something survives because for example we can still detect the virtual hodge polynomial Me personally nothing. No, I don't know what is not about this I mean what what is known? This is this this birationality story if you if you take the Rootnik ring of varieties and just mod out the left sheds motive then what you get is the The monoid ring or up of varieties up to stable birationality For example, but about the kernel of this map I don't know luckily for us in the quiver situation all the calculations will happen in In the sub ring generated by the left sheds motive. Yeah We will only work But this is nothing we know a priori we only know it a posteriori we will only work in the subring generated by by L so everything will be just a Irrational expression in L everything we produce But we only know a posteriori Yeah, so we will make some computations in this ring and then at the end it will turn out that Actually everything is like a polynomial or is this like a rational function in the left sheds motive, but this we don't know from the beginning Okay, so this ends part one of the talk Yes, please Construction of the X and Y They mentioned How do you know they're not the same class given that if you take like Richard Hodge polynomial, they match the same thing Well, I looked this up yesterday evening just to make sure I I don't remember the details, but I mean so I can look up the reference for you and it's a quite a short paper and Not so terry difficult to read apparently And these varieties X and Y are really explicit, but I don't remember No, no so so just if you just take say the the Poincare polynomial, that's not a motivic invariant That's maybe another good example of what is not a motivic invariant. Yes, that's maybe good Poincare polynomial, it's not motivic namely look at a one single point and the complement a one without the point and that just over the complex numbers and let's just look at at comology yeah, and Then for the point Comology with compact support Single acromology with compact support then for the point we have Comological degree and then we have a one-dimensional zero of comology and that's it a one has second compactly supported comology But a one minus a point if you just pinch the then you can retract everything to an s1 and then you have Comology in degree zero and one and you see this doesn't add up Yeah What instead of the Poincare polynomial you can do and this is a specialization of the virtual hodge polynomial It's the virtual Poincare polynomial Which it's not the The Poincare polynomial for compactly supported comology But you take the Lin's weight filtration and the associated graded and that again does the trick Yeah, but that's the reason why why this doesn't work. I mean for for smooth projective varieties You can just take the usual Poincare polynomial usual hodge polynomial. Yeah But for arbitrary singular Non-projective varieties you have to take these virtual guys All right crevasse So now we have this good degree of varieties, which is not only useful for for this enumerative Geometry of crevasse, which we will do here But this is also very useful for the whole topic of for example, what if it integrations Motivic zeta functions of varieties Namely the motivic one possible motivic zeta function of variety was it a function usually is Something involving the arithmetic of variety Where you count point over finite fields But how do you do this with a with a complex variety? Well, the idea in motivic integration for motivic zeta functions is to take a complex variety and take its Its jet spaces the nth jet space So kx mod x to the n valued points take the motors of all of them and put them together into Generating series zeta function. Yeah, and this is also a whole area, which opens up when you know this Courtney bring of varieties crevasse So this is usually a Topic where you can spend lots of time because it involves lots of notation. So I Will just start somewhere and if I don't give enough notation cover notation then please tell me so in particular If I've never seen these and their representations this will be Quite difficult and I have to spend more time on that. So please just tell me if you want more details Okay, so quiver is a finite quiver q is a finite Directed graph with a set of vertices Which we call q zero and with arrows Which I will just write as as maps alpha from i to j is an arrow between Vertices i and j so that's a quiver and Examples that's a great quiver. That's the quiver. We have to study first just a single vertex Okay, a single vertex and a loop Also makes a very interesting quiver Two vertices and a single arrow something we'll study to arrow two vertices and two parallel arrows two vertices and two arrows in both directions Vertex with two loops. Well, and of course lots of complicated things Well, whatever. Yeah, so Loops at vertices multiple edges everything is allowed But we will actually be happy with studying these these very small quivers so that's a quiver and What else do we need Okay, we need representations of a quiver So I promised at the very beginning of the talk This will be a class of categories, which is quite similar to coherent sheets on on smooth projective curves So let me introduce this category of representations category of representations of such a quiver q Over a field, which is just for us just the complex numbers. So what are the objects? What are the representations the objects are? tuples Vi sorry vi index by i and F alpha Index by alpha and let me explain So the objects in this category are tuples where this is a complex finite dimensional complex vector space So you put a finite dimensional complex vector space at each vertex of your graph Okay, so if you put a vector space at each vertex then at each arrow you can put a linear map See linear map and that's it. That's a quiver representation. Yeah So a quiver representation is a configuration of vector spaces and linear maps along a certain graph So for example a representation of this quiver means you choose two vector spaces a map from the left to the right And from the right to the left linear maps and that's it Okay, that's the that's an ob that's the object and what are the morphisms? so morphism Phi from V to W where V is A collection of vector spaces and linear maps and W is also a collection of vector spaces and linear maps a morphism fry from V to W is a collection of linear maps Between the vector spaces which are involved Such that So the easiest way to remember this definition is such that all diagrams commute and then trying to figure out what these diagrams are You already see the definition Let's do this Such that all diagrams commute. What diagrams do we get from all this data? Okay, so here we have a quiver representation V and here we have a quiver representation W and now we have one arrow alpha from i to j in our graph Associated to this arrow. We have a linear map f alpha from the vector space vi to vj That's this data. We have something similar for the second representation Wi wj and a map say g alpha okay, so Now a morphism from V to W consists of morphism linear maps between the vector spaces So we have a linear map here phi i and the linear map here phi j That's the square diagram and you can ask it to commute and This should hold for all arrows alpha from i to j That's it. Okay That's the objects and now we need that's morphisms and we need a composition of morphisms Well, that's easy because we can compose such linear maps Component wise composition is component wise That's it so that's a category you you can define out of a graph and Now the question is why do you want to do this and? Let me tell you Well, first of all you might Define this category because you're interested in solving linear algebra problems. That's a quite natural problem You have a configuration of vector spaces and linear maps and you want to classify it up to base change And this is precisely what this definition of morphism does So just look at this diagram for a second and assume that these maps here are isomorphisms then this means that The second representation you get from the first one by a base change First you take a base change here in the origin then you take this map and then you perform base change in the target so note that isomorphism classes in This category rap cq, which I just defined Classify certain linear algebra classifier configurations classifier configurations of vector spaces and Linear maps namely configurations along a graph Along q up to base change So this is a category Where the isomorphism problem solves a linear algebra problem of classifying configurations of vector spaces and linear maps Just quite good. Okay, maybe not what we are interested in you are interested in or originally so fact is That this category Has all the nice properties you expect from categories of modules or sheeps namely it is equivalent to the category of modules Over an algebra non-commutative algebra called the path algebra of q so called path algebra of q So representations of a quiver form a category of modules in particular It is an abelian category It is a category of finite dimensional modules. So all objects have finite length Filtrations you have the Jordan-Hurther theorem. You have the Krull-Schmidt theorem You can do homological algebra because this category has enough projectives and injectives and so on very nice very nice abelian categories and And one important thing is that a Global dimension of this category of modules or of this algebra is just one Yeah, so and this is the similarity to coherent sheeps on smooth projective curves We're talking about hereditary categories. We only have to take care of x zero and one and All higher x vanish anyway, which is great news in particular for defining modular spaces Yeah, if you have ever worked with modular spaces of vector bundles on smooth projective curves You really appreciate vanishing of higher x Because for example, it makes the modular spaces smooth and so on okay that's this category and What else do we need before I can define All right, we need the so-called homological Euler form so Let me define the so-called dimension vector Dimension vector of a representation V. Well, what could be the the dimension of a representation V Well, the representation V in particular involves vector spaces namely one vector space for each vertex So let's just take the tuple of all the dimension of the vector spaces VI and this defines An element in n q zero. So that's the dimension vector of the representation and then I Will define the so-called Euler form And this is then the final ingredient for definitions. I think more or less the Euler form Acute brackets is defined. These are two vectors Defined as sum over all I di e I minus sum over all arrows Di e j So this is the Euler form of of the quiver q at the moment that that's just a combinatorially defined thing because it just involves the graph structure Yeah, it involves the structure of vertices and arrows of our graph But now we will see that this Euler form as you can already guess from the name is the homological Euler form of this category of representations so So this this formula Okay, write it down And then discuss it We take the space of homomorphisms from V to W namely homomorphisms of quiver representations Yeah, and the notion of morphisms of quiver representations as we defined it above Do we have this notion now? I Do hope so. Ah, here we go. These are morphisms They actually form a vector space This is a K linear category and so you can take the dimension of the space of homomorphisms We have enough projective and injective so we can define x1 So the next term in the homological Euler form would be x2, but this vanishes identically So that's the homological Euler form That's just the difference of x0 and x1 and this is given by evaluating this special form at the dimension vectors of V and W so This Euler form is really just given in terms of this of the graph structure because it just involves the structure of Vertices and arrows so this is something you can directly calculate and this is the homological Euler form So this is of the same Importance as Riemann-Roch is for the theory of of of sheaves on curves Yeah, all right That's why this form is so important. Okay, and now I should really come to the final definition Okay so the fancy way of Continuing is to say there is something like the called the modulized stack of Isomorphism classes of quiver representations and we just take the generating functions of the classes of all these stacks But this is not really fair because I haven't defined what the class the motive of a stack is So let me do this in a more elementary way so let me define something like the modulized stack of Representations But I don't really want to use stacks so I try to avoid it and do it in a more elementary way namely We write down a universal parameter space for quiver representations of a fixed dimension vector and Then we mod out by the equivalence relation of taking isomorphism classes And we'll see that this is a quotient stack by a product of groups GL And I think I can use these five five minutes five minutes definitely enough. Okay Okay So fix a Dimension vector D Then I define Rd of Q as the direct sum along all the arrows of The space of linear maps from a di dimensional to a dj dimensional vector space a Point in here is a quiver representation on the vector spaces C to the di point or C valued point a point in this space is a Quiver representation on the vector spaces C to the di and Since the vector spaces are fixed anyway up to isomorphism once we have fixed that I mentioned this is no restriction at all Yeah So instead of taking quiver representations on arbitrary vector spaces vi We can always assume that we have quiver representations on spaces C to the di so a point in this here is a quiver representation So when our two quiver representations isomorphic I already explained this the important keyword is base change and So I will define a group action on this By the group Gd and the group Gd is nothing else than a product over general linear groups and this acts on this variety by base change and The formula will actually resemble the actual action for a group just conjugation action Let me write down the formula for this action Because we should have it here on the blackboard Here's the formula for the action.  Sorry This is a base change action. You're doing the inverse in the origin then going f alpha then Phi j in the target Phi i inverse f alpha phi j Okay, so you have a group action on a variety and the observation is So and this is a total logical observation the Gd orbits in Rd of q are the isomorphism classes of representations of q of dimension vector d And we should have a 30 second meditation on this on this observation and really see that it is total logical So a point in this affine space here This is just affine space just a direct sum of spaces of linear maps Just an affine space a point in this affine space is Equivalent representations on these vector spaces and we can always assume without loss of generalities that the rect vector space is involved of the c to the di to such points Define isomorphic river representations By this definition of morphisms even only if they are related by this formula So even only they are conjugate under this group action So if and only if they are in the same orbit for the group action Yeah, so just from the very definition the Gd orbits are The isomorphism classes of representations Okay, and this brings us to the final definition for today and to the end of the talk because now we can Say what this modular stack should really be and what the counting of quiver representations should be This brings us back to the logic from the very beginning So this modular stack should be nothing else than the corrosion stack of The space by the group so these brackets now mean the corrosion stack But I don't want to use stacks anyway But just as a side remark the modular stack by definition is the corrosion stack of this space by this group Okay, so now we can say what is the count of quiver representations? So what's counting quiver representations? Now means the following Well, first of all we can count in any dimension in any dimension vector D in any fixed dimension vector D We should take the count of points of this quotient stack So we can define this namely we take the corresponding classes in the goten die group of varieties we take the motive of the space and divide by the motive of this group and If you solve this little exercise Computing the motive of GL of GL n then you will see that everything appearing here The denominator is something we localized at anyway Well for good reasons, which I can't explain explain at the moment. We will take the virtual motives and Then at the end we should form a huge partition function. So we should Sum up overall Dimension vectors keeping track of the dimensions because that's a numerical invariant and this is a function This is a motivic generating function aq Great sound showing the importance of this of this definition. So this is the the central definition So, okay, I haven't told you yet where this lives So what are these extra former variables t to the d this I will explain tomorrow and then we will try to Factor this. Well, this is something like a partition function or zeta function or whatever And of course the impulse is then to factor it into a product of something Yeah, like you do with any zeta function or partition function and this will do here and in trying to factor this All sorts of modular space is associated to quiver representations will pop up almost automatically and that's the the miracle Okay, that's enough for today. Thank you very much Thank you are there any question How do you okay like you do in commutative algebra Like you just do the formal localization in any ring Yes, exactly Exactly, yeah, so the the localization which which I which I considered is really in the sense of So it's really like you have an arbitrary commutative ring RS you really Join a form of variable t and then mod out by s times t equals 1 to to make t invertible and Yes, of course if this is zero divisor, then you make certain things zero, so in I wrote down this relation in the gotenick ring of varieties where you have two kalabi house Which after multiplying by the six power of the left sheds motive becomes zero so in particular in our Localized ring of motives this thing is zero. So these classes are the same So that just means this localized gotenick ring cannot distinguish many many varieties, which are definitely non isomorphic but Well, we know that at least something survives and that's enough for us at the moment Yeah There is one question in the room Is it possible to analytically continue the construction with respect to the dimension vector? analytically continue Sometimes Well, okay, so unfortunately, I didn't have time for for the first example so what we will do tomorrow as a start is taking this this series and Writing down a factorization in in these two rings. Let me let me just show you this this Yeah, let me give it as an exercise So If Q is the trivial quiver Well, that's the same as an algebraic geometry if you have a new concept Then you should first explore what does it mean for the variety a single point and there you should understand it Yeah before starting to do it for whatever variety And so if you have a concept for quiver representation, just take the quiver Which is just a single vertex the category of representations. It's just the category of vector spaces That's the category you really understand so we should understand this motivic generating series And even then this motivic generating series is nothing Completely trivial it admits a factorization and this we will see tomorrow As an infinite product over one Minus l to the i plus one-half times formal variable t so and that's kind of a typical phenomenon and Well, okay, then you can start exploring the analytic continuation properties of such infinite products Yes, how much of a Q can we recover from a Q? Ha ha So formally Well, okay Not that much not as much as you would expect because I was cheating a little bit It's not only about the series But it's also the ring the so-called motivic quantum torus in which we consider it and This ring in which we consider this aq and in which we'll factor it will contain more Information than aq itself. So for example, this aq is the same At the moment whether you consider this quiver or this quiver, but these quivers are drastically different in their representation theoretic behavior and It will depend on on on the motivic quantum torus in which we will consider and factor this thing And this is something we will only see tomorrow The aq is is not dependent on this but but the ring in which we'll view it because I the ring in which so we will view this in some In some form of power series ring which will depend on on Q really on the orientation Yeah, so there is some extra bit which I couldn't define yet There is one more question. Yes How the formula of the other form of dimension vectors which was stated is proved How it is proved with a with a standard resolution. Yeah, you write down a standard projective resolution This is quite classical and Wow, okay, so I can't do it now because I had to introduce Bit of notation yes, I can sketch it. Okay Maybe not in all details, but let me just give you the flair of how you write down this the standard resolution and Okay, either with a standard resolution or with the following exact sequence. Yes, okay, let me do it like this I'm almost done and then I can Explain so in the these two middle terms here are just spaces of linear maps yeah, and an element in here looks like a couple of these files and A couple of to this such tuple of the files I associate precisely the thing which I asked to commute namely this F alpha phi j minus phi i G alpha indexed by alpha from i to j Okay, so this is the thing which commutes in this diagram defining morphisms So in particular this means if phi i is mapped to zero under this map Then phi i defines a homomorphism of quiver representations Okay, on the other hand if you realize the x1 and In the naive sense namely as equivalent equivalence classes of exact sequences Then writing this down in all details you will see that x1 is actually elements in here Modulo the image of this map or you can see it by some standard Projective resolution of representations and this gives you such a four-term exact sequence now. Just compare compare dimensions Dimensions of this minus dimension of this is the homological Euler form It's the same as dimension of this space minus dimension of this space and this difference is precisely given by the Euler form, so Fancy would be to really work with standard resolutions, but it's just a linear algebra thing actually there was one more question in the audience so if you take a Representation value the difference of alien time within vector spaces. How much can we do the similar thing as in the vector space? Ah, so if you take quiver representations in some other abelian category and Korean sheeps for example, yeah Yes, there are relative versions of many of these constructions. So for example There is an analog of of of this standard resolution and of these homological properties which shows that the Global dimension of the category of Representations in a category a is one more than the global dimension of a yeah, so there exist relative versions of all this No No, this factorization And a very deep point uses the fact that everything is hereditary We are really in global dimension one and You can you can push this from Yeah, I mean all these factorizations really work smoothly only for a hereditary category And you can push it to the two kalabi yaw or three kalabi yaw situation in certain situations But that's it But if you just consider quiver representations in some arbitrary category of coherent sheeps I doubt that you get such nice factorizations. I'm afraid Okay Yes, there is a sergiality which classically is called the australian translation so there exists some australian translation tall Which you can realize which you can write down as you take the X one with With the path algebra itself, which is something like the regular representation in the second component and then dualizing But now I did I wrote down to our inverse That's now, okay, and then you have Formula X one MN is isomorphic to home and tower M Dualized and that's really quite literally sergiality in this one-dimensional setup Yeah, you have this duality from X one to X zero dualized by applying this the serf hunter And you have a question Is your virtual class definition of varying in any sense? I don't know what definition Situation I Don't know All right, no more questions. Let's thank Marcus again. Thank you


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Alright, thanks. I have a, as you can see, a large topic to cover, and I do want to acknowledge the help of the co-chairs for the current CERC work group, Ingrid Holman, also for the Consent and Community Consultation work group in Emerge 1, Ellen Clayton, who were both helpful with this presentation, as well as the work groups themselves. So I want to cover briefly things that we've accomplished in these work groups, because I think that's been a fair number of things. And one certainly that's been mentioned over and over is issues related to biobanking and consent, and a couple of the things that we've done is developed model consent language, which is online with NHGRI. And currently, with the new arrival of our pediatric biobanks, we have continued working on model consent language, but really for pediatric biobanking model. So that's currently in process and making, you know, I think there are a lot of interesting issues that are different, and so it's been good to get that going as well. I think another large area that we've worked in is developing a framework for addressing return of results within the network. And in Emerge 1, we looked at this as an issue that we would be dealing with going forward, and certainly as part of the GWAT studies, there were results that many of the groups debated whether or not they were returnable. And so really the work of the group was to set up a framework that other networks, as well as Emerge, but similar networks could use and adopt for themselves in ways of addressing what was returnable and how to think about actually doing that. And that was actually published paper as well. Other things that we have worked on across the network, both at our individual sites, as well as in group activities, was to engage stakeholders related to a variety of issues, issues that we were dealing with in Emerge 1 and 2 to inform our further discovery and science-related issues. And I think some of those have been biobank governance and consent, which led to a group paper, data sharing and related privacy issues, return of results, the value of genomic research, integrating genomic data into the electronic health record and clinical decision support, which led to recent paper as well. And in all these engagement activities, we have worked with a variety of different stakeholders, which I'll address a little bit later, but from the patient and the public on to clinicians and other types of health plan and administrative stakeholders. So there have been a variety of different people involved. We've also worked on educational methods for patients and physicians about genomic medicine, which is at a critical area for moving genomic medicine into the clinic. Some of the areas we focused on have been working with the clinical decision support, getting education at the point of care to physicians, patient portal, developing materials for those, and sharing those across the network, as well as a patient website. So those have been some of the things that we have developed. We have assessed, and this was particularly in Emerge One, the application of data sharing guidelines within the network. And that's obviously been a critical piece for our work with electronic health records, sharing phenotypes, and other types of data. And we have looked at how our varying institutions have applied oversight to those guidelines and recognize that there has been a gap in knowledge around oversight for data sharing, as well as consenting issues related to data sharing, and how those issues are enforced. And so we have done, looked at that quite a bit, as well as just review across our institutions of consent, particularly for the pharmacogenomics project and how varied that ended up being. And one of the other large things that I'll mention is that we've obtained supplemental funding for a survey that we are conducting across all of our tenemers sites. And that's related to the notice of proposed rule making, and we are focusing particularly on the acceptance of broad consent in bio-banking research, as well as public views on data sharing. And we hope that this project will inform a number of bioethics and policy issues going forward, particularly related to this rule. And I think it's a unique project similar to our PGX project, in that it's similar across all the sites. But I think what's more unique about this project is it's almost exactly the same at every site. And the type of project doing a survey demands that kind of methodology, and so I think we're experiencing what it's like to conduct something that's the very same across all of our institutions. So that's been something that has been a learning experience, as well. But I think we'll contribute to a lot of information going forward. So some of the things that we have learned that I want to mention is the role of LC projects in our merge work. And we've already mentioned it numerous times today in this meeting about engagement, role of consent. And I think that it's clear that in the preclinical discovery phase, going towards implementation, that the LC work is critical to all of those stages. We've also certainly seen that community and stakeholder consultation is essential for this work, particularly as we move towards implementation, that it's impossible to do this without stakeholder engagement. Consent for genomic research is many strategies. Educating stakeholders is a critical aspect, oversight and consenting, and the importance of interacting with other networks and investigators. And finally, what we have to offer in this area. So our future directions, I think in terms of where eMERGE3 can go, we would like to see the integration of bioethics aims into our scientific studies. And I think, as I mentioned, that's become clear how important that is as we talk about implementation. Assessing the impact of genomics medicine, there is a lot of room for looking at healthcare systems, for payers of healthcare services and tests, other stakeholders, administrators, health plan administrators, as well as patients and providers. And again, when we look at the impact on patients and providers, these are the right kinds of outcomes to look at. And I think that's a big question, particularly we've noted in the PGX project. Continuing to engage stakeholders, evaluating, assessing new models for consultation, developing breast practices, and examining the role of stakeholder preferences and developing policies in this area. Continue to look at consent, assessing our model languages and developing new models for consenting. EHR and clinical decision support, assessing point of care education, using those clinical decision support tools, assessing when is clinical decision support useful, what policies and processes need to be in place for genomic data to be entered into the EHR, and how do those policies affect individuals. And finally, because I'm a genetic counselor, I would be remiss if I didn't say anything about family history. And so I think thinking about family history data in the EHR is, I think all of us around the table know how poorly that's gathered, and I just want to put a plug-in for the importance of thinking about that with integrating that into our electronic system. Also engaging in educating IRB panel members and other institutional officials about genomic medicine and research, and that we can see how variable that is, and it's so critical to moving this type of work forward. And also, exploring new models for supporting physicians and other healthcare providers and clinical decisions around tests. We've identified clinical decision support, but I am sure that there are many other models, or other ways of working on that, as well as other models for patient and public education. Okay, thank you, Maureen, and we'll go now to the designated reactor, and it'll be Wendy Chun. Hi, can everyone hear me? We can. Okay, very good. So, next slide, please. So I think one of the things that's emerged over the discussion this morning and this afternoon is that Emerge 3 may be at a point of some changing in terms of information that may be obtained in terms of sequencing and potentially decisions to be made in terms of what information will be returned to participants. So just some thoughts in terms of thinking about how that may change over time and realizing that the next section will be on return of results and so not wanting to seal that thunder. I think the research community, when we think about samples that have been collected before the area when they were consented specifically with the idea of doing these comprehensive exomer genome sequencing, I think I'm going to bring up a couple points to this, but I think one of the things the community has realized is that there's no single correct solution in terms of approaching the things that I'm going to talk about. And so just because Emerge has so many different sites and some of the issues may be site specific, well hopefully there will be consensus and common methods of consenting, educating the community. I just encourage everyone to realize that there's not necessarily going to be one standard answer that absolutely every site must fit. And so just realizing that local community representatives, local IRBs may have issues with this, hopefully there can be some guidance in terms of Emerge in terms of governance overall. But I think to realize that there may be local issues is important to understand and to acknowledge. One of the things as we've, at Columbia we've actually done some surveys of the research community both in terms of online surveys as well as semi-structured interviews. And as we've done that, trying to think about this issue specifically of samples that were collected before this genomic era of whole exome genome sequencing and then what to do about return of both incidental findings as well as return of individual research results. One of the major issues that came out of surveying the research community over 250 researchers was that there seems to be quite a bit of variability between the IRBs. Variability both in terms of knowledge and expertise around genomic issues and quite a bit of education that needs to be done. And what we are hearing recurrently is that the same issue different IRBs would in fact have different rulings on this and that these issues hadn't been specifically addressed in the original consent form that it was very dependent upon local IRBs, their composition, their understanding of this information. And so just in reflecting in a position where Emerge 3 may be, I hope that it's an opportunity to study that process. In fact to gain some experience and some understanding about what may lead to some of these local differences as well as potentially the opportunity to develop centrally materials to educate or materials to be able to explain this to IRBs because where there should be more consensus that is building, hopefully it's not just simply doing this understanding of simple sort of medical and genetic issues in terms of this. So I think that's something that if Emerge is able to do that it's a more sort of it's a broader issue across the research community in terms of how to deal with this and in fact just because there will be ten sites to be able to do this across could provide some really useful information in terms of the larger community. Next slide. Next slide please. Thank you. So in terms of consent, one of the issues with consenting has been across many smaller studies that again, consents largely didn't address some of the issues that may start to emerge. And so thinking about this and thinking that there may be different ways of dealing with the consent, there's again I just urge people to think about there may not be one size that fits all for this. Clearly just over time what participants may have been expecting may have changed so that when many of the Emerge participants original and consented they nor we I think we're thinking about some of the things that are possible to know from the genomic information and so they although they may have signed a very broad sweeping consent may not have thought about some of the details about what's now possible to be returned to them and so again thinking about how to educate the community about that either retrospectively on prior consent to patients or prospectively on newly consented patients really is going to take some creative ways of educating the community about this. So many people thought about how to be able to approach this in the standard written consent unfortunately is not the most effective way of educating our participants and so one of the things that many people have thought about doing is having either video educational materials or online resources things that participants you know can be able to go to with the online resources be able to take deeper dives even potentially and be able to go back to it iteratively over time even you know speak with other family members or other valued sources physicians or other health care providers to gain more information but that material can be very useful and one of the things that we've learned in doing that process is that it needs to be very accessible and that some of the very complicated things that we'll do in a genetic counseling session for instance may not be what you would want to include in one of these very broad educational sessions when talking probably about different types of results that could be returned and again it is possible especially with this online education to provide deeper layers for individuals who really want to get into it but realizing that many of our research participants if we give them all that information up front don't even they literally tune out they get saturated by this information and really can't absorb a lot of the critical details and want to know what more on the need to know basis when it's something that's relevant to them and then dive much deeper when they know that it's something that they really need to pay attention to and tune into so in thinking about that some of the different groups have thought about a staged consenting process or staged information process that is the original time one participant's consent you know may not be the time to overwhelm them will follow this information but it's more on the need to know basis and so as it comes the opportunity in terms of being able to think about return of particular results or situations that may arise being able to then give more relevant information at a time that's proximal to when that's relevant to them this also can be an issue for participants who have been enrolled many many years ago just in terms of their life stage what's happened to them over life their preferences may in fact have changed over that time period and so it may be relevant for them to rethink these issues you know at a proximal time to when it might be relevant to them one of the wonderful things about a merge of courses by many of the patient portals that are available that actually provides a lot of the infrastructure to be able to do that and it's something that again as we talk to the larger research community many many researchers wish they had that as part of what they could do to more easily streamline in terms of recontacting and reeducating participants I will say the one pushback we've heard from the research community about this idea of a stage consent however is that it may actually alert research participants if they feel as if they've been singled out during that process to alert them that there may be something you know that sort of lingering or something that they should be worried about and so as individual sites think about governance and how they might do this to just keep that in mind on whether they're going to do this in terms of a community wide effort or whether they're going to target or single out individuals might have specific information if you return to them next slide so I'm again going to try and focus on the LC issues in terms of the return of results rather than the next group they'll speak more broadly about this but again these can be very complicated and depending on whether or not this is done all up front at the consent initially or in a staged manner the issues can be quite complicated but it is in our opinion sort of necessary to be able to make these as streamlined and simple and sort of thought sweeping in terms of concepts rather than getting into too much of the nitty gritty one of the issues that will come across you know has come across a merge because of the addition of the pediatric population and again because it's gone on now for several years is that there are special populations in certain situations have just naturally changed over time so there are special issues when it comes to minors and what information and what sort of ability they have to provide their ascent into being able to have any information provided back to them and of course developmentally those children may change over time so that at one period of time they may be minors in the study and they may be of maturity later within that study and need to essentially go back and re-consent those individuals and clearly the pediatric sites have been thinking about this. In addition individuals may actually have differences even in their vital status there may be individuals obviously who are deceased over time but that information could still be potentially quite important to other family members for hereditary conditions and so trying to incorporate and think about that in terms of the consenting process for return of results would be important to do as well as individuals that may lose cognitive capacity over time again thinking about a healthcare proxy who might have a vested interest in that information and how that might influence in terms of information being returned. Another issue that frequently comes up is with such large biobanks obviously there are many, many different users of that information and in terms of governance realizing that many of those secondary users may not feel the same sense of obligation in terms of annotating or returning that information in its detailed way and so individual governance at each of the sites will be important in terms of being able to coordinate return of that or annotation cataloging in detailed ways from some researchers who in fact are expert in terms of understanding that but may not necessarily be motivated in terms of prioritizing for that return that will be important for the central sites to be able to do. If I could just go back I think I didn't quite finish with that slide. Thanks very much. And then an issue that will be coming up as again you make some decisions in terms of what sequencing to do. Again we discussed the ACMG guidelines in terms of mandatory return of results. That'll be I'm sure a very hot area of discussion with an emerge to try and decide whether or not to what to do in terms of that policy. But just to realize that again I would urge to realize that the clinical requirement that we have in terms of return of that results may not be necessarily what gets adopted in terms of return of research results within that. Again it's already been mentioned but just to emphasize there's a tremendous opportunity to be able to educate providers sort of on demand with the info buttons and other information and really to just emphasize that I think Emerge has a tremendous opportunity here in terms of implementation to be able to figure out best practices and essentially disseminate that throughout the rest of the clinical community because I do think you're going to have the ability within different EHR systems to be able to figure out what works and that really is going to be tremendously valuable to others next slide. And I'll just wrap up by saying that you know being able to do this is you know really invaluable to emerge and it's clearly what many of the rest of those of us outside of Emerge would find useful and to be able to just as you're thinking about doing all of these things to be able to collect data on the process as you're going through and to learn from this I think is going to be tremendously valuable and to realize that there may be some as well regulatory issues that come up clearly the FDA is starting to think about how to regulate some of these and so there may be things that will come up as obstacles but hopefully not barriers in terms of implementation. And I think that's my last slide. Thank you so now we'll go on to read Pirates as the for the summary.


The first thing we need to do is we need to include the libraries that are already being brought in for us, and that's React and React DOM. Now React is what we're going to be focusing this course on, and that's the API for components. React DOM is what helps us connect that to a website. Each platform has an independent package. Now for us, that's going to be React DOM since we're working on a web project. So let's include those into our project now. First, we're going to import React from React. This is assigning a local identity of React from our imported NPM package, and we're going to import React DOM the same from the NPM package React DOM. Great, now it's a little bit more stable and less refreshing. Now from these packages, we're going to learn about just two things. We're going to learn about React create element and React DOM render. These are the two functions that we're going to cover in this lesson, and they're all that we need to make a React app on the web. We're already getting a helpful error saying that we aren't using React DOM render correctly. It's pointing to the line, line six. Now the way React DOM works is that it takes a what and a where, and it's going to take that what and render it into the where. This project already has an HTML file with an empty div with an ID of root, and that will be our where. So let's collect that with just some regular old JavaScript. Const where is document dot get element by ID root. I am Groot. Now that we have our where to find, we need to work on the what, and the what is going to be our new React element. The first argument for React element is going to be the type of element that we want to render. Any type of HTML tag will work here when wrapped in a string like this. The second argument is going to be the options for that element. So these are going to be like class name and ID and any data attributes, things of that nature. Finally, in the last position, we have the inner text or the children of this element. And I'm just going to say hello, React. And just like that, with just these few lines of code, we have our first working React app.


How do you date with younger children? I have waited to introduce my child for six months. When is too soon for my son was hurt when it came to an end? OK, when is the right time to introduce children to your relationship? I'm a believer when two people have agreed to be monogamous and exclusive, and they call each other boyfriend and girlfriend. Usually somewhere between the three month and the six month mark would be a good time. This is just an arbitrary number, but it would be a good time to introduce children to this potential partner. Because here's the bottom line. What happens if you wait a year to introduce your children? You've gotten entrenched in a relationship. The man meets the children and goes, I want no part of this. The reality is if you want to be joined together at some point, the children are a part of the process. It doesn't take that long to get to know each other. Look, it takes roughly 100 hours of face to face time to get to know someone at level one, at level one, to get to know them at level one. So once you've invested 100 hours of doing shared activities, hobbies, mutual interests, doing stuff with friends, that sort of thing traveling, that might be a good time when you feel like this is going. And by the way, it might be also important to ask, is this a serious long term relationship or is this a casual relationship? Because if something is serious in long term, someone wants to pursue a long term with you, I would want to know that before I introduce my child. And you could literally say that, ladies, look it, I want to introduce my children to you, but I don't want to introduce them in that this is a short lived relationship.  Because if this is casual for you, then, and I'm not going to introduce my children, quite frankly, I don't want to date you then. I mean, that's, look at ladies, you can do casual relationships all you want. I'm not here to suggest you can't do that.  And maybe you can use your children as the backdrop for the conversation because a genuine guy who knows he's not going to go the distance with you will avoid meeting your children. And ultimately, he'll probably back out. So talk about it sooner rather than later. That's my invitation for you. And I make the world go around, what do you do? All right, great question, Kimberly. Thank you so much.