Symplectic geometry Puns

I happened to come across some controversy in the field of symplectic geometry while I was searching for some related resources. I know nothing of this, but after reading through it and noticing that nothing has been updated, and that there are many more accounts of the dispute still present on A. Zinger's website, I wanted to ask if anyone on here knew any more of this.

From AZ's account, it seems as if experts in the field have just brushed aside major flaws in their peers work, these types of controversies are usually a big story (I know these are pretty different scenarios, but seems like this should be bigger than it is?)

Thanks!

Hello, I'm taking an advanced computational physics class and we missed out on a lot of lectures before due professor's schedule. Now due to Coronavirus, the professor decided to change the class format to a project based and that's all we are graded on. So, I'm looking for a project in symplectic geometry. It can be anything as long as it's not too short. Let me know if you have any suggestions

Today's topic is Symplectic geometry.

This recurring thread will be a place to ask questions and discuss famous/well-known/surprising results, clever and elegant proofs, or interesting open problems related to the topic of the week.

Experts in the topic are especially encouraged to contribute and participate in these threads.

These threads will be posted every Wednesday.

If you have any suggestions for a topic or you want to collaborate in some way in the upcoming threads, please send me a PM.

For previous week's "Everything about X" threads, check out the wiki link here

Next week's topics will be Mathematical finance

Would someone be kind enough to share a connection between those subjects? I’ve been studying algebraic topology, cohomology theories in particular, and recently I heard there’s a connection to symplectic geometry.

1. What is SG?
2. Is there a useful connection between the two?

Hi,

I have a BS in physics and in my senior year I was introduced to Hamiltonians and symplectic area, but didn't dive too deep. If I wanted to learn about sypmlectic geometry more formally what are some pre-reqs you'd recommend?

I have a strong background in calculus and linear algebra. I know the very basics of tensor stuff and non-Riemannian differential geometry for context.

Thanks.

Ready, set, go!

P.S. - Thanks in advance!

I will be applying to PhD programs soon. I am particularly interested in differential geometry (things like geometric flows, minimal surfaces, applications to mathematical physics). I see that lots of academics focus on symplectic geometry and would like a good introduction for someone with a pretty good grasp with DG at the graduate level. I hear that it seems to be the "natural setting" for classical mechanics, but do not know what that really means yet or why people claim that. I like sources to be more thorough.

I have an interview for a PhD in Symplectic Geometry at King's College London, on Skype, with a committee (I don't know the people who will be there) and the professor interested in taking me as his student (it will be around 30min long). The Phd is based on a Bursary from the Royal Society obtained by the professor, so I think he will be the one to decide at the end if I am admitted or not, but of course the committee can veto... I was told by the professor that the interview was the standard procedure, with specific questions about courses that I have taken, and more general questions about what excites me in math, or what specific questions would I want to work on during my Phd. In math, it's very difficult to know in advance on what one is going to focus during the PhD, so this kind of questions can be very tricky to answer. I would like to know if someone has gone through this kind of interview and could give me some advice. Thanks !

This recurring thread will be for questions that might not warrant their own thread. We would like to see more conceptual-based questions posted in this thread, rather than "what is the answer to this problem?". For example, here are some kinds of questions that we'd like to see in this thread:

• Can someone explain the concept of maпifolds to me?
• What are the applications of Represeпtation Theory?
• What's a good starter book for Numerical Aпalysis?
• What can I do to prepare for college/grad school/getting a job?

Including a brief description of your mathematical background and the context for your question can help others give you an appropriate answer. For example consider which subject your question is related to, or the things you already know or have tried.

Many undergraduate linear algebra classes motivate the introduction of bilinear forms via inner products. Suppose the instructor at the end wanted the students to study alternating bilinear forms and needed some motivation. What could the students be given that would make sense at their level?

While Im sure there's a lot of people who might consider the last homotopical shift in algebraic geometry to be part of the original categorical shift of Grothendieck in the 60s, I think that the fact that there is at the very least a cultural divide in mathematicians who work at the level of schemes and those who have seen a need to expand into the higher categorical realms is a good argument to say there's been two. There are of course also people who work with honest algebraic varieties, perhaps just with the compromise of using modern language but mostly caring about the more classical problems and techniques.

So, what is it with algebraic geometry? Are there other branches of math that have gone through something like that somewhat recently ? ( I mean, post 1900's formalization )

Are there branches of math that might go there?

Recently Kewei Zhang provided a new proof of the uniform Yau--Tian--Donaldson conjecture for Fano manifolds, a central problem in Kähler geometry which was resolved (at least in the same generality as Zhang's new proof) in 2012 by Chen--Donaldson--Sun. This appeared in my last post about the same area, which was more concerned with significant advancements in the algebraic-geometry side of the theory.

This paper jumped out to me as a somewhat incredible application of a purely physical idea to Kähler geometry, that really has no business working as well as it does. The concept of quantization is of course central in physics, and there are certain contexts in which it makes sense mathematically, but the novelty of Zhang's paper is taking a very hard "classical" problem (the existence of a Kähler--Einstein metric on a complex manifold), "quantizing" it (turning it into a problem on some Hilbert spaces that algebraic approaches let us solve), and then "taking the classical limit" to return to the original problem. Whilst this proof is fundamentally mathematically rigorous, the fact that it works seems to me to be very deep and be intimately related to the nature of quantization in physics.

Hopefully I will be able to impart, to the interested reader, why this paper caught my eye.

#Yau--Tian--Donaldson conjecture

Very briefly, the YTD conjecture asserts that solutions to a very hard global PDE on compact complex manifolds, the Kähler--Einstein equations, exist precisely when a certain purely algebro-geometric condition is satisfied, called K-stability. In principle, this algebraic condition is meant to be "much easier" to check than doing some kind of hard analysis to prove existence of the PDE some other way, so the YTD conjecture takes a hard problem in geometric analysis and converts it to an easier problem in algebra. In practice it turns out that K-stability is also very hard to check, not because it is equally as hard as solving the PDE, but because it turns out algebra is also very hard!

Just to explain the term "uniform" in the title of Zhang's article, K-stability takes the form

"for every (X,L) associated to a compact complex manifold (X,L), the rational number DF(X,L) is st

I recently got a summer job as a pizza delivery driver and have spent my time on the road listening to podcasts. One of these is the Numberphile podcast, which has been awesome and I totally recommend listening to.

One trend I've noticed with the people being interviewed was the method they went about choosing topics they focused on, or rather the lack of method.

Some just had a good professor in the class and continued in the field while others got lucky with a PhD program. Others still knew since day 1 they wanted to do one type of math

How did you pick your speciality? If you work in industry, how did you choose to be in that type of work vs something else? Would you make the same choice again given the choice?

TLDR: confused maths + physics undergrad is looking for clarity on big sexy questions in math neuro.

I'm a maths + physics undergraduate who's gotten extremely interested in theoretical neuroscience over the past year. However, I'm having a lot of trouble figuring out what math is being used and what big questions people are working on beyond simply "building a model of the brain".

In contrast, while physics is certainly about "building models of the universe", there are precise overarching goals in each field that guide theoretical research. For high energy people, this goal is finding a consistent, testable theory of quantum gravity. Similarly, particle physics these days is heavily focused on moving beyond the Standard Model to better model dark matter. Further, there are clear mathematical tools for sub-disciplines; quantum mechanics draws heavily form functional analysis, classical mechanics can be rigorously formulated with symplectic geometry, and statistical mechanics is basically all probability theory.

From what I understand so far, neuroscience theory operates on distinct layers (say L1 to L5) of abstraction where L1 is all about the structure/function/dynamics of a single neuron and L5 is human consciousness. However, since the field is so young, work has been focused on layers L1-L2 and the theory-experiment loop isn't too productive; I haven't heard of any predictions that were made by the theoretical people and then validated in the lab.

Here's my (rudimentary) summary of work at each level. Feel free to add or correct if I'm wrong.

L1: A single neuron

From the introductory chapters of this, it seems like the big question of this layer is "can we precisely determine a neuron's spike train given an arbitrary electrochemical stimulus". As of today, we don't have an answer and some people even debate the spike train as a representation of neural activity. In terms of mathematical tools, research at this layer is all PDEs and dynamical systems.

L2: A few neurons

This is where I'm starting to get lost. Initially, it seemed like the goal was to answer the same question as in L1, but scaled up to a few neurons. That is, "can we precisely determine the spike trains of all neurons in a small cluster given an arbitrary electrochemical stimulus". However, upon digging deeper, it now seems like there are three different camps of theorists.

1. Th

I don't want to step on anybody's toes here, but the amount of non-dad jokes here in this subreddit really annoys me. First of all, dad jokes CAN be NSFW, it clearly says so in the sub rules. Secondly, it doesn't automatically make it a dad joke if it's from a conversation between you and your child. Most importantly, the jokes that your CHILDREN tell YOU are not dad jokes. The point of a dad joke is that it's so cheesy only a dad who's trying to be funny would make such a joke. That's it. They are stupid plays on words, lame puns and so on. There has to be a clever pun or wordplay for it to be considered a dad joke.

Again, to all the fellow dads, I apologise if I'm sounding too harsh. But I just needed to get it off my chest.

The nurse asked the rabbit, “what is your blood type?”

“I am probably a type O” said the rabbit.

The doctor says it terminal.

Alot of great jokes get posted here! However just because you have a joke, doesn't mean it's a dad joke.

THIS IS NOT ABOUT NSFW, THIS IS ABOUT LONG JOKES, BLONDE JOKES, SEXUAL JOKES, KNOCK KNOCK JOKES, POLITICAL JOKES, ETC BEING POSTED IN A DAD JOKE SUB

Try telling these sexual jokes that get posted here, to your kid and see how your spouse likes it.. if that goes well, Try telling one of your friends kid about your sex life being like Coca cola, first it was normal, than light and now zero , and see if the parents are OK with you telling their kid the "dad joke"

I'm not even referencing the NSFW, I'm saying Dad jokes are corny, and sometimes painful, not sexual

So check out r/jokes for all types of jokes

r/unclejokes for dirty jokes

r/3amjokes for real weird and alot of OC

r/cleandadjokes If your really sick of seeing not dad jokes in r/dadjokes

Punchline !

Edit: this is not a post about NSFW , This is about jokes, knock knock jokes, blonde jokes, political jokes etc being posted in a dad joke sub

Edit 2: don't touch the thermostat

Do your worst!

Hey everyone,

First off, sorry if this is not the correct reddit for these types of posts. I have a ton of math books from my undergraduate/graduate studies. A lot of them are in good condition, others are in ok condition. I'm looking to sell them. I don't have a full list of titles or don't know how much is be willing to sell each book for yet.

Does anyone have any experience with selling to a local bookstore or just selling old math books? Most of the books I'm selling are springer/AMS titles (most of them in topology/geometry) and doubt that some of the local bookstores near me would be interested.

I've never sold online/shipped out a book but would be willing to look into it and would be open to shipping to anyone here if there is interest.

Ill try and post a list later today, can't right now as I'm at work.

But yeah, If anyone has experience with selling them online, I'd like to hear how you went through with it.

I'm also open to local pickup if you're in the Chicago area. Just send me a private message.

Edit: Alright its a huge list, but I thought maybe some people on this subreddit would be interested in buying some, and would rather sell them to people who would actually read them/learn from them. Send me a private message and we can discuss pricing and condition of book if interested in any.

(Also, yeah a lot of topology/geometry)

John Lee's intro to Topological, Smooth, and Riemannian manifolds books - (3 books, each 2nd ed)

Stein & Shakarchi - Fourier and Real analysis (2 books) (Stein Real Analysis - Sold)

John B Conway - Functions of one complex variable, 2nd ed, hardcover

Ahlfors - Complex Analysis (hardcover)

M. A. Armstrong - Basic Topology

Pugh - Real Mathematical Analysis

Hans Samelson - notes on lie algebras

Gareth A. Jones and J. Mary Jones - Elementary Number Theory

Francois Treves - Basic Linear PDE and Topological Vector Spaces, Distributions, and Kernels

Axler - Linear Algebra Done Right, 3rd edition

Matsumoto - An intro to Morse Theory

Spivak - Calculus on Manifolds

Steen and Seebach - Counterexamples in topology

Morita - Geometry of Differential forms

Velleman - How To Prove It

Sutherland - Intro to Metric and Topological Spaces

Rudin - Real and Complex Analysis

Bishop and Goldberg - Tensor Analysis on Manifolds

Milnor - Lectures on the H-Cobordism Theorem

Millman and Parker - Elements of Differential Geometry

Strogatz - Nonlinear Dynamics and Chaos, 2nd ed

Rotman - An intro to Algebraic top

How the hell am I suppose to know when it’s raining in Sweden?

Mathematical puns makes me number

We told her she can lean on us for support. Although, we are going to have to change her driver's license, her height is going down by a foot. I don't want to go too far out on a limb here but it better not be a hack job.

Ants don’t even have the concept fathers, let alone a good dad joke. Keep r/ants out of my r/dadjokes.

But no, seriously. I understand rule 7 is great to have intelligent discussion, but sometimes it feels like 1 in 10 posts here is someone getting upset about the jokes on this sub. Let the mods deal with it, they regulate the sub.

So, I've got some questions. Hope someone can answer any!

1. Are there some fields of math you would advice against a grad student trying to enter unless they already have a significant head start in graduate material?
2. For those of you who do research in stringy geometry type things, how long did you spend studying (perhaps after passing qualifying exams) before starting to read papers?

Big blob of context:

I've been talking to the faculty at some of the grad schools I've been accepted at. I'd started college doing physics and got quite deep into it before I transitioned to math, but I'm still quite interested in math inspired by physics. In particular I've exchanged some messages with a professor who does research related to mirror symmetry (they work in some mix of algebraic, complex and symplectic geometry). The professor was very kind and inviting, saying that although nothing can be guaranteed in the future, they're happy to take on a hard working and interested graduate student if they pass quals. I wanted a feel for what kind of math is involved, so I asked them and they replied with a list of topics/books they want their students to have a strong background in before starting to seriously read recent research papers...

And it was terrifying. Don't get me wrong, I'm excited to learn lots of new stuff, but it would take a ridiculous amount of time to learn it all from a standard undergrad background (estimating altogether it's probably comparable to 20-25 semester long graduate classes). Thankfully I know a little graduate geometry and topology, but it'll still take me the better part of 2-3 years to get comfortable with what this professor considers to be the foundations. Hell, it looks like even the students at places like Harvard (where they come in knowing this) or Cambridge (where they come in knowing a bunch of these) might still take at least 1 year, maybe even 2, to learn all those recommended topics well.

When I expressed my concern at the time it would take to learn all of it, the professor admitted that it is a lot, and that other people might have different ideas of what the core background is, so I might want to solicit other opinions. On the other hand, the professor does have a strong record of placing students into academic positions!

Can anyone point me to any sources on this? Thanks.

TLDR: confused maths + physics undergrad is looking for clarity on big sexy questions in math neuro.

I'm a maths + physics undergraduate who's gotten extremely interested in theoretical neuroscience over the past year. However, I'm having a lot of trouble figuring out what math is being used and what big questions people are working on beyond simply "building a model of the brain".

In contrast, while physics is certainly about "building models of the universe", there are precise overarching goals in each field that guide theoretical research. For high energy people, this goal is finding a consistent, testable theory of quantum gravity. Similarly, particle physics these days is heavily focused on moving beyond the Standard Model to better model dark matter. Further, there are clear mathematical tools for sub-disciplines; quantum mechanics draws heavily form functional analysis, classical mechanics can be rigorously formulated with symplectic geometry, and statistical mechanics is basically all probability theory.

From what I understand so far, neuroscience theory operates on distinct layers (say L1 to L5) of abstraction where L1 is all about the structure/function/dynamics of a single neuron and L5 is human consciousness. However, since the field is so young, work has been focused on layers L1-L2 and the theory-experiment loop isn't too productive; I haven't heard of any predictions that were made by the theoretical people and then validated in the lab.

Here's my (rudimentary) summary of work at each level. Feel free to add or correct if I'm wrong.

L1: A single neuron

From the introductory chapters of this, it seems like the big question of this layer is "can we precisely determine a neuron's spike train given an arbitrary electrochemical stimulus". As of today, we don't have an answer and some people even debate the spike train as a representation of neural activity. In terms of mathematical tools, research at this layer is all PDEs and dynamical systems.

L2: A few neurons

This is where I'm starting to get lost. Initially, it seemed like the goal was to answer the same question as in L1, but scaled up to a few neurons. That is, "can we precisely determine the spike trains of all neurons in a small cluster given an arbitrary electrochemical stimulus". However, upon digging deeper, it now seems like there are three different camps of theorists.

1. Th