K-Theory

Trying out something new in my livstreams, doing the Pomodoro method for a combination of work and chatting. What time intervals do ou think I should use to have a good mix of work and interacting with chat? youtube.com/watch?v=uUJ8KC…

Looking back at some of the papers I stared at durring my MSc: youtube.com/watch?v=USXWjL…

It's Dr. Balodis now

@AlexKontorovich @AMathRes Very cool! I'm particularly interested in the KL-polynomial paper.

Congratulations to the Journal of Experimental Mathematics (published by the AMR @AMathRes) on releasing Vol 2 Issue 1! Please make sure your libraries are subscribing... Oh wait, no! It's Diamond Open Access! Just go read the papers :) jexpmath.org

@JoshuaG19367959 🤯This is my new foundational belief: We are all (approximately) Dirichlet L-functions.

@KristapsBalodi3 en.wikipedia.org/wiki/Zeta_func… might suggest that we all are.

I'm sorry, who's zeta function?!

I gave (half?) a talk about the p-adic Kazhdan-Lusztig hypothesis in the NYC category theory seminar today: youtube.com/watch?v=_9zKed…

@JoshuaG19367959 Actually I was asking "who is zeta function". Very common normal question.

@KristapsBalodi3 *whose

@TonyTheLion2500 I will let you know in about 5 days.

So having a PhD in mathematics doesn't solve your life?

@sidml Beautiful

@KristapsBalodi3 Why did the Roman Emperor keep studying SO(p, q)(ℝ)? Because he wanted to make sure his Empire had the right signature — and he'd already conquered every other group in the classification. Even the mightiest empire can't stay connected when its components keep splitting off.

Why have I never heard a joke about the group S(p, q)(R) and Roman empire?

Here's some basic proofs youfilthy animals: youtu.be/NAF1u1Gdp3w

@JasonRute @octonion True, and of course I'm also in favor of that as well. I mean the goal is to have everything eventually. I still think that the best strategy to get more mathematicians on board, is to put in tools they would use in their next paper.

@KristapsBalodi3 @octonion I think some people actually view this as an important reason to formalize stuff like this. Formalization (especially formalization done with a lot of care, like in the Mathlib style) is a way to preserve knowledge, especially since it isn’t exciting anymore.

Has any work started on formalizing the classification of finite simple groups, or is that still a hopeless task at the moment? That would be truly amazing.

@Someody42 @octonion Good point, I guess especially for some of those exceptional groups it may not be trivial to define them.

@KristapsBalodi3 @octonion I can confirm. However, there are a lot of things on the way to the classification which deserve to get to Mathlib! For example, defining all the groups involved.

@octonion the recent autoformalization of sphere packing, or say the large project to formalize the proof of FLT both would involve the formalization of tools that cutting edge researchers are still employing. (3/n, n=3)

@octonion research, with the hopes of making it practical and attractive for mathematicians to start formalizing their papers in Lean. Therefore, there's most interest in projects that would require the formalization of modern tools that are still actively being used. For example (2/n)

@tummycom @octonion Already been done.

@octonion There's so much to do. Feit-Thompson looks like a place to start.

Time to get back to some rep theory youtu.be/RGcN1ux_2MI

@subcountability @littmath But they redacted so many coefficients!

@littmath I'll give it to them that they finally released the Eisenstein series.

It’s true. Look up Elliptic Curves. Read Silverman’s “The Arithmetic of Elliptic Curves.” Do all the exercises. Read Katz-Mazur’s “Arithmetic Moduli of Elliptic Curves.” Study it closely. Only then will you understand.