anton_hilado

anton_hilado, 2 months ago to random

Let us now sketch an argument that bun is good

anton_hilado, 3 months ago to random

One can meaningfully enrich Bun

anton_hilado, 3 months ago to random

Geometric Langlands update: The final part of the claimed proof of geometric Langlands (the multiplicity one theorem, formerly known as "goblins.pdf") has now been posted:

https://people.mpim-bonn.mpg.de/gaitsgde/GLC/

anton_hilado, 4 months ago to random

I'm teaching some (very basic) group theory to my students this semester, and I'm introducing the identity element as the "do nothing" operation

I tell my students: "In math, just like in life, doing nothing is very important"

anton_hilado, 6 months ago to math

Today's #MathTopicOfTheDay is derived categories! When I see "derived" I often think "chain complexes".

The objects of a derived category (of sheaves, modules, etc.) are chain complexes (of sheaves, modules, etc.) but the morphisms are different (e.g. they are only considered up to chain homotopy, and if two complexes have the same homology then they will be isomorphic in the derived category).

https://en.m.wikipedia.org/wiki/Derived_category

#Math #Mathematics

anton_hilado, 6 months ago to random

I work on a lot of things named after Galois, (e.g. Galois representations) but for essentially all of these, none of them were actually developed by Galois.

Even the Galois theory taught in a basic abstract algebra class is barely due to Galois, it was developed by many people after him (reaching its modern form we now know via the work of Emil Artin).

Galois died early, so he only had a very embryonic form of the theory we name after him when he died. Moreover, it was essentially ignored for a long time until it was rediscovered and further developed. Were he alive today, he would probably not recognize at all most of the things we named after him.

I don't mind things being named after Galois, he's at least not as horrible as some of the people we name things after in math, but it shows how naming in math can obscure a lot of the history behind a concept.

anton_hilado, 8 months ago to math

Our new preprint is out on the arxiv! I have really wonderful coauthors and I'm really very proud of this project for many reasons (some of them deeply personal).

I'm probably gonna write a blog post (or thread) about this project soon but in the meantime please check it out!

#Math #Mathematics #NumberTheory

https://arxiv.org/abs/2309.13665

anton_hilado, 8 months ago to random

When bunnies come into contact with other soft things (including other bunnies) they become even softer. The mechanism behind this mysterious phenomenon remains poorly understood

anton_hilado, 9 months ago to math

Challenge: Name a mathematician from the areas highlighted in blue.

Alternatively, if you are a mathematician from these places, feel free to introduce yourself, I'd like to meet more people like me!

#Math #Mathematics

(By "blue" I mean any shade of blue on the map.)

anton_hilado, 11 months ago to math

I don't know if this is already well-known here, but regardless, the "What is..." column in the Notices of the AMS is a wonderful way to learn about new (and sometimes old) mathematical objects. Prof. Armin Straub has compiled them here:

https://arminstraub.com/math/what-is-column

#Math #Mathematics #Reading

anton_hilado, 11 months ago to Philippines

Okay so maybe I'll do another #Introduction since it seems timely. I'm Anton, I'm from the #Philippines and I'm currently a #PhD student in #Mathematics at University of Vermont.

Within mathematics I specialize in #NumberTheory and within number theory I specialize in #ArithmeticGeometry. If I have to be even more particular, I work on automorphic forms, Galois representations (including p-adic Hodge theory), Shimura varieties, and arithmetic manifolds which cannot give rise to Shimura varieties. All of these things which seem rather broad are related to and somewhat unified by what is known as the Langlands program.

I also have a master's degree in #Physics; I currently do not do research related to physics (though some of the math that I use, such as the theta correspondence, were inspired by physics) but I have a soft spot for #MathematicalPhysics (maybe in the future I'll be able to work on that).

Besides math I like a lot of stuff especially #CuteAnimals and especially #Bunnies. I also like #VideoGames especially of the #JRPG genre, though I'm both too busy and too poor currently to play them. Like a lot of Filipinos who grew up in the 90's and 2000's I like #Anime and #Manga (especially from that era). I also like #Art by which I just mean anything that looks cool to me. I mainly want to discuss #Math on here, but by no means will I be posting about only that.

My website is here:

https://sites.google.com/view/antonhilado

I also have a blog on math and physics:

https://ahilado.wordpress.com/

anton_hilado, 11 months ago to random

Elliptic curves

anton_hilado, 11 months ago to random

Mathematics

anton_hilado, 1 year ago to random

"You do math? You must be good with numbers"

"Oh no, the kind of math I do is different, I don't have to be good with numbers"

"What kind of math do you do?"

"Number theory"