NTSGrad Fall 2021/Abstracts: Difference between revisions

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(Created page with "This page contains the titles and abstracts for talks scheduled in the Fall 2021 semester. To go back to the main GNTS page, click here. == Sep 14 ==...")
 
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| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Qiao He'''
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''TBA'''
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| bgcolor="#BCD2EE"  align="center" | ''Supersingular locus of Unitary Shimura variety''
| bgcolor="#BCD2EE"  align="center" | ''TBA''
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| bgcolor="#BCD2EE"  |I will give a summary of supersingular locus of Unitary Shimura variety. This description is really the first and an important step to understand the structure of Unitary Shimura variety. Turns out that the description of such locus will boil down to certain linear algebra. The final result will be the supersingular locus have a stratification, and the incidence relation will be closely related with the Bruhat-Tits building of unitary group. Also, each strata is closely related with affine Deligne Lustig variety. The Dieudonne module theory will be summarized. Take it for granted, all the remaining material can follow easily!
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| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Ivan Aidun'''
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''TBA'''
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| bgcolor="#BCD2EE"  align="center" | ''Simple Sieving''
| bgcolor="#BCD2EE"  align="center" | ''TBA''
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| bgcolor="#BCD2EE"  |The idea of sieving out primes is among the oldest in mathematics.  However, it has proven incredibly fruitful, and now sieve techniques lie behind some of the most striking results in modern number theory, such as the results of Zhang, Maynard, and the Polymath project on bounded gaps between primes.  In this talk, I will develop some of the basic sieve constructions, from Eratosthenes and Legendre to Brun, and hint at some of the developments that lie beyond.  This talk will be accessible to a general mathematical audience.
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| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Asvin G'''
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''TBA'''
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| bgcolor="#BCD2EE"  align="center" | ''F_un with F_1''
| bgcolor="#BCD2EE"  align="center" | ''TBA''
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| bgcolor="#BCD2EE"  | You have probably heard of a field with one element in various places and might have been, very understandably, confused. How can there be a field with one element and even if there is, how could it possible be interesting? I will try and explain the philosophy behind why this is a reasonable thing to wish for and various mathematical facts that *should* be interpreted through this lens.
| bgcolor="#BCD2EE"  | TBA
 
The talk will just be a bunch of examples of the various manifestations of the field with one element throughout mathematics!
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| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Yu Fu'''
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''TBA'''
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| bgcolor="#BCD2EE"  align="center" | ''CM liftings of Abelian Varieties''
| bgcolor="#BCD2EE"  align="center" | ''TBA''
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| bgcolor="#BCD2EE"  | This will be a introductory talk to introduce the CM liftings of Abelian Varieties.
| bgcolor="#BCD2EE"  |  
Honda-Tate theory tells us every abelian variety over a finite field can be lifted to an abelian variety with smCM in characteristic 0. There are various lifting problems if you drop/change some of the conditions, i.e. Is it an isogeny or residue class field extension necessary? Can we lift any abelian variety over a finite field to a normal domain up to isogeny? Etc.etc.
Let's explore with some fun examples!
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| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Will Hardt'''
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''TBA'''
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| bgcolor="#BCD2EE"  align="center" | ''Linear Relations Among Galois Conjugates''
| bgcolor="#BCD2EE"  align="center" | ''TBA''
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| bgcolor="#BCD2EE"  | In 1986, Smyth asked, and conjectured an answer to, the question of what can be the coefficients of a linear relation among Galois conjugates over Q. That is, for which (a_1,...,a_n) in Z^n do there exist Galois conjugates \gamma_1, ..., \gamma_n such that \sum_{i=1}^n a_i \gamma_i = 0? I will talk about joint work with John Yin in which we answer the analogous question over the function field F_q(t). We also formulate what we think is the right generalization of Smyth's Conjecture over a general number field.
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| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Di Chen'''
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''TBA'''
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| bgcolor="#BCD2EE"  align="center" | ''Negative Pell Equations''
| bgcolor="#BCD2EE"  align="center" | ''TBA''
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| bgcolor="#BCD2EE"  | I will review negative Pell equations and introduce Stevenhagen’s conjecture briefly. Then I discuss its relation with 2^k-rank of class groups and introduce basic tools like genus theory, Artin pairing, Redei matrices and Redei reciprocity.
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| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Hyun Jong Kim'''
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''TBA'''
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| bgcolor="#BCD2EE"  align="center" | ''Comparison of A1-degrees''
| bgcolor="#BCD2EE"  align="center" | ''TBA''
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| bgcolor="#BCD2EE"  | I recently talked about the Grothendieck-Witt ring and some A1-enriched enumerations, such as degrees, during my specialty exam. I will go into some more detail on when and how some of A1-enumerations, such as Morel's A1 Brouwer degree, the local A^1 Brouwer degree, the enriched Euler number and the A1-degree of maps of more general maps of schemes, are defined.
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| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Asvin Gothandaraman'''
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''TBA'''
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| bgcolor="#BCD2EE"  align="center" | ''Computational number theory''
| bgcolor="#BCD2EE"  align="center" | ''TBA''
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| bgcolor="#BCD2EE"  | I will talk about computational number theory. It will all be pretty elementary and I will cover topics like how to factor integers quickly using number fields or elliptic curves and some related topics.
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| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Ruofan Jiang'''
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''TBA'''
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| bgcolor="#BCD2EE"  align="center" | ''Galois theory over k(x)''
| bgcolor="#BCD2EE"  align="center" | ''TBA''
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| bgcolor="#BCD2EE"  | When k=C, this is the very classical theory of Riemann surface; for other k, especially when k is char p, the Galois theory of k(x) becomes much wilder. One way to study it is via rigid geometry, which enable us to talk about “analytical patching” in a much general context....
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| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Jiaqi Hou'''
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''TBA'''
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| bgcolor="#BCD2EE"  align="center" | ''Hecke algebras for p-adic groups''
| bgcolor="#BCD2EE"  align="center" | ''Hecke algebras for p-adic groups''
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| bgcolor="#BCD2EE"  | Given a smooth representation of some p-adic group, we can associate it with modules over Hecke algebras.  We will introduce the Satake transform which identifies the spherical Hecke algebra of a reductive group w.r.t a special maximal compact subgroup with a commutative ring of Weyl group invariants. The Satake isomorphism can help us understand spherical representations.
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| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Yunus Tuncbilek'''
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''TBA'''
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| bgcolor="#BCD2EE"  align="center" | ''Three of the Biggest Questions That Science Can’t Answer''
| bgcolor="#BCD2EE"  align="center" | ''TBA''
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| bgcolor="#BCD2EE"  | I will present three problems that I really enjoyed working on. The problems will be combinatorial in nature and will look very simple, but their actual difficulties will range from challenging to extremely difficult, slash possibly impossible. The talk assumes no background — literally. I presented one of the problems to my Calc 2 class today.
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| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Yu Fu'''
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''TBA'''
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| bgcolor="#BCD2EE"  align="center" | ''Chabauty method at bad reduction''
| bgcolor="#BCD2EE"  align="center" | ''TBA''
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| bgcolor="#BCD2EE"  | This is an introduction talk to the Chabauty-Coleman method at a prime of bad reduction. I will talk about results, progress and also include a proof by using intersection theory. Let's also take a look at some examples to estimate if the bound is sharp or we can obtain a better one.
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| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Sang Yup Han'''
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''TBA'''
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| bgcolor="#BCD2EE"  align="center" | ''Arithmetic Invariant Theory''
| bgcolor="#BCD2EE"  align="center" | ''TBA''
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| bgcolor="#BCD2EE"  | This talk will give a very general overview of arithmetic invariant theory of Bhargava, Gross, and Wang, including background motivation and examples.
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Revision as of 17:46, 2 September 2021

This page contains the titles and abstracts for talks scheduled in the Fall 2021 semester. To go back to the main GNTS page, click here.


Sep 14

TBA
TBA



Sep 21

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TBA


Sep 28

TBA
TBA


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Oct 5

TBA
TBA
TBA



Oct 12

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TBA


Oct 19

TBA
TBA


Oct 26

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TBA


Nov 2

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TBA


Nov 9

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TBA


Nov 16

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TBA



Nov 23

TBA
Hecke algebras for p-adic groups



Nov 30

TBA
TBA



Dec 7

TBA
TBA



Dec 14

TBA
TBA



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