Department of

# Mathematics

Seminar Calendar
for events the week of Tuesday, September 29, 2020.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
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Monday, September 28, 2020

3:00 pm in zoom,Monday, September 28, 2020

#### Toric Mirror symmetry via GIT windows

###### Jesse Huang (UIUC)

Abstract: Every toric variety is a GIT quotient of an affine space by an algebraic torus. In this talk, I will discuss a way to understand and compute the symplectic mirrors of toric varieties from this universal perspective using the concept of window subcategories. The talk is based on results from a work of myself and a joint work in progress with Peng Zhou.

5:00 pm in Altgeld Hall,Monday, September 28, 2020

#### organizational meeting

###### Marius Junge

Abstract: We will discuss topics Join Zoom Meeting https://illinois.zoom.us/j/87316015196?pwd=dU9XZE0rbVZQeWRyY2w2TklDR051dz09 (ID: 87316015196, password: 828625)

Tuesday, September 29, 2020

11:00 am in Zoom,Tuesday, September 29, 2020

#### Partitions into primes in arithmetic progression

###### Amita Malik (AIM)

Abstract: In this talk, we discuss the number of ways to write a given integer as a sum of primes in an arithmetic progression. While the study of asymptotics for the number of ordinary partitions goes back to Hardy and Ramanujan, partitions into primes were recently re-visited by Vaughan. If time permits, we compare our results with some known estimates in special cases and discuss connections to certain classical results in analytic number theory.

2:00 pm in Zoom,Tuesday, September 29, 2020

#### Ramsey graphs and anti-concentration

###### Matthew Kwan (Stanford University)

Abstract: Anti-concentration inequalities provide limits on the extent to which random variables can be concentrated: for example, they commonly give uniform upper bounds on the probability that a random variable takes any particular value. In this talk I'll discuss some of the many connections between anti-concentration and combinatorics, initially focusing on applications to Ramsey graphs but also touching on a few other topics such as the polynomial Littlewood-Offord problem and permanents of random matrices.

Please Email Sean at SEnglish (at) illinois (dot) edu for Zoom information.

Thursday, October 1, 2020

3:00 pm in Zoom,Thursday, October 1, 2020

#### The fundamental theorem of finite semi-distributive lattices

###### Hugh Thomas   [email] (Université du Québec à Montréal)

Abstract: The fundamental theorem of finite distributive lattices of Birkhoff says that any finite distributive lattice can be realized as the set of order ideals of a poset, ordered by inclusion. Semidistributive lattices are a generalization of distributive lattices, introduced by Jónsson in the 60s; he showed that free lattices are semidistributive. Among the interesting examples of finite semidistributive lattices are weak order on finite Coxeter groups and the torsion classes of an algebra (supposing there are only finitely many). I will present a theorem characterizing finite semidistributive lattices, formally similar to the fundamental theorem of finite distributive lattices. In a sense, this is a combinatorialization of the structure of torsion classes, but our construction does not actually use any representation theory, and I will not assume any knowledge of representation theory in my talk. This talk is based on arXiv:1907.08050, joint with Nathan Reading and David Speyer. Please email Colleen at cer2 (at) illinois (dot) edu for the Zoom ID and password.

Friday, October 2, 2020

1:00 pm in Zoom,Friday, October 2, 2020

#### To Be Announced

###### Gayana Mahaarachchige Sarajakumara Jayasinghe (UIUC Math)

Abstract: TBA

4:00 pm in Zoom (email ruiyuan at illinois for info),Friday, October 2, 2020

#### T-convex T-differential fields and their immediate extensions (Part 1)

###### Elliot Kaplan (UIUC Math)

Abstract: Let T be an o-minimal theory extending the theory of ordered fields. A T-convex T-differential field is a model of T equipped with a T-convex valuation ring and a continuous T-derivation. This week and next week, I will discuss some of my recent work on immediate extensions of T-convex T-differential fields. This week will be focused on background (what a T-convex valuation ring is, what a T-derivation is, what immediate extensions are) and on examples of T-convex T-differential fields.