Department of

Mathematics


Seminar Calendar
for events the day of Friday, November 8, 2019.

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Friday, November 8, 2019

2:00 pm in 347 Altgeld Hall,Friday, November 8, 2019

Cohomology for Hopf algebras and dualities

Cris Negron (University of North Carolina)

Abstract: In studies of finite-dimensional Hopf algebras one makes consistent use of a number of standard operations. The most fundamental of these operations include linear duality, (cocycle) deformation, and twisting by so-called Drinfeld twists. Many numerical invariants of Hopf algebras are known to be stable under these operations. However, one can see from examples, that the cohomology ring H*(A,k) for a finite-dimensional Hopf algebra A with trivial coefficients is not preserved under deformation or duality of A. In joint work with J. Plavnik we conjecture that, although the cohomology ring itself may vary, the Krull dimension of cohomology should be invariant under a general class of ``duality operations" which includes linear duality, deformation, and Drinfeld twisting. I this talk I will give the necessary definitions and examples, discuss the aforementioned conjecture, and provide some positive results obtained jointly with J. Plavnik.

3:00 pm in Illini Hall 1,Friday, November 8, 2019

On two central binomial series related to $\zeta(4)$

Vivek Kaushik (UIUC)

Abstract: In this expository talk, we prove two related central binomial series identities: $\sum_{n \geq 0} \frac{{2n}\choose{n}}{2^{4n}(2n+1)^3}=\frac{7 \pi^3}{216}$ and $\sum_{n \in \mathbb{N}} \frac{1}{{n^4}{{2n}\choose{n}}}=\frac{17 \pi^4}{3240}.$ These series resist all standard approaches used to evaluate other well-known series such as the Dirichlet $L$ series. Our method to prove these central binomial series identities in question will be to evaluate two log-sine integrals that are equal to the series representations. The evaluation of these log-sine integrals will lead to computing closed forms of polylogarithms evaluated at certain complex exponentials. After proving our main identities, we discuss some polylogarithmic integrals that can be readily evaluated using the knowledge of these central binomial series.

4:00 pm in 345 Altgeld Hall,Friday, November 8, 2019

O-minimal complex analysis (Part 5)

Elliot Kaplan (UIUC)

Abstract: I will continue discussing Peterzil and Starchenko's treatment of definable functions on the algebraic closure of an o-minimal field.

4:00 pm in 141 Altgeld Hall,Friday, November 8, 2019

Finite Element Exterior Calculus

Nikolas Wojtalewicz (UIUC)

Abstract: In this talk, we will begin by discussing a basic example of a finite element method. We will state the basic formulation of this method, and then briefly discuss some of its limitations. We will follow up by talking about Hilbert complexes (such as the De Rahm complex), discretizing such complexes, and then about Finite Element Exterior Calculus. If time permits, we will show some examples where FEEC has been particularly successful.

4:00 pm in 347 Altgeld Hall,Friday, November 8, 2019

EG Tableaux and Complexity

Anna Chlopecki & Jackie Oh (UIUC Math/UIUC Computer Science)

Abstract: The purpose of this talk is to examine a counting problem in algebraic combinatorics. We will be discussing connections between reduced words, Young tableaux, and the Lascoux-M.-P. Schützenberger transition algorithm in hopes to provide an intuition for proving that counting the number of Edelman Greene tableaux for a given permutation w and partition λ is in #P.

5:00 pm in 241 Altgeld Hall,Friday, November 8, 2019

Stochastic Differential Equations and Unitaries

Marius Junge (University of Illinois at Urbana-Champaign)

Abstract: Part II.