Department of

Mathematics


Seminar Calendar
for events the day of Friday, October 8, 2021.

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Friday, October 8, 2021

2:00 pm in 347 Altgeld Hall,Friday, October 8, 2021

Discrete Methods for the Non Linear Schrödinger Equation

Kesav Krishnan (UIUC)

Abstract: The Non Linear Schrödinger Equation (NLS) has been the subject of intense study by the Harmonic Analysis and PDE community. Primarily this is because it is one of the canonical examples of dispersive PDEs that have Soliton solutions. In this talk I will survey results for the discrete analogue of the focusing NLS, and the use of the discrete equation to construct invariant measures. I will conclude with a discussion of Sourav Chatterjee's work on resolving the Soliton resolution conjecture.

3:00 pm in 243 Altgeld Hall,Friday, October 8, 2021

Simplicial Localizations and How to Find Them

Doron Grossman-Naples (UIUC Math)

Abstract: Abstractly defining \(\infty\)-categorical localization is easy, but explicitly constructing it is hard. Following a series of papers by Dwyer and Kan, I will describe the construction known as the hammock localization and use it to obtain a clearer picture of some important \(\infty\)-categories.

4:00 pm in Altgeld Hall 347,Friday, October 8, 2021

An Introduction to Geometric Quantization

Levi Poon (UIUC)

Abstract: The notion of quantization has its origin in physics, where we seek to relate classical systems to their quantum counterparts. It turns out that the mathematical structures of classical and quantum mechanics are surprisingly similar, despite their apparent differences, and it is possible to formalize and (greatly) generalize the process of quantization to a large class of symplectic manifolds. Geometric quantization is one such approach, with interesting connections to representation theory. In this talk, I will give an introduction to geometric quantization. If time permits, I will discuss some interesting questions inspired by this construction. No backgrounds in physics or symplectic geometry will be assumed.