Department of

Mathematics


Seminar Calendar
for events the day of Thursday, November 1, 2018.

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Thursday, November 1, 2018

11:00 am in 241 Altgeld Hall,Thursday, November 1, 2018

Quantum chaos and arithmetic

Simon Marshall (University of Wisconsin-Madison)

Abstract: If M is a compact manifold of negative curvature, Laplace eigenfunctions on M with large eigenvalue are expected to behave chaotically, reflecting the correspondence principle between classical and quantum mechanics. I will describe this chaotic behavior, and explain what can be proved about it using methods from harmonic analysis. I will also explain why harmonic analysis alone has a hard time giving us the complete picture, and how we can see more of it using tools from number theory.

12:30 pm in 464 Loomis,Thursday, November 1, 2018

To Be Announced

Wati Taylor (MIT)

3:00 pm in 345 Altgeld Hall,Thursday, November 1, 2018

Genus Two Generalization of $A_1$ spherical Double Affine Hecke Algebra

Semeon Artamonov   [email] (UC Berkeley)

Abstract: Spherical Double Affine Hecke Algebra can be viewed as a noncommutative (q,t)-deformation of the SL(N,C) character variety of the fundamental group of a torus. This deformation inherits major topological property from its commutative counterpart, namely Mapping Class Group of a torus SL(2,Z) acts by atomorphisms of DAHA. In my talk I will define a genus two analogue of $A_1$ spherical DAHA and show that the Mapping Class Group of a closed genus two surface acts by automorphisms of such algebra. I will then show that for special values of parameters q,t satisfying $q^n t^2=1$ for some nonnegative integer n this algebra admits finite dimensional representations. I will conclude with discussion of potential applications to TQFT and knot theory. Based on arXiv:1704.02947 joint with Sh. Shakirov