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for events the day of Thursday, September 26, 2019.

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Thursday, September 26, 2019

11:00 am in 241 Altgeld Hall,Thursday, September 26, 2019

Large prime gaps and Siegel zeros

Kevin Ford (Illinois Math)

Abstract: We show that the existence of zeros of Dirichlet L-functions very close to 1 ("Siegel zeros") implies larger prime gaps than are currently known. We also present a heuristic argument that the existence of Siegel zeros implies gaps of larger order than $\log^2 x$, that is, larger than the Cramer conjecture.

12:00 pm in 243 Altgeld Hall,Thursday, September 26, 2019

Finite Rigid Sets in Arc Complexes

Emily Shinkle (Illinois Math)

Abstract: The arc complex is a simplicial complex associated to a surface. In this talk, I will describe my recent result about the existence of finite rigid sets in arc complexes: finite simplicial subcomplexes such that any injection into the arc complex of another surface with arc complex of the same dimension is induced by a homeomorphism of the associated surfaces. I will give a brief overview of my proof and also discuss some related results.

1:00 pm in 464 Loomis,Thursday, September 26, 2019

Holographic entanglement and quantum gravity in finite regions

Will Donnelly (Perimeter Institute)

Abstract: The T\bar{T} deformation of two-dimensional holographic conformal field theory is conjectured to be dual to quantum gravity in a finite region of three-dimensional anti-de Sitter spacetime. We study entanglement entropy in this theory and its relation to quantum fluctuations of the dual geometry. We derive the correspondence between the T\bar{T} flow equation and the Wheeler-DeWitt equation with a negative cosmological constant. By fixing the resulting emergent diffeomorphism symmetry, we obtain a differential equation for the sphere partition function which can be solved exactly. The solution can be expressed as a Euclidean path integral along a particular complex contour. We then apply this result to study entanglement entropy of the boundary theory for an entangling surface consisting of two antipodal points on the sphere. The entanglement entropy gives the Ryu-Takayanagi formula for a geodesic in a finite region plus quantum corrections. We suggest an interpretation of the latter as entropy of fluctuations of the bulk geodesic length, in accordance with the proposal of Faulkner, Lewkowycz, and Maldacena.

3:00 pm in 347 Altgeld Hall,Thursday, September 26, 2019

Ehrhart theory of Newton polytopes in algebraic combinatorics

McCabe Olsen   [email] (The Ohio State University)

Abstract: Motivated by the work of Monical, Tokcan, and Yong on the saturated Newton polytope (SNP) in algebraic combinatorics, we study Ehrhart theoretic properties of theses polytopes. We focus primarily upon classifying when these polytopes are Gorenstein and when they have the integer decomposition property. Often, the existence of SNP for these polynomials allows for short combinatorial proofs of the integer decomposition property. For this talk, we will mostly consider the Newton polytopes for Schur polynomials and symmetric Grothendieck polynomials. This is ongoing work which originated at the 2019 Graduate Research Workshop in Combinatorics and is joint with Margaret Bayer, Bennet Goeckner, Suji Hong, Tyrrell McAllister, Casey Pinckney, Julianne Vega, and Martha Yip.

4:00 pm in 245 Altgeld Hall,Thursday, September 26, 2019

Fall Department Faculty Meeting

Abstract: The Fall Department Faculty Meeting will be held at 4 p.m. in 245 Altgeld Hall, followed by a reception in 239 Altgeld Hall.