Titles and abstracts

Speaker: Bram Petri

Title: Linear programming techniques in two-dimensional hyperbolic geometry
 
Abstract: After a reminder on the geometry of hyperbolic surfaces, I will talk about a joint project with Maxime Fortier Bourque. In this project, we use ideas coming from the theory of sphere packings, due to Cohn-Elkies and Gorbachev, in order to prove new bounds on geometric and spectral invariants associated to hyperbolic surfaces.
 

Speaker: Julian Sahasrabudhe

Title: A new lower bound for sphere packing
 
Abstract: What is the maximum proportion of d-dimensional space that can be covered by disjoint, identical spheres? In this talk I will discuss a new lower bound for this problem, which is the first asymptotically growing improvement to Rogers' bound from 1947. Our proof is almost entirely combinatorial and reduces to a novel theorem about independent sets in graphs with bounded degrees and codegrees. This is based on joint work with Marcelo Campos, Matthew Jenssen and Marcus Michelen.
 

Speaker: Mathilde Gerbelli-Gauthier

Title: Fourier Interpolation and the Weil Representation
 
Abstract: In 2017, Radchenko--Viazovska proved a remarkable interpolation result for even Schwartz functions on the real line: such a function is entirely determined by its values and those of its Fourier transform at square roots of integers. The result can be viewed as a one-dimensional analogue of the breakthroughs that led to the solution of the sphere-packing problem in dimensions 8 and 24. In this talk, I will explain how this one-dimensional version can be understood through the lens of the Segal--Shale--Weil representation, an infinite-dimensional representation that originally arose in the context of quantum mechanics.
 

Speaker: Maryna Viazovska

Title: Sphere packings, cyclotomic fields, and subconvexity bounds
 
Abstract: In this lecture I will talk about lattice packings constructed from number fields. I will present recent joint work with Nihar Gargava, Vlad Serban and Ilaria Viglino. We analyze the number of short vectors in the ideal and modular lattices.
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