Dan Romik (UC Davis)
Title:聽Sphere packing in dimension 8, Viazovska's solution, and a new human proof of her modular form inequalities.
Abstract: Maryna Viazovska in 2016 found a remarkable application of complex analysis and the theory of modular forms to a fundamental problem in geometry, obtaining a solution to the sphere packing problem in dimension 8 through an explicit construction of a so-called "magic function" that she defined in terms of classical special functions. The same method also led shortly afterwards to the solution of the sphere packing problem in dimension 24 by her and several collaborators. One component of Viazovska's proof consisted of proving a pair of inequalities satisfied by the modular forms she constructed. Viazovska gave a proof of these inequalities that relied in an essential way on computer calculations. In this talk I will describe the background leading up to Viazovska's groundbreaking proof, and present a new proof of her inequalities that uses only elementary arguments that can be easily checked by a human.
In person:聽Burnside Hall, Room 920
Zoom link: