Number Theory

Title: Golden Gates in PU(n) and the Density Hypothesis
Speaker: Shai Evra
Speaker Info: IAS
Brief Description:
Special Note:

In their seminal work from the 80’s, Lubotzky, Phillips and Sarnak gave explicit constructions of topological generators for PU(2) with optimal covering properties. Recently, Sarnak gave a new application of these LPS generators to the theory of theoretical quantum computations, showing that they form an excellent universal gate set for PU(2) (from both a mathematical and an algorithmic point of view). In this talk I will describe some recent works that extends the LPS construction to higher dimensional compact Lie groups.

A key ingredient in the work of LPS is the Ramanujan conjecture for U(2), which follows from Deligne's proof of the Ramanujan-Petersson conjecture for GL(2). Unfortunately, the naive generalization of the Ramanujan conjecture is false for higher rank groups. Following a program initiated by Sarnak in the 90's, we prove a density hypothesis and use it as a replacement of the naive Ramanujan conjecture.

This talk is based on a joint work with Ori Parzanchevski.

Date: Friday, November 22, 2019
Time: 3:00PM
Where: Lunt 107
Contact Person: Ilya Khayutin
Contact email: khayutin@northwestern.edu
Contact Phone:
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