Fourier Transform and Finite Analogues

Abstract: We are now about 200 years since the introduction of Fourier transform (for functions on the real line). This has become one of the most important tools not only in pure mathematics but also in applied math and engineering. In this talk we will discuss some of its analogues when the real line is replaced by something finite. The two main topics of the talk are: 1) How to write Fourier transform over a symplectic vector space over the field with two elements as a triangular matrix? 2) A nonabelian analogue of Fourier transform (related to representation theory).

mathematical physicsalgebraic geometrycategory theoryrepresentation theory

Audience: researchers in the topic

UMass Amherst Representation theory seminar