Date:
Wed, 26/12/201812:00-13:00
Location:
Room 70, Ross Building
Title: Fuglede's spectral set conjecture for convex polytopes.
Abstract:
A set \Omega \subset \mathbb{R}^d is called spectral if the space L^2(\Omega) admits an orthogonal basis of exponential functions. Back in 1974, B. Fuglede conjectured that spectral sets could be characterized geometrically as sets which can tile the space by translations. This conjecture inspired extensive research over the years, but nevertheless, the precise connection between the notions of spectrality and tiling, is still a mystery.
In the talk I will survey the subject, and discuss some recent results, joint with Nir Lev, where we focus on the conjecture for convex polytopes.
Abstract:
A set \Omega \subset \mathbb{R}^d is called spectral if the space L^2(\Omega) admits an orthogonal basis of exponential functions. Back in 1974, B. Fuglede conjectured that spectral sets could be characterized geometrically as sets which can tile the space by translations. This conjecture inspired extensive research over the years, but nevertheless, the precise connection between the notions of spectrality and tiling, is still a mystery.
In the talk I will survey the subject, and discuss some recent results, joint with Nir Lev, where we focus on the conjecture for convex polytopes.