Date and location: October 31, 2024, 2 p.m. Hylan 1106A

Speaker: Nate Shaffer, University of Rochester



Title: Effective support, Dirac combs, and signal recovery

Abstract: A classical question in signal processing asks whether it is possible to to reconstruct the signal exactly and uniquely if the Fourier transform of a signal is transmitted with a given set of frequencies unobserved due to interference, noise or other obstructions. In this talk we are going to discuss signal recovery in the case when the signal is a Dirac comb, a linear combination of a finite number of indicator functions of disjoint sets.


Date and location: November 8, 2024, 2 p.m. Hylan 1106A

Speaker: Jeremy Chapman, Lyons College



Title: Integer distances in vector spaces over finite fields

Abstract: The Erdos-Anning Theorem states that an integer distance set in the Euclidean plane is either finite or must have all of its points on a single line. Erd\H os found an upper bound of $4(\delta +1)^2$ points for a non collinear distance set with a diameter of $\delta$. We prove a finite field version of this result for dimensions two and three, showing that if $E \subset {\mathbb F}_q^d, q=p^2$, where p is an odd prime and the distance set of $E$ is ${\mathbb F}_p$, then the size of $E$ is at most $p^d$.