Events for 02/19/2016 from all calendars

Algebra and Combinatorics Seminar

Time: 3:00PM - 4:00PM

Location: BLOC 628

Speaker: Laura Matusevich, Texas A&M University

Title: What is the volume of a lattice polytope?

Abstract: A lattice polytope is the convex hull of finitely many points with integer coordinates. The goal of this survey talk is to give different ways to compute the Euclidean volume of such an object, finishing with an algebraic method that uses Hilbert polynomials.

Linear Analysis Seminar

Time: 4:00PM - 5:00PM

Location: BLOC 220

Speaker: Nico Spronk, University of Waterloo

Title: On similarity for completely bounded representations of Fourier algebras

URL: Event link

Geometry Seminar

Time: 4:00PM - 5:00PM

Location: BLOC 113

Speaker: Igor Zelenko, TAMU

Title: On Reed-Solomon Type Matrix Completion for Constrained Maximal Distance Separable Codes

Abstract: I will discuss the following matrix completion problem taking its origin in coding theory: we want to construct a linear code of dimension $k$ and length $n$ over a sufficiently large field such that in the generator matrix $G$ of this code in some basis each row has zeros in $k-1$ prescribed positions, all maximal minors of the matrix $G$ are not equal to zero (or, equivalently, the minimal Hamming distance of the code is maximal possible), and the code is of the Reed -Solomon type, i.e. each code-word is obtained by the evaluation of some polynomial at the fixed $n$ distinct elements of the field. Our conjecture is that this completion is possible if and only if the prescribed zeros in the generator matrix do not occupy a submatrix of a size $r\times s$ with $r+s=k+1$ (which is an obvious necessary condition for the completion). I will discuss some reformulations of this conjecture in algebra-geometric and graph-theoretic terms and also a surprising determinantal identity for the matrix involving elementary symmetric functions that I obtained in an attempt to prove this conjecture. This project is in collaboration with Alex Sprintson, Muxi Yan (TAMU, Electrical and Computer Engineering), and Hoang Dao (Urbana-Champaign).

Graduate Student Organization Seminar

Time: 5:00PM - 6:30PM

Location: BLOC 220

Speaker: Roberto Barrera, Texas A&M University

Title: Envy-free division of cakes and necklaces

Abstract: The classical cake-cutting problem of Steinhaus asks how to fairly divide a cake among several players. Our notion of a fair division will be one in which each player believes that their piece of cake is at least as good as any other piece. We will present a solution to the classical cake-cutting problem using an approach by F.W. Simmons and then give two combinatorial analogues of the classical cake-cutting problem. This is joint work with Kathryn Nyman, Amanda Ruiz, Francis Edward Su, and Yan X. Zhang.