Mathematics Colloquium Calendar

Upcoming Mathematics Colloquia

 

On Thursday, September 21, Dr. John Goodrick, Associate Professor of Mathematics at Los Andes University, Colombia, will present a colloquium on Counting integer points in polytopes with an extension of Presburger arithmetic. The talk will take place at 4 pm, in Room 320 of 7800 York Road, with light refreshments served at 3:30 pm.

Abstract: Fix some polytope \(P\) in \(\mathbb R^d\) whose vertices have integer coordinates. Then for any positive integer \(t\), one can ask to compute the number \(f_P(t)\) of points in the lattice \(\mathbb Z^d\) that lie within the \(t\)-th dilate of \(P\). By a theorem of Ehrhart, the function \(f_P(t)\) is always a polynomial.

In this talk, we will present a generalization of this result (from joint work with Tristram Bogart and Kevin Woods): If \(f(t)\) counts the number of integer points within a bounded region of \(\mathbb R^d\) which is defined by a certain type of first-order logical formula, then \(f(t)\) is eventually periodically polynomial (“eventually quasi-polynomial”). We call such families “parametric Presburger families” in analogy with the logical theory of Presburger arithmetic. 

Recent Mathematics Colloquium Talks

Date Topic Speaker
Sept 14, 2017 Constructing nonstandard finite difference (NSFD) schemes for dynamical systems Seye Adekanye,
Howard University
Apr 27, 2017 Prediction methods for semi-continuous data with applications in climate science Dr. Nagaraj K. Neerchal, UMBC
Apr 18, 2017 Lyapunov rank in conic optimization Dr. Michael Orlitzky,
UMBC
Apr 7, 2017 Managing default risk in affordable housing finance Dr. Tyler T. Yang,
IFE Group
Mar 9, 2017 Covariates-contributed sufficient dimension reduction Dr. Kofi Placid Adragni, UMBC
Nov 10, 2016 Dimensions of spline spaces and commutative algebra Dr. Michael DiPasquale,
Oklahoma State University
Oct 13, 2016 A lattice theorist's apology Dr. Jonathan Farley,
Morgan State University
Oct 6, 2016 The idea of dimension in model theory and discrete mathematics Dr. Cameron D. Hill, Wesleyan University
Sept 22, 2016 Jonathan Farley's mathematical terror theory: The structure of perfect terrorist cells with a single leader Ms. Zeinab Bandpey,
Morgan State University