Author: Rogers, Luke

REU Seminars 2020

July 17th: Luke Rogers, UConn

Can I measure it with mathematics?

July 10th: Emily Meehan, Gallaudet University

Title: Baxter posets.

July 3rd: Daniel Labardini-Fragoso, UNAM

Title: Introduction to Hyperbolic Geometry

June 26th: Masha Gordina, University of Connecticut

Title: Isoperimteric inequalities

Abstract: The classical isoperimetric problem asks: among all figures with a given perimeter, which one encloses the greatest area? There are many different proofs of the isoperimetric inequality and interesting stories about the authors of these proofs. We will review different tools that can be used to prove such an inequality (plane geometry, calculus of variations and maybe even Fourier series), and if time permits we’ll describe how this type of problem is still an active area of research in analysis and geometry.

June 19th: Ivan Contreras, Amherst College

Dynamics and Topology on Graphs.

June 12th: Nadia Lafrenière, Dartmouth University

Derangements and their use in research (Algebraic Combinatorics)

June 5th: Greg Muller, University of Oklahoma

Title: Counting paths with linear algebra

Abstract: Counting paths in a graph is an elementary but important problem with many applications. Something remarkable happens if you assemble these counts into a matrix: the determinants of submatrices count certain collections of paths. This simple observation has a simple proof, but wide-ranging applications. Time permitting, I will review some applications to Pascal’s triangle, matrix factorizations, total positivity, and electrical networks.