Combinatorics, Algebra, & Topology Seminar
Fall 2019
All talks are from 12001300 in the designated room unless otherwise specified.

Nov18

The size Ramsey number of pathsDeepak BalMontclair State UniversityTime: 12:00 PM
View Abstract
Given a graph H, let sr(H) be the minimum m such that there exists a graph G with m edges such that in every 2coloring of the edges G, there is a monochromatic copy of H. Let P_n be the path on n vertices. To prove that sr(P_n)>m, one must show that every graph on m edges can be 2colored such that every monochromatic path has order less than n. We discuss known bounds on sr(P_n) and prove that sr(P_n)>(3.75−o(1))n thereby improving the previous bestknown lower bound of (2.5−o(1))n due to Dudek and Pralat. We also discuss some results concerning the rcolor version of the problem. This is joint work with Louis DeBiasio.

Nov15

Explicit problems in the padic theory of modular formsJohn BergdallBryn Mawr CollegeTime: 12:00 PM
View Abstract
Modular functions are complex functions that transform remarkably with respect to Möbius transformations. They are central objects in mathematics, encoding in their Fourier coefficients quantities as varied as the number of representations of integers as sums of squares, the dimensions of irreducible representations of the monster group, and point counts of solutions to cubic equations modulo primes. Our talk will focus on arithmetic questions, with the chief aim being the behavior of Fourier coefficients with respect to the nonArchimedean norm associated with a fixed prime number. The open questions, and sparse results, are in analogy will wellunderstood, deep, results for the usual complex norm. We will include both historical and more recent results and questions in the talk.

Nov12

Erin MegerRyerson UniversityTime: 12:00 PM

Nov04

Title: Graphs and binary matroids whose odd circuits all have size three or fiveCarolyn ChunTime: 12:00 PM

Oct08

Equations for Matroid VarietiesWill TravesUSNATime: 12:00 PM

John AsplundDalton State UniversityTime: 12:00 PM