Combinatorics, Algebra, & Topology Seminar

Fall 2019

All talks are from 1200-1300 in the designated room unless otherwise specified.

• Nov

  18
• The size Ramsey number of paths

  Deepak Bal

  Montclair State University

  Time: 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 2-coloring 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 2-colored 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 best-known lower bound of (2.5−o(1))n due to Dudek and Pralat. We also discuss some results concerning the r-color version of the problem. This is joint work with Louis DeBiasio.

• Nov

  15
• Explicit problems in the p-adic theory of modular forms

  John Bergdall

  Bryn Mawr College

  Time: 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 non-Archimedean norm associated with a fixed prime number. The open questions, and sparse results, are in analogy will well-understood, deep, results for the usual complex norm. We will include both historical and more recent results and questions in the talk.

• Nov

  12
• Erin Meger

  Ryerson University

  Time: 12:00 PM

• Nov

  04
• Title: Graphs and binary matroids whose odd circuits all have size three or five

  Carolyn Chun

  Time: 12:00 PM

• Oct

  08
• Equations for Matroid Varieties

  Will Traves

  USNA

  Time: 12:00 PM

• John Asplund

  Dalton State University

  Time: 12:00 PM