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Mathematics Department

Combinatorics, Algebra, & Topology Seminar

Fall 2019

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

  • Nov
  • 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
  • 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
  • Erin Meger
    Ryerson University
    Time: 12:00 PM
  • Nov
  • Title: Graphs and binary matroids whose odd circuits all have size three or five
    Carolyn Chun
    Time: 12:00 PM
  • Oct
  • Equations for Matroid Varieties
    Will Traves
    Time: 12:00 PM
  • John Asplund
    Dalton State University
    Time: 12:00 PM
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