Discrete Math Seminar (DMS)

The Discrete Math Seminar (DMS) is intended for Kennesaw State faculty working in the various areas of algebra, number theory, and discrete mathematics to get together to discuss their current work or related questions. Seminars often involve advanced mathematical knowledge. However, the seminars are open to anyone who is interested in attending.

In Fall 2020, all talks will be scheduled from 2:30-3:30pm and will be held virtually in Microsoft Teams.

Upcoming Events

Friday, October 2, 2020

  • SPEAKER: Dr. Mikhail Lavrov, Kennesaw State University
  • TIME/LOCATION: 2:30-3:30pm online in Microsoft Teams: Link to Join
  • TITLE: "Monochromatic squares, Hales-Jewett numbers, and why 5 is harder than 4"
  • ABSTRACT: I'll begin this talk by talking about a Ramsey problem in the hypercube. This is a distant cousin of the problem for which the record-setting Graham's number was invented, but we'll be less ambitious and accordingly our upper bound will be much smaller: 78. (This result is joint work with John Mackey and Mitchell Lee.)

    The proof technique generalizes to solve a different problem. The Hales-Jewett theorem is a Ramsey result for monochromatic lines in a high-dimensional grid; it implies many other results in Ramsey theory, but is very hard to find good upper bounds for. We show how to bound the (two-color) Hales-Jewett number when the grid has side length 4. Finally, we'll see why generalizing to side length 5 or more is hard and needs new ideas.

Friday, November 6, 2020

  • SPEAKER: Dr. Julianne Vega, Kennesaw State University
  • TIME/LOCATION: 2:30-3:30pm online in Microsoft Teams
  • TITLE: "Integer Decomposition Property of Schur and Symmetric Grothendieck Polynomials"
  • ABSTRACT: In this presentation we will consider Newton polytopes arising from two families of polynomials in algebraic combinatorics: Schur polynomials and inflated symmetric Grothendieck polynomials. In both cases, we show that these polytopes have integer decomposition property. This work is joint with Margaret Bayer, Bennet Goeckner, Su Ji Hong, Tyrrell McAllister, McCabe Olson, Casey Pickney, and Martha Yip.

Friday, December 4, 2020

  • SPEAKER: TBA
  • TIME/LOCATION: 2:30-3:30pm online in Microsoft Teams
  • TITLE: TBA
  • ABSTRACT: TBA

 

Past Events

Friday, September 4, 2020

  • SPEAKER: Dr. Andrew Wilson, Kennesaw State University
  • TIME/LOCATION: 2:30-3:30pm online in Microsoft Teams
  • TITLE: "The combinatorics of harmonic polynomials"
  • ABSTRACT: Polynomials in n variables carry an action of the symmetric group on n symbols. If we take the orthogonal complement of the polynomials which are invariant under this action, we get what is called the space of harmonic (or co-invariant) polynomials. In 1942, Emil Artin showed that this harmonic space has dimension n!. Recent work has extended this result to allow the symmetric group to act "diagonally" on multiple sets of variables and to allow some of these variables to anti-commute, motivated by ideas from mathematical physics. I will give an overview of this work, focusing on the combinatorial objects which arise, including permutations, parking functions, and ordered set partitions.
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