Math Seminar - Fall 2019
The math seminar at Marquette will be held in Cudahy 401 from 1-2pm unless otherwise noted.
- Wednesday, September 11 - Dr. Wim Ruitenburg (Marquette), From logic and models to algebra
We sketch classical logic and model theory
with sufficient detail so as to be able to
give non-trivial applications to algebra.
- Wednesday, September 18 - Dr. Wim Ruitenburg (Marquette), From logic and models to algebra II
- Wednesday, October 2 - Dr. Wim Ruitenburg (Marquette), From logic and models to algebra III
- Wednesday, October 9 - Dr. John Engbers (Marquette), How many ways can you color a tree?
We discuss several vertex coloring schemes,
with the aim of finding the trees with the maximum and minimum
number of such colorings.
- Wednesday, October 16 - Dr. Jay Pantone (Marquette University), Counting with Language Theory
A decade before the first computer was built, Alan Turing devised a generalized model
of computation that he called an "a-machine", now known today as a "Turing machine". Among
the hierarchy of computational models, two of the simplest are finite-state machines and pushdown
automata. These two models correspond directly to two important concepts in language theory: regular
languages, and context-free grammars.
We introduce these concepts in the first of two or three talks, and demonstrate how they can be
useful tools for enumerating combinatorial objects of all kinds by representing the objects as a
language, constructing an automaton that accepts that language, and extracting a counting formula
from the automaton.
We then present some preliminary research with Michael Albert (recent visitor and colloquium
speaker, University of Otago), David Bevan (University of Strathclyde), and Michael Engen
(University of Florida), in which we build a framework from these ideas that permits enumeration
of a wide variety of combinatorial objects at all once.
- Wednesday, October 30 - Dr. Jay Pantone (Marquette), Counting with Language Theory II
- Wednesday, November 6 - Dr. Francis Pastijn (Marquette), Geometries with parallelism and regular bands
Some geometries with parallelism can be encoded as bands (idempotent semigroups). We
explore how algebraic concepts - quasivarieties, subdirectly irreducibles - may
contribute to a classification of such geometries.
- Wednesday, November 13 - Dr. Ibrahim Saleh (Marquette/UW-Whitewater), Introduction to Cluster Algebras
Cluster algebras were introduced by Fomin and Zelevinsky in 2000 as a frame work to study total positivity
and dual canonical basis. But have since appeared in many other contexts, from algebras
of homogeneous functions on the Grassmannians, to Grothendieck rings of some monoidal
categories. In this talk I will introduce the basic definitions and properties of
cluster algebras and quivers mutations and will illustrate how this framework naturally
arises.
- Wednesday, November 20 - Dr. Ibrahim Saleh (Marquette/UW-Whitewater), Introduction to Cluster Algebras II
Previous Semesters:
Fall 2018
Spring 2019
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