Department of

Mathematics


Seminar Calendar
for events the day of Tuesday, February 11, 2020.

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Tuesday, February 11, 2020

11:00 am in 243 Altgeld Hall,Tuesday, February 11, 2020

Vanishing and Realizability

Shane Clark (University of Kentucky)

Abstract: The Reidemeister trace of an endomorphism of a CW complex is a lower bound for the number of fixed points (up to homotopy) of that endomorphism. For an endomorphism $f$, the Reidemeister trace of $f^n$ is a lower bound for the number of fixed points of $f^n$, however it can be a far from an optimal lower bound. One method of addressing this discrepancy constructs an equivariant map, the n^{th} Fuller trace $f$, which carries information about the periodic points of a map $f$. However, we must ask how much information is retained by this equivariant construction? In this talk we show that the n^{th} Fuller trace of $f$ is a complete invariant for describing a minimum set of periodic points for maps of tori.

1:00 pm in 241 Altgeld Hall,Tuesday, February 11, 2020

The Borel complexity of quotient groups

Joshua Frisch (Caltech Math)

Abstract: The theory of Borel equivalence relations gives us rigorous methods to says when one classification problem/equivalence relation is more "complicated" than another. Given a countable group it's outer-automorphism group naturally has the structure of a borel equivalence relation. Motivated by this example, in this talk I will give a brief introduction to the theory of countable borel equivalence relations, describe some previously known connections with the theory of groups and, finally, describe a new new result explaining exactly how complicated the Borel complexity of quotient groups (which generalize outer-automorphism groups) can be. This is joint work with Forte Shinko.

2:00 pm in 243 Altgeld Hall,Tuesday, February 11, 2020

Large triangle packings and Tuza's conjecture in random graphs

Patrick Bennett (Western Michigan University)

Abstract: The triangle packing number $\nu(G)$ of a graph $G$ is the maximum size of a set of edge-disjoint triangles in $G$. Tuza conjectured that in any graph $G$ there exists a set of at most $2\nu(G)$ edges intersecting every triangle in $G$. We show that Tuza's conjecture holds in the random graph $G=G(n,m)$, when $m \le 0.2403n^{3/2}$ or $m\ge 2.1243n^{3/2}$. This is done by analyzing a greedy algorithm for finding large triangle packings in random graphs.