## PIMS-UVic Distinguished Lecture: Karen Gunderson

• Date: 11/06/2020
Speaker(s):
Karen Gunderson, University of Manitoba
Location:

None

Topic:

Turán numbers for a 4-uniform hypergraph

Description:

For any $$r\geq 2$$, an $$r$$-uniform hypergraph $$\mathcal{H}$$, and integer $$n$$, the Turán number for $$\mathcal{H}$$ is the maximum number of hyperedges in any $$r$$-uniform hypergraph on $$n$$ vertices containing no copy of $$\mathcal{H}$$. While the Turán numbers of graphs are well-understood and exact Turán numbers are known for some classes of graphs, few exact results are known for the cases $$r \geq 3$$. I will present a construction, using quadratic residues, for an infinite family of hypergraphs having no copy of the 4-uniform hypergraph on 5 vertices with 3 hyperedges, with the maximum number of hyperedges subject to this condition. I will also describe a connection between this construction and a `switching' operation on tournaments, with applications to finding new bounds on Turán numbers for other small hypergraphs.

Schedule:

Friday, November 6th @ 11 am PST.