This week's seminar is given by our own Aleksei Gordeev, Umeå universitet.
Title: Combinatorial Nullstellensatz, list colorings and Turán numbers
Abstract: Combinatorial Nullstellensatz, formulated by Alon in 1999, is a celebrated theorem with various applications in additive combinatorics, graph colorings and other areas.
In this talk we will outline how Combinatorial Nullstellensatz can be used to estimate list coloring numbers of graphs, i.e. the Alon-Tarsi method. We will discuss applications of this method to direct products of a graph and an even cycle. We will also show how this method can be extended to 2-colorable hypergraphs.
Finally, we will show how Lasoń's generalization of Combinatorial Nullstellensatz can be used to estimate Turán numbers of complete r-partite r-uniform hypergraphs and give an example of such construction
