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Graduate Seminar

Zilin Jiang
Carnegie Mellon University
Title: Classification of Bipartite Algebraic Graphs without Quadrilaterals

Abstract: For a graph $H$, define the Turan number $ex(n, H)$ as the maximum number of edges that a graph on $n$ vertices can have without containing a copy of $H$. When $H$ is bipartite, for example, a complete bipartite graph $K_{s,t}$, the problem of pinning down the order of magnitude of the Turan number remains in general as one of the central open problems in combinatorics. Despite the lack of progress on the Turan problem, there are certain complete bipartite graphs for which the problem has been solved asymptotically, or even exactly. The constructions that match the upper bounds in theses cases are similar to one another, and they are all algebraic. In this talk, we restrict our attention to algebraic bipartite graphs defined over algebraically closed fields and we shall discuss a structural theory of those graphs that do not contain $K_{s,t}$ as a subgraph.

Date: Tuesday, November 17, 2015
Time: 5:30 pm
Location: Wean Hall 8220
Submitted by:  Zilin Jiang