# Zarankiewicz’s problem for semilinear hypergraphs

## Abdul Basit, Iowa State University

## Date and time: 2pm (New York time), Tuesday, December 14, 2021

## Place: On Zoom (details provided on the seminar mailing list)

Zarankiewicz's problem in extremal graph theory asks for the maximum
number of edges in a bipartite graph on n vertices which does not
contain a copy of $K_{k,k}$, the complete bipartite graph with $k$
vertices in both classes. We will consider this question for
incidence graphs of geometric objects. Significantly better bounds
are known in this setting, in particular when the geometric objects
are defined by systems of algebraic inequalities. We show even
stronger bounds under the additional constraint that the defining
inequalities are linear. We will also discuss connections of these
results to combinatorial geometry and model theory.

No background is assumed, and the talk will be accessible to
non-experts. Joint work with Artёm Chernikov, Sergei Starchenko,
Terence Tao, and Chieu-Minh Tran.