|Joint IAS/Princeton University Number Theory Seminar|
|Topic:||The polynomial method|
|Affiliation:||University of Wisconsin-Madison|
|Date:||Thursday, December 11|
|Time/Room:||1:30pm - 2:30pm/Fine 214, Princeton University|
In 2008, Zeev Dvir gave a surprisingly short proof of the Kakeya conjecture over finite fields: a finite subset of $F_q^n$ containing a line in every direction has cardinality at least $c_n q^n$. The "polynomial method" introduced by Dvir has led to a wave of activity in applications of algebraic and arithmetic geometry to extremal problems in combinatorial geometry, including a theme semester at IPAM in spring 2014. I'll give a general talk about this line of work, including results of Guth and Katz, Kollar, and some of my own (joint with Oberlin-Tao and Hablicsek) and talk about some open questions and ideas for further progress.