Quantitative real algebraic geometry and its applications

Series: 
School of Mathematics Colloquium
Thursday, September 15, 2016 - 11:05
1 hour (actually 50 minutes)
Location: 
Skiles 006
,  
Perdue University
Organizer: 
Effective bounds play a very important role in algebraic geometry with many applications.  In this talk I will survey recent progress and open questions in the quantitative study ofreal varieties and semi-algebraic sets and their connections with other areas of mathematics -- in particular,connections to incidence geometry via the polynomial partitioning method. I will also discuss some results on the topological complexity of symmetric varieties which have a representation-theoretic flavor. Finally, if time permits I will sketch how some of these results extend to the category of constructible sheaves.