Designs: a fun Mix of Analysis, Combinatorics  and Graph/Number/Spectral Theory

Designs: a fun Mix of Analysis, Combinatorics and Graph/Number/Spectral Theory

Frontiers In Mathematics Seminar

Stefan Steinerberger (Yale University)

Wednesday, November 20, 2019 -
3:15pm to 4:15pm
Location: 
Physics 119

Spherical Designs are sets of points on the sphere with the property that the average of a low-degree polynomial over the points is the same as the average on the sphere. They are classical yet full of mysteries; the moment we consider the problem on other manifolds, we run into Analytic Number Theory and PDEs. In what came as a surprise, the definition can be suitably interpreted to make sense on a Graph as well. The arising structures are breathtaking (I have pictures). As it turns out, they are naturally related to Extremal Combinatorics where classical Theorems (Erdos-Ko-Rado, Deza-Frankl, ...) suddenly turn into beautiful special cases of these "Graphical Designs". I promise beautiful pictures and many open problems.

Last updated: 2019/11/19 - 2:42pm