## Combinatorics Seminar

When: Sunday, November 7, 10am
Where: Schreiber 309
Speaker: Alex Samorodnitsky, Hebrew University
Title: Lower bounds for designs in symmetric spaces
## Abstract:

A design is a (small) subset of points in space on which simple
functions ("low-degree polynomials") average to their total
average.
We will discuss what 'simple' means in various nice spaces (it
will mean lying in the span of low-eigenvalue eigenvectors of
a nice linear operator) and give new proofs to some known
(and possibly some new) bounds on the cardinality of designs.
In particular, the following geometric claim holds: a design is
large, because a union of "spheres" around its points "covers" the
whole space.