##### Department of Mathematics,

University of California San Diego

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### Joint seminar between Analysis and CCOM

## Stefan Steinerberger

#### Yale University

## Spherical Designs and the Heat Equation

##### Abstract:

Spherical Designs are finite sets of points on the sphere with the property that the average of low-degree polynomials over the sphere coincides with the average over the finite set. These objects are very beautiful, very symmetric and have been studied since the 1970s. We use a completely new approach that replaces delicate combinatorial arguments with the a simple application of the heat equation; this approach improves the known results and extends to other manifolds. We also discuss some related issues in Combinatorics, Irregularities of Distribution and Fourier Analysis.

Host: Alex Cloninger

### March 13, 2018

### 3:30 PM

### AP&M 6402

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