**Speaker**: Yan Zhu (朱艷), Shanghai Jiao Tong University

**Date**: Sat, Jun 13, 2015

**Time**: 09:45 - 10:45

**Venue**: Middle Meeting Room

**Title**: On tight spherical designs of harmonic index $t$ (or $T$)

**Abstract**:

Let $T$ be a finite subset of positive integers. A finite subset $Y$ of the $(n-1)$-sphere $\mathbb{S}^{n-1}$ is called a spherical design of harmonic index $T$, if $\sum_{\mathbf{x}\in Y}f(\mathbf{x})=0$ is satisfied for all homogeneous harmonic polynomials $f(x_1,\ldots,x_n)$ of degree $k\in T$.

This talk is about spherical designs of harmonic index $T$, including the special case of $T$ being a singleton set $\{t\}$. We give a Fisher type lower bound for the size of such a design and discuss the tightness of our bound.

This is joint work with Eiichi Bannai, Etsuko Bannai, Kyoung-Tark Kim and Wei-Hsuan Yu.