## Preliminary list of abstracts

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*Keywords:*Spherical designs, Brouwer degree; Brouwer degree; Marcinkiewiczâ€“Zygmund inequalities

- Viazovska, Maryna (MPIM Bonn, Bonn University, Germany)

A spherical $t$-design is a finite set of $N$ points on the $d$-dimensional unit sphere $S^d$ such that the average value of any polynomial $P$ of degree $t$ or less on this set is equal to the average value of $P$ on the whole sphere. For each $N\ge c_dt^d$ we prove the existence of a spherical $t$-design on the sphere $S^d$ consisting of $N$ points, where $c_d$ is a constant depending only on $d$. This result proves the conjecture of Korevaar and Meyers concerning an optimal order of minimal number of points in a spherical $t$-design on $S^d$ for a fixed $d$.