# TBA

Dylan Langharst

## Institution:

Kent State University

## Time:

Monday, September 19, 2022 - 12:00pm

Zoom

# Mean inequalities for symmetrizations of convex sets

## Speaker:

Katherina von Dichter

## Institution:

Technische Universität München

## Time:

Monday, September 12, 2022 - 12:00pm

## Location:

Zoom

The arithmetic-harmonic mean inequality can be generalized for convex sets, considering the intersection, the harmonic and the arithmetic mean, as well as the convex hull of two convex sets. We study those relations of symmetrization of convex sets, i.e., dealing with the means of some convex set C and -C. We determine the dilatation factors, depending on the asymmetry of C, to reverse the containments between any of those symmetrizations, and tighten the relations proven by Firey and show a stability result concerning those factors near the simplex.

# TBA

Kristina Skreb

## Institution:

University of Zagreb

## Time:

Monday, March 7, 2022 - 12:00pm

# TBA

Vjekoslav Kovac

## Institution:

University of Zagreb

## Time:

Monday, May 2, 2022 - 12:00pm

# TBA

Olli Saari

## Institution:

Mathematisches Institut der Universität Bonn

## Time:

Monday, April 25, 2022 - 12:00pm

# TBA

UCLA

## Time:

Monday, April 18, 2022 - 12:00pm

# TBA

Alina Stancu

## Institution:

Concordia University

## Time:

Monday, April 11, 2022 - 12:00pm

# On the Fourier-Entropy Conjecture

Dor Minzer

MIT

## Time:

Monday, April 4, 2022 - 12:00pm

## Location:

Characterizing Boolean functions with small total influence is one of the most fundamental questions in analysis of Boolean functions.

The seminal results of Kahn-Kalai-Linial and of Friedgut address this question for total influence $K = o(\log n)$, and show that

a function with total influence $K$ (essentially) depends on $2^{O(K)}$ variables.

The Fourier-Entropy Conjecture of Friedgut and Kalai is an outstanding conjecture that strengthens these results, and remains

meaningful for $K \geq \log n$. Informally, the conjecture states that the Fourier transform of a function with total influence $K$,

is concentrated on at most $2^{O(K)}$ distinct characters.

In this talk, we will discuss recent progress towards this conjecture. We show that functions with total influence $K$ are concentrated

on at most $2^{O(K\log K)}$ distinct Fourier coefficients. We also mention some applications to learning theory and sharp thresholds.

Based on a joint work with Esty Kelman, Guy Kindler, Noam Lifshitz and Muli Safra.

# TBA

## Speaker:

Diogo Oliveira e Silva

## Institution:

University of Birmingham

## Time:

Monday, March 28, 2022 - 12:00pm

# TBA

Evita Nestoridi

Princeton

## Time:

Monday, March 21, 2022 - 12:00pm