# Dor Minzer “New sharp thresholds results and applications in extremal combinatorics”

May 21, 2020
19.00 MSK (UTC +3)

# Dor Minzer "New sharp thresholds results and applications in extremal combinatorics"

Dor Minzer from IAS in Princeton will give the talk "New sharp thresholds results and applications in extremal combinatorics" on the labs' Big Seminar.

The talk will be held in zoom
Meeting ID: 279-059-822
Password: First six digits of $\pi$ after the decimal point

You can also write to Alexander Polyanskii (alexander.polyanskii@yandex.ru) or to Maksim Zhukovskii (zhukmax@gmail.com) if you want to be added to mailing list.

Abstract:

The classical hypercontractive inequality for the Boolean hypercube lies at the core of many results in analysis of Boolean functions. Though extensions of the inequality to different domains (e.g. the biased hypercube) are known, they are often times quantitatively weak, making them harder to apply.

We will discuss new forms of this inequality and some of their consequences, such as qualitatively tight version of Bourgain's sharp threshold theorem, as well as a variant that applies for sparse families. Time permitting, we will also discuss applications to two problems in extremal combinatorics: the (cross version) of the Erdos matching conjecture, and determining the extremal size of families of vectors in $\{0,1,...,m-1\}^n$ avoiding a fixed intersection size, for $m\geq 3$.

Based on joint works with Peter Keevash, Noam Lifshitz and Eoin Long.

## Watch the lecture on youtube:

Everyone is invited to attend. The language of the lecture is English. The event is aimed at master and graduate students, as well as researchers in the field of combinatorics.