Date:

Mon, 24/12/201811:00-13:00

Location:

Rothberg CS room B500, Safra campus, Givat Ram

Speaker: Benny Sudakov, ETH, Zurich

Title: Subgraph statistics

Abstract:

Consider integers $k,\ell$ such that $0\le \ell \le \binom{k}2$. Given

a large graph $G$, what is the fraction of $k$-vertex

subsets of $G$ which span exactly $\ell$ edges? When $G$ is empty or

complete, and $\ell$ is zero or $\binom k 2$,

this fraction can be exactly 1. On the other hand if $\ell$ is not one

these extreme values, then by Ramsey's theorem, this

fraction is strictly smaller than 1.

The systematic study of the above question was recently initiated by

Alon, Hefetz, Krivelevich and Tyomkyn who proposed several natural conjectures.

In this talk we discuss a theorem which proves one of their

conjectures and implies an

asymptotic version of another. We also make some first steps towards analogous

question for hypergraphs. Our proofs involve some Ramsey-type arguments, and a

number of different probabilistic tools, such as polynomial anticoncentration

inequalities and hypercontractivity.

Joint work with M. Kwan and T. Tran

Title: Subgraph statistics

Abstract:

Consider integers $k,\ell$ such that $0\le \ell \le \binom{k}2$. Given

a large graph $G$, what is the fraction of $k$-vertex

subsets of $G$ which span exactly $\ell$ edges? When $G$ is empty or

complete, and $\ell$ is zero or $\binom k 2$,

this fraction can be exactly 1. On the other hand if $\ell$ is not one

these extreme values, then by Ramsey's theorem, this

fraction is strictly smaller than 1.

The systematic study of the above question was recently initiated by

Alon, Hefetz, Krivelevich and Tyomkyn who proposed several natural conjectures.

In this talk we discuss a theorem which proves one of their

conjectures and implies an

asymptotic version of another. We also make some first steps towards analogous

question for hypergraphs. Our proofs involve some Ramsey-type arguments, and a

number of different probabilistic tools, such as polynomial anticoncentration

inequalities and hypercontractivity.

Joint work with M. Kwan and T. Tran