• D

0

# Video of the week

## Post-edited

Sarnak, Peter (Author of the conference)

integral points on hypersurfaces 3 and higher dimensions cubic surfaces Markoff surfaces and dynamics diophantine analysis of Markoff surfaces integral points on a fixed surface and strong approximation connection to Painlevé strong approximation - the basic conjecture results towards the main conjecture Markoff numbers outline of some points in the proofs

# Latest Videos

## Post-edited Interview at CIRM: Peter Sarnak

Peter Sarnak is a South African-born mathematician with dual South-African and American nationalities. He has been Eugene Higgins Professor of Mathematics at Princeton University since 2002, ...

## Post-edited Multiple ergodic theorems: old and new - Lecture 1

The classic mean ergodic theorem has been extended in numerous ways: multiple averages, polynomial iterates, weighted averages, along with combinations of these extensions. I will give an overview of ...

## Post-edited Applications of algebra to automatic sequences and pattern avoidance - Lecture 1

We will cover some of the more important results from commutative and noncommutative algebra as far as applications to automatic sequences, pattern avoidance, and related areas. Well give an overview ...

## Post-edited Some new inequalities for the Cheeger constant

We discuss some new results for the Cheeger constant in dimension two, including:
- a polygonal version of Faber-Krahn inequality;
- a reverse isoperimetric inequality for convex bodies;
- a ...

## Multi angle The unsolved problems of Halmos

Sixty years ago Paul Halmos concluded his Lectures on Ergodic Theory with a chapter Unsolved Problems which contained a list of ten problems. I will discuss some of these and some of the work that ...

## Multi angle Primes with missing digits

We will talk about recent work showing there are infinitely many primes with no $7$ in their decimal expansion. (And similarly with $7$ replaced by any other digit.) This shows the existence of ...

## Multi angle xThe diameter of the symmetric group: ideas and tools

Given a finite group $G$ and a set $A$ of generators, the diameter diam$(\Gamma(G, A))$ of the Cayley graph $\Gamma(G, A)$ is the smallest $\ell$ such that every element of $G$ can be expressed as a ...

## Multi angle Ergodicity of the Liouville system implies the Chowla conjecture

The Chowla conjecture asserts that the signs of the Liouville function are distributed randomly on the integers. Reinterpreted in the language of ergodic theory this conjecture asserts that the ...
Z