**Du****e to the Coronavirus outbreak summer school the is POSTPONED. **

**The CMS invites you to take part in our Summer School 2021:**

__Paroles, Paroles__

__Paroles, Paroles__

**A Summer School on Words**

#### July 25-29, 2021

Analysing the images of polynomials is a classical line of research in Number Theory. The analog in Group Theory is the study of images of word maps. Several remarkable results established in the last two decades rely on the study of word maps. Among these are the proof of Ore’s conjecture that every element of a finite simple group is a commutator (by Liebeck-O’Brien-Shalev-Tiep), and the proof of Serre’s conjecture that every finite-index subgroup of a finitely generated profinite group is closed (by Nikolov-Segal). Other applications concern random walks on groups and expanders. The works in the field use various tools from group theory, representation theory, algebraic geometry, combinatorics and topology. The school will focus on the study of verbal width and of word measures.

**There will be four mini courses, given by:**

Michael Magee (Durham University)

Nikolay Nikolov (Oxford University)

Doron Puder (Tel Aviv University)

Aner Shalev (The Hebrew University)

**Organizers**: Chen Meiri (Technion), Doron Puder (Tel Aviv)