Summer School 2022: Paroles Paroles

The CMS invites you to take part in our Summer School 2022:

Paroles, Paroles

A Summer School on Words

July 17-21, 2022


The program will start on Sunday at 10:30, and end on Thursday around 15:00

Registration is now closed

Useful information:

List of participants

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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): Word maps on unitary groups
Nikolay Nikolov (Oxford University): Verbal width in infinite groups
Doron Puder (Tel Aviv University): Word measures on symmetric and other groups
Aner Shalev (The Hebrew University): Word maps, covering and probability

Additional research talks by:
Danielle Ernst-West (Tel Aviv University): Measures induced by words on GLn(q) and free groups alegebras

Itay Glazer (Northwestern): On singularity properties of word maps and applications to random walks on compact p-adic groups
Lars Louder (University College London): Negative immersions, some equations in free groups, and coherence of (most) one-relator groups

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

This conference is also supported by the European Research Council (ERC) under the European Union’s
Horizon 2020 research and innovation programme (grant agreement WordMeasures No. 850956).

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