## LARA seminar by Sandro Mattarei

On 16th of May we had a seminar within the Lincoln Algebra Research Afternoons (LARA), with Sandro Mattarei reporting on his recent work on Generalizations of self-reciprocal polynomials.

The next LARA seminar will be delivered on 30th May 2017 by Dr Alejandra Garrido (Duesseldorf), as part of her visit to Lincoln for the forthcoming conference “Maximal Conditions and Embeddings of Profinite Groups” .

## Visit by Professor Andrei Jaikin-Zapirain

Professor Andrei Jaikin-Zapirain (Autonomous University of Madrid, currently at University of Oxford) visited Lincoln School of Mathematics and Physics on 10 May 2017. He gave a talk “On l2-Betti numbers and their analogues in positive characteristicat the Algebra research seminar (Abstract)

## AMS Special Session at Hunter College, City University of New York

Hunter College, City University of New York  [Image source]

The Special Session on Infinite Permutation Groups, Totally Disconnected Locally Compact Groups and Geometric Group Theory organised by Simon Smith (University of Lincoln) and Delaram Kahrobaei (City University of New York) took place this weekend, as part of the huge American Mathematical Society Spring Eastern Sectional Meeting held at Hunter College, City University of New York.

The idea behind the special session was to bring together three areas of infinite group theory that share a powerful tool: the analysis of group structure through an action on a locally finite graph. Subdegree-finite permutation groups act on an orbital graph, finitely generated groups act on a Cayley graph, and compactly generated totally disconnected locally compact groups act on a Cayley–Abels graph.

In the Special Session there were speakers from across the world: USA, Australia, Europe and South America. The talks were excellent. James Maynard (University of Oxford) gave the prestigious Erdös Memorial Lecture to the entire Sectional Meeting, where he spoke about his work on finding large gaps in the prime numbers.

#### List of speakers in the Special Session

Joaquín Brum, Universidad de la Republica, Uruguay
Vladimir Shpilrain, The City College of New York, USA
Phillip Wesolek, Binghamton University, USA
Benjamin Steinberg, City College of New York, USA
Luke Morgan, University of Western Australia, Australia
Lisa Carbone, Rutgers University, USA
Catherine E Pfaff, University of California Santa Barbara, USA
Cheng Chang, Mercy College, USA
Juan Alonso, Universidad de la Republica, Uruguay
Daniela B Nikolova-Popova, Florida Atlantic University, USA
Zoran Sunic, Texas A&M University, USA
Keivan Mallahi-Karai, Jacobs University, Germany
Rögnvaldur G. Möller, Science Institute, University of Iceland
Matias Carrasco, Universidad de la Republica, Uruguay
James B Wilson, Colorado State University, USA
Dmytro M Savchuk, University of South Florida, USA
Gerhard Rosenberger, University of Hamburg, Germany
Cristóbal Rivas, Universidad de Santiago de Chile
Benjamin Fine, Fairfield University, USA

## New paper accepted in Journal of Algebra

The paper by Evgeny Khukhro and Pavel Shumyatsky “Almost Engel compact groups”http://dx.doi.org/10.1016/j.jalgebra.2017.04.021, has just been accepted for publication in Journal of Algebra.

Abstract: We say that a group $G$ is almost Engel if for every $g\in G$ there is a finite set ${\mathscr E}(g)$ such that for every $x\in G$ all sufficiently long commutators $[...[[x,g],g],\dots ,g]$ belong to ${\mathscr E}(g)$, that is, for every $x\in G$ there is a positive integer $n(x,g)$ such that $[...[[x,g],g],\dots ,g]\in {\mathscr E}(g)$ if $g$ is repeated at least $n(x,g)$ times. (Thus, Engel groups are precisely the almost Engel groups for which we can choose ${\mathscr E}(g)=\{ 1\}$ for all $g\in G$.) We prove that if a compact (Hausdorff) group $G$ is almost Engel, then $G$ has a finite normal subgroup $N$ such that $G/N$ is locally nilpotent. If in addition there is a unform bound $|{\mathscr E}(g)|\leq m$ for the orders of the corresponding sets, then the subgroup $N$ can be chosen of order bounded in terms of $m$. The proofs use the Wilson–Zelmanov theorem saying that Engel profinite groups are locally nilpotent.

## Sandro Mattarei gives a talk at the University of Milano Bicocca

On 28th April 2017 Sandro Mattarei gave a talk at the University of Milano Bicocca, on Generalizations of self-reciprocal polynomials.  Sandro is approaching the end of a one-month stay at the University of Milano Bicocca as visiting professor, which has been a very exciting time. Besides completing a research project with Marina Avitabile, Sandro has had many opportunities for fruitful discussions with other members of the local Algebra group.

## Maths Students and Staff Easter Party

On 6 April maths students and staff had an Easter Party in Tower Bar. Everybody enjoyed refreshments and pizzas, along with discussions and socializing.

View original post

## Algebra Seminar in Lincoln: talk by Andrei Jaikin-Zapirain

Professor Andrei Jaikin-Zapirain (Universidad Autonoma de Madrid) will speak in the Algebra seminar on Wednesday,  10 May 2017, at 2:00pm in room JBL0C05 (Joseph Banks Laboratories, which is building 22 on the university’s map). The title of his talk is On l2-Betti numbers and their analogues in positive characteristic, and here is an Abstract.

## Simon Smith and Delaram Kahrobaei are organising a conference in New York City with the American Mathematical Society

Simon Smith (University of Lincoln, UK) and Delaram Kahrobaei (City University of New York, USA) are organising a conference on infinite permutation groups, totally disconnected locally compact groups, and geometric group theory. It is a special session at the American Mathematical Society Eastern Meeting, and will take place at the City University of New York on May 6th-7th 2017.