This post is full time and permanent at 1.0 FTE.

**Please note that interviews for this post will take place on both 11th and 12th of July 2023.**

Lecturer salary from £36,333 per annum.

Senior Lecturer salary from £41,931 per annum

Are you passionate about research and teaching in mathematics?

The University of Lincoln opened the School of Mathematics and Physics in September 2014 as part of the College of Science. The school provides undergraduate and postgraduate education and conducts research in a number of areas of pure and applied mathematics and physics.

We are now seeking suitably qualified applicants for the post of Lecturer / Senior Lecturer in Mathematics, with research interests ideally complementing our current strengths within the Charlotte Scott Centre for Algebra. Our successful candidate would be required to provide teaching in the range of mathematics modules offered by the school, including modules in Algebra. For an appointment at Senior Lecturer level, you will have substantial experience in teaching and teaching development / administration.

We are especially encouraging applications from underrepresented groups in STEM subjects. Candidates with a career break are also encouraged to apply.

Our post holder will join a friendly community at the School of Mathematics and Physics, and be part of the continued success of the University, located at the heart of our historic city. The University of Lincoln offers exciting career opportunities with the chance to grow and develop to reach your full potential. We also offer a wide range of staff benefits, including a generous annual leave allowance, progressive pay rates, access to discounts at popular stores and more. If you will need to relocate to Lincoln from within the UK or internationally for this opportunity, we understand how difficult this can be. We have dedicated support in place to make the process as simple for you as possible.

If you would like to know more about this opportunity, please contact Prof Andrei Zvelindovsky, Head of School, at azvelindovsky@lincoln.ac.uk

]]>This Wednesday 10th of May, 2023, **Elena Tielker (Bielefeld University)** has given a digital talk entitled *Polytopes and Permutations* at the Charlotte Centre for Algebra.

**Abstract: **It is well-known that the numerator of the Ehrhart series, the so-called h-polynomial, of a lattice polytope has nonnegative coefficients. Only in a few cases (e.g., for simplices) we are able to interpret the coefficients in the context of another counting problem. We present two further families of polytopes whose h-polynomials can be interpreted in terms of permutation statistics. In this context we give new definitions of the major index and descent statistic on signed multiset permutations. In this talk we give a brief introduction to Ehrhart theory and permutation statistics (and their generalisations).

On Wednesday the 26th of April 2023, **Jonas Deré** (KU Leuven KULAK) digitally payed a visit to the Charlotte Centre for Algebra and talked about his work on *Rational forms in Lie algebras associated to graphs* in the joint research seminar of Lincoln University and Lund University.

**Title:** Rational forms in Lie algebras associated to graphs

**Abstract:** By the classic work of Mal’cev, studying finitely generated torsion-free nilpotent groups up to commensurability is equivalent to studying finite dimensional rational nilpotent Lie algebras. Given a field and a graph, one can construct a 2-step nilpotent Lie algebra over the field, where the Lie bracket between vertices is fully described in terms of the edges. This interesting class of Lie algebras intermediates between abelian and free 2-step nilpotent Lie algebras. For example, both the Heisenberg algebra and the direct sum of two Heisenberg algebras lies in this class. It is well-known that the direct sum of two real Heisenberg Lie algebras contains many different rational forms, i.e. rational subalgebras such that every basis over Q forms a basis for the real Lie algebra as well. In this talk, we present a general method to describe all the rational forms in these Lie algebras associated to graphs (and thus also of all the corresponding torsion-free nilpotent groups) by using the so-called coherent components of the graph. This is joint work with Thomas Witdouck.

On Wednesday the 12th of April 2023, **Mireille Soergel** (Université de Bourgogne/ ETH Zürich) digitally visited Charlotte Centre for Algebra and gave a talk entitled *Dyer groups* at the research seminar of Lincoln University.

**Abstract:**

One can observe that Coxeter groups and right-angled Artin groups share the same

solution to the word problem. On the other hand, in his study of reflection subgroups of Coxeter groups Dyer introduces a family of groups, which we call Dyer groups, which contains both, Coxeter groups and right-angled Artin groups. After recalling the solution to the word problem for Coxeter groups and right-angled Artin groups, we will introduce Dyer groups, and mention some of their properties.

International conference “**Finite and Residually Finite Groups**” celebrating **Pavel Shumyatsky’s 60th birthday** will take place in Bilbao (Spain), on 20–23 June, 2023. Prof. Shumyatsky is a member of the Advisory Board of the Lincoln School of Mathematics and Physics and maintains close research links with Lincoln.

* Invited Speakers: *Cristina Acciarri (University of Modena and University of Brasilia), Rostislav Grigorchuk (Texas A&M University), Evgeny Khukhro (University of Lincoln), Benjamin Klopsch (Heinrich-Heine-Universität), Mahmut Kuzucuoğlu (Middle East Technical University), Andrea Lucchini (University of Padova), Mercede Maj (University of Salerno), Natalia Maslova (Ural Federal University), Marta Morigi (University of Bologna), Gunnar Traustason (University of Bath), Pavel Zalesski (University of Brasília), Efim Zelmanov (University of California San Diego), and Pavel Shumyatsky — special anniversary speaker (University of Brasília).

The format for the conference will also include a limited number of contributed talks and a poster session. Further details, including how to register and how to submit a talk/poster proposal, can be found at the conference website.

*Contact*: pavel60conference@gmail.com.

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On Wednesday 29th March 2023, the Charlotte Centre for Algebra had the pleasure of virtually welcoming** Cristina Acciarri (University of Modena and Reggio Emilia & University of Brasilia)** for a talk entitled *On profinite groups with restricted centralizers of π-elements* at the research seminar of Lincoln University.

**Abstract: **A group G is said to have restricted centralizers if for each g in G the centralizer C_{G}(g) either is finite or has finite index in G. This notion was introduced by A. Shalev, who proved that a profinite group in which all centralizers are restricted is virtually abelian, that is, has an abelian subgroup of finite index. In this talk we will consider a much more general situation, where the restrictedness condition is imposed only on *π*-elements of a profinite group G, for an arbitrary set of primes *π*.

**Abstract:** We investigate fixed-point properties of automorphisms of groups similar to R. Thompson’s group F. Revisiting work of Gonçalves-Kochloukova, we deduce a cohomological criterion to detect infinite fixed-point sets in the abelianization, implying the so-called property R∞. Using the BNS Σ-invariant and drawing from works of Gonçalves-Sankaran-Strebel and Zaremsky, we show that our tool applies to many F-like groups, including Stein’s F_{2,3}, Cleary’s F_{τ’}, the Lodha-Moore groups, and the braided version of F.

The *Groups St Andrews* conferences started in 1981 and have grown to be one of the largest group theory conferences on earth. The conferences take place roughly every 4 years; an article about their history can be found here.

Groups St Andrews was the first conference Simon ever attended, a year before he started his first post-doc, so it was a huge honour for him to be invited to give a one hour plenary talk at the Groups St Andrews conference in 2022. Simon spoke about his joint work with Colin Reid on the theory of local action diagrams. A survey article on his talk will be published in the conference proceedings later this year.

]]>**Ged Corob Cook** and **Paula M Lins de Araujo** will be invited speakers at the forthcoming international workshop “Asymptotic Algebra 2023”, which will take place on March 9th – 10th, 2023 in the FernUniversität in Hagen (Germany).