On Tuesday, 9th May 2017, the Lecture Theater of the Isaac Newton Building, was used for the first time for an outreach event, organised by Sandro Mattarei in collaboration with the university’s Marketing Team. Students from the Lincoln College attended a double lecture in Maths and Physics. Marco Pinna’s lecture on the mathematics of bird flocking was followed by a lecture on Platonic solids delivered by Sandro Mattarei.

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On 11th July 2017 several members of the School of Mathematics and Physics will contribute lectures and workshops to a Headstart residential course at the University of Lincoln (see EDT Headstart). Thirty students in Year 12 from all over the country will stay from 10th to 13th July to experience several taster session of Mathematics, Physics, and Engineering.

The Maths and Physics activities will span six hours of 11th July and include sessions on the following topics:

- What is Chaos?
- Patterns in nature: mathematical views of the natural world
- Group Theory: algebra of transformations
- Pascal’s triangle and the Sierpinski gasket
- There’s more to light than meets the eye!

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On 24th May 2017 Sandro Mattarei visited the University of Cambridge and gave a seminar talk on *Generalisations of self-reciprocal polynomials.*

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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.

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**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 l*^{2}-Betti numbers and their analogues in positive characteristic, and here is an Abstract.

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Sandro Mattarei is staying for one month at the University of Milano Bicocca, invited as visiting professor. He is continuing a long collaboration with Dr Marina Avitabile on a new joint project. As you may guess from the notes on the blackboard behind them, binomial coefficients seem to always crop up in Sandro’s research one way or another (although the present topic is actually motivated by the theory of modular Lie algebras).

On a lighter note, here is a glimpse of Milan’s bubbling nightlife as seen from the safe distance of Sandro’s accommodation.

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**Dr Rachel Camina (University of Cambridge) ****will speak in the Algebra seminar on Wednesday, 29 March 2017, at 1:30pm in room MB1019 (Minerva Building, which is building 1 on the university’s map). She will talk about ***Vanishing Class Sizes.*

Abstract: For many years authors have considered the algebraic implications of arithmetic conditions on conjugacy class sizes for finite groups. We look at recent results and consider the restricted case when just vanishing class sizes are considered.

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Sandro Mattarei and Roberto Tauraso, *From generating series to polynomial congruences,* 24 pages, submitted, 2017;* *arXiv:1703.02322.

Abstract: Consider an ordinary generating function , of an integer sequence of some combinatorial relevance, and assume that it admits a closed form . Various instances are known where the corresponding truncated sum , with a power of a prime , also admits a closed form representation when viewed modulo . Such a representation for the truncated sum modulo frequently bears a resemblance with the shape of , despite being typically proved through independent arguments. One of the simplest examples is the congruence being a finite match for the well-known generating function .

We develop a method which allows one to directly infer the closed-form representation of the truncated sum from the closed form of the series for a significant class of series involving central binomial coefficients. In particular, we collect various known such series whose closed-form representation involves polylogarithms , and after supplementing them with some new ones we obtain closed-forms modulo for the corresponding truncated sums, in terms of finite polylogarithms .

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On 14th March 2017 we enjoyed another seminar within the Lincoln Algebra Research Afternoons (LARA), with Evgeny Khukhro reporting on his recent study of *Almost Engel finite, profinite, and compact groups*.

The next LARA seminar will be delivered by Sandro Mattarei on 16th May 2017.

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February 23, 2017 – 15:08
We have recently started to run an informal seminar within our Lincoln Algebra group, where we tell each other about some topic that we are working on, or interested in working on, with the aim of promoting possible collaborations between us. This is run in a more informal way than the ordinary Algebra Seminar with outside speakers. We highly encourage interruptions for questions and discussions at any time.

Our PhD student Valentina Iusa started the series on 17th January 2017, by reporting on a problem she studied in 2015 as a final project for her Italian Laurea Magistrale (which is roughly equivalent to a master’s degree). She described a new take on Hans Zassenhaus’ classification of finite near-fields.

Anitha Thillaisundaram (in the photo) followed on 14th February 2017. She gave us an introduction to branch groups and some interesting problems in the area.

The next seminar will be given by Evgeny Khukhro on 14th March 2017. He will tell us about almost Engel groups*.*

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