## 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.

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## 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.

## Sandro Mattarei visiting the University of Milano Bicocca

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.

## Visit by Dr Rachael Camina

Dr Rachel Camina (University of Cambridge)  visited School of Mathematics and Physics on  29 March 2017. She gave a talk “Vanishing Class Sizes” at the Algebra research seminar.

## Algebra Seminar in Lincoln: talk by Rachel Camina

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.

## New paper

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

Abstract: Consider an ordinary generating function $\sum_{k=0}^{\infty}c_kx^k$, of an integer sequence of some combinatorial relevance, and assume that it admits a closed form $C(x)$. Various instances are known where the corresponding truncated sum $\sum_{k=0}^{q-1}c_kx^k$, with $q$ a power of a prime $p$, also admits a closed form representation when viewed modulo $p$. Such a representation for the truncated sum modulo $p$ frequently bears a resemblance with the shape of $C(x)$, despite being typically proved through independent arguments. One of the simplest examples is the congruence $\sum_{k=0}^{q-1}\binom{2k}{k}x^k\equiv(1-4x)^{(q-1)/2}\pmod{p}$ being a finite match for the well-known generating function $\sum_{k=0}^\infty\binom{2k}{k}x^k= 1/\sqrt{1-4x}$.

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 $\mathrm{Li}_d(x)=\sum_{k=1}^{\infty}x^k/k^d$, and after supplementing them with some new ones we obtain closed-forms modulo $p$ for the corresponding truncated sums, in terms of finite polylogarithms $\pounds_d(x)=\sum_{k=1}^{p-1}x^k/k^d$.

## Anita Thillaisundaram in Women in Maths.

University of Lincoln Lecturer, Anita Thillaisundaram has been featured in Women in Maths.