## Category Archives: News and announcements

### Dr Stephen P. Glasby from the University of Western Australia visited the University of Lincoln

Dr Stephen P. Glasby from the University of Western Australia’s Centre for the Mathematics of Symmetry and Computation visited Dr Simon Smith at the University of Lincoln School of Mathematics and Physics this week.

### Maths & Physics at Lincoln: EDT Headstart residential course

The University of Lincoln has hosted a EDT Headstart  residential, where thirty students in Year 12 from all over the country have stayed from 10th to 13th July to get an introduction to university life at Lincoln, to visit the facilities of our campus, but especially to experience several lectures and workshops in Mathematics, Physics, and Engineering. Two of the three half-day sessions devoted to academic tasters were held by the School of Mathematics and Physics, and coordinated by Dr Sandro Mattarei. Three hours in the morning and three in the afternoon of 11th July the students enjoyed the following sessions:

• What is Chaos? – A lecture given by Dr Andrea Floris
• Patterns in nature: a mathematical view – A lecture given by Dr Danilo Roccatano
• Group Theory: algebra of transformations – A lecture given by Dr Evgeny Khukhro (whose presentation is available for download)
• Pascal’s triangle and the Sierpinski gasket – A lecture given by Dr Sandro Mattarei followed by a computer implementation presented by Dr Bart Vorselaars
• There’s more to light than meets the eye! – A lecture given by Dr Matt Booth

Before the last lecture the students sat a short test on the contents of the previous lectures, and at the end of the afternoon the best performers received a prize and a certificate for their effort:

Alex Blake – First prize

Lisa Fordham – Second prize

Alice Harray – Second prize

Eleanor Mckay – Second prize

Amir Allidina – Third prize

### New paper accepted in Journal of Number Theory

The paper by Sandro Mattarei and Roberto Tauraso, From generating series to polynomial congruenceshas been accepted for publication in Journal of Number Theory.

(You may find the final version in preprint form at https://arxiv.org/pdf/1703.02322.pdf.)

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

### Industrial and Financial Mathematics module in Lincoln

Mathematics students in their second year gave great feedback on their Industrial and Financial Mathematics module. This module is intended to showcase some of the industrial applications of mathematics, with an emphasis in the second half on finance.

A series of guest lectures were given by people from industry who use mathematics in their line of work. Talks were given by people who have worked in:

• Banking (Goldman Sachs and Santander)
• Logistics (SYSTRA)
• Engineering (Siemens)
• Medicine (University Medical Center Groningen)

Students also had to produce a report for a simulated food-tech start-up in which they used big data analytical techniques to help launch a new product line.

### Conference “Groups, Rings and the Yang–Baxter equation”

Evgeny Khukhro gave an invited talk at the international conference “Groups, Rings and the Yang–Baxter equation”, which was held in Spa, Belgium, on June 18–24, 2017. He spoke on “Almost Engel finite, profinite, and compact groups”.

### Maths and physics outreach lectures in Isaac Newton Building

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.

### Maths & Physics at Lincoln: EDT Headstart residential course

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!

### Call for new Kourovka problems in Group Theory

Evgeny Khukhro announced a start for preparation of the new 19th edition of the Kourovka Notebook” — the famous collection of unsolved problems in Group Theory and related areas. This publication originated in Novosibirsk in 1965, since then gained world-wide popularity and now includes more than 1000 problems by about 400 authors from all over the world. Nowadays it is published on the web but still retains discrete issues appearing every 3–4 years, with more frequent updates online.

For more than 50 years the “Kourovka Notebook” has served as a unique means of communication for researchers in Group Theory and nearby fields of mathematics. Maybe the most striking illustration of its success is the fact that more than 3/4 of the problems from the first issue have now been solved! (Of course, it is often easier to propose a new problem than to solved an old one…)

Everybody is welcome to propose new problems to be included in the new edition. Problems may “belong” to those who propose them, or otherwise. In the latter case, one can indicate the author(s) of the problem (if different from the person proposing), or simply that this is a “well-known problem”. In order that the progress would be “measured” and seen, the preference is usually given to concrete questions that admit “yes” or “no” answers.

The Editors also welcome any other comments on, or/and solutions of, existing problems; the current version on Arxiv incorporates all comments so far.

The problems and comments can be sent to any of the Editors (preferably by e-mail):

Evgeny Khukhro khukhro@yahoo.co.uk or Victor Mazurov mazurov@math.nsc.ru

### Algebraic conference in Lincoln

School of Mathematics and Physics conducted the conference “Maximal Conditions and Embeddings of Profinite Groups” in University of Lincoln on 2nd June. The conference was supported by a grant of the London Mathematical Society under the ‘Celebrating New Appointments’ scheme, which was secured by Dr Anitha Thilaisundaram.  The participants included Prof Dugald Macpherson (Leeds), Prof Rögnvaldur G. Möller (University of Iceland, Reykjavik), Prof Peter Neumann (Oxford), Prof Dan Segal (Oxford), Prof John Wilson (Oxford), as well as young researchers from Australia, Germany, and UK. The talks were given by Alejandra Garrido (Düsseldorf), Simon Smith (Lincoln), Anitha Thillaisundaram (Lincoln), and John Wilson (Oxford); see the programme here.

After the conference a wine reception was addressed by the Pro Vice Chancellor of UoL / Head of College of Science and Engineering Prof Libby John and Prof John Wilson (Oxford). The reception was followed by the conference dinner.

### Two talks at LARA seminar by Prof Rögnvaldur G. Möller and by Dr Colin Reid

Another enhanced Lincoln Algebra Research Afternoon (LARA) before the conference “Maximal Conditions and Embeddings of Profinite Groups” on 2nd June. On 31th of May we had two talks:

Prof Rögnvaldur G. Möller (University of Iceland), Minimal valency of a Cayley–Abels graph and group properties,

Dr Colin Reid (ARC DECRA Fellow at University of Newcastle, Australia), Chief series of locally compact groups.

Prof R. G. Möller

Dr C. Reid