Author Archives: Sandro Mattarei

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

Alex Blake – First prize

Lisa Fordham - Second prize

Lisa Fordham – Second prize

Alice Harray - Second prize

Alice Harray – Second prize

Eleanor Mckay - Second prize

Eleanor Mckay – Second prize

Amir Allidina - Third 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.

 

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

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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!

Sandro Mattarei gives a talk in Cambridge

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

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.

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.

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.

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.

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