# Seminário *O que é…?* / *What is…?* seminar

*O que é…?*

*What is…?*

Upcoming seminars | Previous | What is the ** What is…?** seminar? | Organizers

## Upcoming seminars

## Previous seminars

Previous seminar are available at CMA-UBI Youtube channel.

**> What is… the Langlands Program? Sérgio Mendes**** (ISCTE – IUL & CMA-UBI, Portugal)**

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July, 21th, 2021 | 4 pm (Portugal time, GMT/UTC+0)

Let f ∈ Z[x] be an irreducible monic polynomial of degree n > 0 with integer coefficients. Given a prime p, reducing the coefficients of f modulo p, gives a new polynomial which can be reducible. A reciprocity law is the law governing the primes modulo which f factors completely. The celebrated quadratic reciprocity law, introduced by Legendre and completely solved by Gauss, is the case when f has degree two. Many other reciprocity laws due to Eisenstein, Kummer, Hilbert and others lead to the general Artin’s reciprocity law and (abelian) class field theory in the early 20th century.

In 1967, in a letter to André Weil, Robert Langlands paved the way for what is known today as the Langlands Program: a set of far reaching conjectures, connecting number theory, representation theory (harmonic analysis) and algebraic geometry. It contains all the abelian class field theory as a particular case, and another special case plays a crucial role in Wiles’s proof of Fermat’s Last Theorem.

There is a vast amount of number theory problems than can be studied in the framework of the Langlands Program, namely: (i) non-abelian class field theory; (ii) several conjectures regarding zeta-functions and L-functions; (iii) and an arithmetic parametrization of smooth irreducible representations of reductive groups.

In this talk we will give an elementary introduction to the Langlands Program, dedicating special attention to the local Langlands correspondence and explain how it can be seen as a general non-abelian class field theory. We shall concentrate more on examples, avoiding general and long definitions.

If time permits, an application to noncommutative geometry will also be presented.

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**> What is… Ramsey theory? Manuel Silva**** (Universidade Nova de Lisboa, Portugal)**

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June, 23th, 2021 | 4 pm (Portugal time, GMT/UTC+0)

**> What is… a moduli space? ****André Oliveira (CMUP & UTAD, Portugal)**

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May, 19th, 2021 | 4 pm (Portugal time, GMT/UTC+0)

**> What is… Symbolic Dynamics? ****Yuri Lima**** (Universidade Federal do Ceará, Brazil)**

March, 17th, 2021 | 3 pm (Portugal time, GMT/UTC+0)

Symbolic dynamics is a very useful tool that, in a nutshell, allows to represent dynamical systems by a combinatorial model of sequences of symbols, in a way that many dynamical and statistical properties of the original system are obtained by the study of the combinatorial model. In this talk, we will give a gentle introduction to this topic and explain how a geometrical configuration known as Markov partition allows to construct symbolic dynamics.

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## What is the *What is…?* seminar?

*What is…?*

The Center of Mathematics and Applications of University of Beira Interior (CMA-UBI) is promoting a ** What is…?** seminar series.

The ** What is…?** seminars aim to expose a variety of mathematical themes for a wide audience. The topics go from mathematical culture issues to new and challenging ideas in distinct areas of Mathematics. In the audience we expect mathematicians and graduate students which are not necessarily familiar with the theme. These topics will certainly enrich the mathematical culture of researchers, teachers and students, and spark their curiosity to new subjects.

Due to Covid-19 these seminars will run for the next sessions in an on-line format (ZOOM).

Moreover,

– talks will have from 30 to 45 minutes, plus some additional minutes to questions and comments;

– talks will take place preferably on Wednesdays, 3pm (Portugal time zone: UTC+0/GMT+0, wintertime), but adjustments on schedule can be made;

– talks will not be recorded, unless the speaker suggests; it is also possible to share the notes on the website of the seminar.