**Data e local: 21/07/2021, 10 horas, Organizado por: Departamento de Matemática da Escola Superior de Tecnologia e Gestão do Politécnico de Leiria**

**Orador: Cristiana João Soares da Silva, CIDMA, Dept. Mathematics, University of Aveiro**

**Abstract**

In this talk we analyze the COVID-19 pandemic from a mathematical point of view, applying results from mathematical modeling, complex network and optimal control theories.

We propose a compartmental SAIRP mathematical model, for the transmission dynamics of SARS-CoV-2, given by a system of ordinary differential equations, and fit it to the number of active infected individuals with COVID-19 in Portugal. After, optimal control theory is applied considering the SAIRP model as a control system and maximizing an objective function that represents the number of people returning to ``normal life'' and, at the same time, minimizing the number of active infected individuals with minimal economical costs and a low level of hospitalizations.

We end by constructing a complex network of dynamical systems, in order to take into account the mobilities of individuals, which are known to play a decisive role in the dynamics of the epidemic. Through numerical simulations, we explore the effect of the topology of the network on the dynamics of the epidemics (disposal of connections and coupling strength) and identify which type of topology minimizes the level of infection of the epidemic.

This work is based on references [1, 2] developed under the Project Nr. 147 "Optimal Control and Mathematical Modeling of the Covid-19 Pandemic: contributions to a systemic strategy for community health intervention", in the scope of the "RESEARCH 4 COVID-19" call, financed by the Portuguese Foundation for Science and Technology (FCT).

References:

[1] Cristiana J. Silva, Carla Cruz, Delfim F. M. Torres, Alberto P. Munuzuri, Alejandro Carballosa, Iván Area, Juan J. Nieto, Rui Fonseca-Pinto, Rui Passadouro da Fonseca, Estevão Soares dos Santos, Wilson Abreu, Jorge Mira,

Optimal control of the COVID-19 pandemic: controlled sanitary deconfinement in Portugal,

Sci. Rep. 11, 3451 (2021).

https://doi.org/10.1038/s41598-021-83075-6

[2] Cristiana J. Silva, Guillaume Cantin, Carla Cruz, Rui Fonseca-Pinto, Rui Passadouro da Fonseca, Estevão Soares dos Santos, Delfim F. M. Torres,

Complex network model for COVID-19: human behavior, pseudo-periodic solutions and multiple Journal of Mathematical Analysis and Applications, in press.

https://arxiv.org/abs/2010.02368

https://www.sciencedirect.com/science/article/pii/S0022247X2100250X

Para consultar o cartaz clique aqui

Para mais detalhes visite a página oficial https://www.ipleiria.pt/estg-dmat/

Endereço para transmissão em directo https://bit.ly/3w3EZI3

**Data e local: 21/07/2021, 16h00, Organizado por: Centro de Matemática e Aplicações da Universidade da Beira Interior**

**Orador: Sérgio Mendes, ISCTE & CMA-UBI**

**Abstract**

Let $f \in Z[x]$ 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.

Para mais detalhes visite a página oficial http://wordpress.ubi.pt/cma/what-is/

Endereço para transmissão em directo https://videoconf-colibri.zoom.us/j/83030580321?pwd=Z3VLNjc0c3VXUHNqQWtLN1ZPaHY1QT09