**21st January - 14:30 (****Link: https://videoconf-colibri.zoom.us/j/87292833142****) **

From 2020 on, it goes without saying that the study of epidemics is of the utmost importance. Mathematical models that can explain disease dynamics and evaluate and predict the impact of control measures have long been used, ever since Kermack–McKendrick's theory. We will discuss the possible contributes a mathematician can make for the epidemics' understanding, from more theoretical to more practical aspects of it. We will visit some examples starting from the most basic model the SIR model. Different epidemiological questions will drive different mathematical formulations with the corresponding techniques. Our job is to choose the most appropriate formulation to answer these questions or to develop new ones.

In this presentation, a brief introduction to Mathematical Logic and Incompleteness Theorems will be made, the subject addressed in my Master's Dissertation on Diagonalization in Formal Mathematics.

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I did my basic training in mathematics at FCUL. During my PhD, I have embarked on an adventure, moving to the field of applications to epidemiology. I worked on models for infectious diseases at the Gulbenkian Institute of Science, integrated a multidisciplinary team led by Dr. Gabriela Gomes. I am a professor at FCT since 2001 and a member of CMA (Centro de Matemática e Aplicações) at NOVA. I work in collaboration with several colleagues from CMA. With Paulo Doutor, Fabio Chalub and Maria do Céu Soares we are interested in the influence of human behavior on the success of disease control measures, combining two very interesting study areas - game theory and epidemiology. In collaborations with Gracinda Guerreiro e Manuel Esquível we are studying models with regime switches. More recently, with Magda Rebelo, we became interested in epidemiological models with space distribution. I frequently collaborate with Cristiana J. Silva and Delfin Torres from CIDMA, U Aveiro, on optimal control problems for disease transmission models. At the present moment, I am part of a research project on COVID-19, led by Baltazar Nunes, INSA.

I did my basic training in mathematics at FCT NOVA. My PhD was in dynamical systems and thermodynamic formalism, namely studying multifractal analysis for flows with Luis Barreira in IST. Now I'm interested in epidemiological models and how the human behaviour affects the evolution of the dynamics of the propagation of infectious diseases, considering individual choices regarding vacination and other controls polices. In this field I work with several other researchers in DM and CMA/FCT/UNL. I am a professor at FCT since 1999 and a member of CMA (Centro de Matemática e Aplicações) at NOVA.

Paulo Guilherme Santos is a PhD student at Departament of Mathematics in FCT-NOVA and at Universität Tübingen, and a Fulbrighter at Carnegie Mellon University. His area of study is Mathematical Logic, more specifically the Theory of Demonstration. A prize was awarded to his Master's dissertation which led to the publication of a book by the prestigious scientific publisher Springer.