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Eliana Barriga (Mathematics / Research Visit Fellow / Universidad de los Andes in Bogotá, Colombia), Guilia Fabrini (Mathematics and Statistics / Associated Fellow per Mentorship), Makoto Fujiwara (Mathematics / Research Visit Fellow / Meiji University, Japan), and Patrícia Nabuco Martuscelli (Political Science / AAA Fellow / Universidade de Sao Paulo, Brazil) organised this Jour fixe.

Eliana Barriga presented "New advances on locally definable and approximate groups in tame expansions of o-minimal structures".

Abstract: Groups definable and locally definable in o-minimal structures have been intensively studied for the last three decades, and it is a field of current research. An o-minimal structure is an ordered structure for which every definable subset of its universe is a finite union of points and intervals, as the real numbers. In this talk I will briefly introduce our current research project on new advances on locally definable and approximate groups in tame expansions of o-minimal structures, which is a joint project with Dr. Pantelis Eleftheriou.

Guilia Fabrini´s talk was  entitled "Numerical optimal control for nonlocal parabolic equations modeling the evolutionary dynamics of cancer cell populations under cytotoxic therapy".

Abstract: During the last decades mathematical modelling approaches have become increasingly abundant in cancer research. The complexity of cancer is well suited to quantitative approaches and it provides challenges and opportunities for new developments. The literature deals not only with cancer modeling, but it also focuses on the question of cancer treatment protocols and how to optimize them. In this talk I will present a mathematical model which can be used to study evolutionary dynamics of cancer cell populations. Moreover, I will present an optimal control problem for this model where the aim is to find the optimal strategy which minimize the density of the tumor cells. Finally, I will show the results of the numerical simulations.

Makoto Fujiwara introduced "An axiomatic approach for foundations of constructive reasoning".

Abstract: My research deals with logic and the foundations of mathematics. In particular, we focus on a logical framework for the concept of ‘constructibility’ in mathematics, i.e. a general method for building up complex objects from the ground up in terms of elementary pieces. The notion of constructibility came to the fore during the (in)famous Grundlagenstreit between David Hilbert and L.E.J. Brouwer around 1900. While a lot of research has been done since, a proper axiomatization of the constructive reasoning from a purely logical sense is still missing (in my thought). Toward axiomatizing the constructive reasoning in mathematical proofs, I have investigated the relation between weak logical principles and realizability semantics in the context of arithmetic, which is seemingly the simplest theory to formalize (elementary) mathematics. Assuming general audiences, I would talk about our axiomatic approach for foundations of constructive reasoning (without technical details), and discuss about a possible direction to apply it for finding some connections between mathematics and other fields.

Patrícia Nabuco Martuscelli  talked about " The Family Reunification of Refugees in Brazil".

Abstract: This study aims to understand how the family reunification process for refugees in Brazil is (including the procedure to ask for family reunification visas to the relatives) and what are the best practices and challenges of this policy in Brazil. To access that, I have conducted 20 semi-structured phenomenological interviews with refugees in São Paulo that asked for family reunification to their family members to map how they perceive this policy. I have also conducted 24 interviews with key actors involved in the design and implementation of the policy including experts, authorities- Ministry of Foreign Affairs, National Committee for Refugees – CONARE, UNHCR, and organizations that work directly with the refugee population. I have also conducted archival research where I accessed diplomatic correspondence between the Brazilian consular authorities and the Headquarter of the Ministry of Foreign Affairs to understand how the migration control of family reunification visas is done in Brazilian Embassies and Consulates abroad. I have analyzed how the Brazilian legislation defines family reunification and regulates this procedure and descriptive quantitative data (from CONARE and national NGOs) about the refugees that apply for family reunification: who are they, to whom they ask the visa, where, how long does the process take.