Purely Mathematics
ProverX
João Araújo (DM/FCT NOVA)
João Araújo is a researcher in the Center for Mathematics and Applications, and professor in the Mathematics Department of the Faculty of Sciences and Technology of the New University of Lisbon, works in computational algebra, has about 60 papers in international journals, many of them using ATP to solve open problems in mathematics.
Abstract: ProverX is a system that plays for automated reasoning (ATP) the same role GAP, MAGMA, Wolfram Alpha play in symbolic computation. In this talk we are going to give an overview of the capabilities of the system.
Fractional Calculus and Applications
Magda Rebelo (DM/FCT NOVA) and Beatriz Curioso (MSc Student MMA/FCT NOVA)
Magda Rebelo is a professor at Mathematics Department, NOVA School of Science and Technology (FCT NOVA), and an integrated member of the Center for Mathematics and Applications (CMA). In 2010 she finish her Ph.D in Mathematics, Speciality of Numerical Analysis at Instituto Superior Técnico. Her main interests in research are: integral equations, differential equations with fractional order and numerical analysis applied to the previous problems, among others.
Beatriz Curioso is a Master’s student finalist at NOVA School of Science and Technology (FCT NOVA). She enrolled in a Mathematics Degree in FCT NOVA in 2015 and finished in 2018 with a grade of 17. Beatriz began a Master’s course in Pure Mathematics in 2018 and her thesis is focused in Fractional Differential Equations.
Abstract: Fractional calculus was formulated in 1695, shortly after the development of classical calculus. The earliest systematic studies were attributed to Liouville, Riemann, Leibniz, among others. For a long time, fractional calculus has been regarded as a pure mathematical realm without real applications. But, in recent decades, such a state of affairs has been changed. The subject of fractional calculus has applications in diverse and widespread fields of engineering and science such as electromagnetics, viscoelasticity, fluid mechanics, electrochemistry, biological population models, optics, signals processing, etc. In this talk we present the definition of the fractional derivative given in the Caputo sense and we exploit the advantage of the fractional calculus to model a phenomena. We also present a numerical method, implemented in Python, to approximate the derivatives given in the Caputo sense and the solution of the problem that we exploit.
An Application of the Fundamental Group
José Reis (PhD Student DM/FCT NOVA)
I started my academic life as an undergraduate in Mathematics at Faculdade de Ciências e Tecnologia and finished the degree as the top-class student. Moreover, I had the chance of doing research in the context of the Scholarship Novos Talentos em Matemática. To pursue my studies, I went to London and became a master’s student at Imperial College London. There I was awarded an MSc in Pure Mathematics and wrote a project on The McKay Correspondence under the supervision of Professor Travis Schedler. Afterwards, I received a research scholarship on Hilbert’s 24th Problem and, together with Professor António Malheiro, published the paper: "Identification of Proofs Via Syzygies”. Right now, I am a PhD student under the supervision of Professor Gonçalo Tabuada.
Abstract: In this talk, we will start by defining the Fundamental Group of a Topological Space. After doing such we will compute it for the case of the Circle and we shall give a topological proof of the Fundamental Theorem of Algebra. If time allows we will prove Brouwer Fixed Point Theorem in Dimension 2.