About me

Welcome to my website! Here is a bit about me

I hold a Master of Science degree in Mathematics from the University of British Columbia where I worked under the supervision of Dr. Nassif Ghoussoub. Currently, I work as an Actuary at iA Financial Group.

My main interest is Optimal Transport. I enjoy examining which properties of Classical OT remain valid for measures with infinite mass. I also spend time studying Variational Methods and a pinch of Statistics.

Research projects

The Topology Induced by the extended Wasserstein Distance

with Dr. Hugo Lavenant

The topology induced by the Wasserstein distance is the weak-* topology. This is a standard result in the literature for measures with finite and equal mass. Figalli & Gigli [2010] proved that this is also the case for measures with infinite mass but only in compact domains. In this work with Dr. Hugo Lavenant we prove that this is true also for unbounded domains. Namely, we prove that the topology induced by the extended Wassertein Distance is the weak topology in R^d \setminus {0} where the singleton is an infinite source/reservoir of mass.

The relationship between the Shape Optimization problem and the Dual problem.

With Dr. Nassif Ghoussoub and Dr. Dweik

There exists a one-to-one relationship between the Dual problem and the Shape Optimization problem for the case of measures with finite and equal mass as proved by Bouchitté & Buttazzo [2001]. In this work we prove that, for measures with infinite mass in a compact domain, as soon as we allow the measures to exchange mass with the boundary, the relation holds true. In this setting, the Shape Optimization problem takes the form of a inf-sup-inf type of problem.

Critical Point Theory, Varational Methods and Elliptic Partial Differential Equations.

with Dr. Rubia Nascimento

During undergraduate studies I had the great opportunity to spend an extensive amount of time learning about Differential Equations from Dr. Nascimento. Later, this culminated in a paper on the Concentration-Compactness Principle applied to an elliptic PDE in the critical case.

Publications

This is a selection of works I have written. If the link is not working, please email me. Likely the publication is not available to the public, but I will gladly send it to you.

With H. Lavenant. The topology induced by the extended Wasserstein metric. Manuscript. 2022.

With R.G. Nascimento, J.J. Macedo. Existence and concentration of positive solutions to the fractional Laplacian with critical discontinuous nonlinearity. Submitted for publication to the Journal of Mathematical Analysis and Applications. 2022

With N. Ghoussoub. Monge-Kantorovich Equation and its connections with Shape Optimization and Flow Minimization problems. Master Thesis. 2021.

With V. Silva. The Cauchy Riemann and Cauchy-Goursat Theorems in Complex Analysis and its application in Mathematics and Physics. Undergraduate Thesis. 2019.

With R.G. Nascimento. The Fredholm Alternative and PDE application. Final technical report to PIBIC, CNPQ. 2018.

With R.G. Nascimento. The Dirichlet Problem for Laplace’s Equation. Final technical report PIBIC, CNPQ. 2017

Skills and Techniques

Languages

Portuguese is my mother tongue. I taught English to adults and completed my Master of Science in an english speaking institution.

Programming

I used Matlab and Python to develop various basic computing tools during a Scientific computing class. I also learned Visual Basic, SQL and GGY AXIS to manage actuarial databases. Right now, I am engaged in learning R.

Entrepreneurial ventures

These are some side projects I developed in between proofs and theorems.

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