Pablo González Mazón (ESR5)

Work and Education:

Oct 2020 – Today: Ph.D. at INRIA Sophia-Antipolis, Université Côte d’Azur
Apr 2020 –  Jul 2020: Researcher at the Laboratoire d’Informatique Gaspard Monge
Sep 2019 – Apr 2020: Master’s degree in Mathematics at Université Gustave Eiffel, Labex Bézout fellow. Master’s thesis: “Center sets and the Carathéodory number of real algebraic varieties”
Sep 2014 – Jul 2019: Bachelor’s degree in Mathematics at Universidad de Cantabria
Sep 2014 – Jul 2019: Bachelor’s degree in Physics at Universidad de Cantabria

Research activities:
Birational transformations, geometric modelling for scientific computation and design, semialgebraic geometry, convex algebraic geometry, and combinatorial geometry.

Seminars, Congresses, and Schools:

  • (2021, 1-5 March) I shall attend the Journées Nationales de Calcul Formel
  • (2021, 1-8 Feb) GRAPES’ Doctoral School I, Midterm meeting
  • (2021) AROMATH Seminars. Last 13th of January, I gave the talk “Center sets and the Carathéodory number of real algebraic varieties”
  • (2020) INRIA’s Ph.D. Seminars at INRIA Sophia-Antipolis
  • (2020, 21-15 Sep) Virtual Heidelberg Laureate Forum 2020
  • (2020, 25-28 Feb) 5th EACA International School on “Computer algebra and its applications”. At the school, I gave the talk “Constructive partitioning polynomials and applications”

Social Engagement: 


Research Project: Generation of valid high-order curved meshes
Advisor: Laurent Busé
Institution: INRIA, France

Curvilinear meshes offer more flexibility and better accuracy compared to (more common) simplicial meshes. Their generation is an active area of research: it requires to conform curved elements to a given boundary geometry, enforce a smooth and non-degenerate Jacobian everywhere, and keep the mesh as coarse as possible. Several attempts exist to accommodate these three properties. Building on a new variational approach, called Curved Optimal Delaunay Triangulation (CODT), that has been recently introduced to generate such meshes, the main objective of this project will be to develop new methods in order to generate a valid high-order curved meshes made of Bézier triangles. For that purpose, algebraic and subdivision techniques will be investigated for the detection of self-intersection and surface/surface intersection loci, for the preservation of sharp features and for controlling regularity.

Expected Results: a reliable and robust algorithm to detect intersection and self-intersection of low degree Bézier triangles, and an improved CODT method preserving the topology and sharp features of the input data.

The project will take place at INRIA Sophia-Antipolis. The PhD will be awarded by the University of Nice.

Secondments are planned at Universitat de Barcelona (Barcelona, Spain), and at industrial partner RISC-SW (Linz, Austria).

Publications:

  • (2019) I have translated into Spanish the vignette “Goodstein Sequences: The Power of a Detour via Infinity” from the Blog of the Klein Project
  • (2018) I have been published the solution to the “Problem 327” proposed at La Gaceta de la Real Sociedad Matemática Española, vol. 21, n.2, pp. 341-342, 2018