Umberto Biccari is a Ph. D. Currently he holds a Postdoctoral position at the ERC Advanced Grant project DyCon under the supervision of Prof. Enrique Zuazua (Universidad Autónoma de Madrid and DeustoTech). In the past, he collaborated within the ERC research project NUMERIWAVES.
My primary field of expertise is the analysis of Partial Differential Equations, both from the theoretical and from the numerical point of view, with a particular emphasis on non-local models and control theory. My contributions to the topic spread among different areas of PDE analysis, including:
- The study of controllability properties of hyperbolic, parabolic and dispersive PDE, involving the
fractional Laplacian, integral kernels, singular inverse-square potentials and/or variable degenerate
coefficients, memory terms.
- Numerical controllability for non-local parabolic PDE involving the fractional Laplacian.
- Regularity results for non-local elliptic and parabolic PDE involving the fractional Laplacian.
- Mathematical and numerical asymptotic analysis for the propagation of solutions of wave-like
processes in a local and non-local setting.
- Analysis and control of collecting behavior models and their micro-macro limit.
Besides, I am working on the development of mathematical and computational tools for the model, stability analysis, and control of hybrid AC/DC power grids. This is the core topic of two shared research project between our team, the University of Mondragón (Basque Country), and three industrial partners strongly committed with the topics of control and energy management.
- Ph. D summa cum laude in Mathematics (Sep 2013 – Dec 2016), University of the Basque Country and BCAM – Basque Center for Applied Mathematics, Bilbao, Spain.
- Internship (Mar 2013 – Aug 2013), BCAM – Basque Center for Applied Mathematics, Bilbao, Spain, ERC Advanced Grant FP7-246775 NUMERIWAVES.
- Master degree in applied mathematics (2010 – 2012), University of Florence, Italy.
- Bachelor’s Degree in Mathematics (2007 – 2010), University of Florence, Italy.
On the controllability of Partial Differential Equations involving non-local terms and singular potentials
Advisor: Prof. Enrique Zuazua – Universidad Autónoma de Madrid and DeustoTech – University of Deusto – Bilbao, Spain
Description: In this thesis we study the controllability and observability of certain types of Partial Differential Equations, that describes several phenomena arising in many fields of the applied sciences, such as elasticity theory, ecology, anomalous transport and diffusion, material science, filtration in porus media and quantum mechanics. In particular, we focus on the analysis of PDEs with non-local and singular terms.
View the PhD thesis
A free boundary problem for the $CaCO_3$ neutralisation of acid waters
Advisors: Prof. Riccardo Ricci and Dr. Angiolo Farina – University of Florence, Italy.
Description: In this thesis, we analyze a parabolic free boundary model arising from a problem of neutralization of acid waters via the filtration through calcium carbonate. After having developed the model according to the Physics, we computed an approximate but reliable solution, investigating its properties and its asymptotic behavior. This analysis has been repeated also in cylindrical and spherical geometry, both configurations being relevant in the description of the physical phenomena at the basis of our model.
- 21.08.2019 Controllability of the 1d fractional heat equation under positivity constraints, 8th workshop on Partial Differential Equations, optimal design and numerics, Benasque, Spain, PDF Slides
- 03.04.2019 Dynamics and control for multi-agent networked systems, Universidad de Cantabria, Santander, Spain, PDF Slides
- 14.03.2019 Dynamics and control for multi-agent networked systems, Friedrich-Alexander Universität, Erlangen, Germany, PDF Slides
- 05.12.2018 Controllability of a one-dimensional fractional heat equation: theoretical and numerical aspects, 1st workshop on dynamics, control and numerics for fractional PDE’s, San Juan, Puerto Rico, U.S, PDF Slides
- 30.08.2018 Propagation of one and two-dimensional discrete waves under finite difference approximation, 14th French-Romanian conference in applied mathematics, Bordeaux, France, PDF Slides
- 06.07.2018 Propagation of one and two-dimensional discrete waves under finite difference approximation, University of Craiova, Romania, PDF Slides
- 01.03.2018 Controllability of Partial Differential Equations with integral kernels, MINAKE 2018 – Microlocal and Numerical Analysis, Kinetic Equations Control Conference, Madrid, Spain, PDF Slides
- 29.08.2017 Finite Element approximation of the one-dimensional fractional Poisson equation with applications to numerical control, 7th workshop on Partial Differential Equations, optimal design and numerics, Benasque, Spain, PDF Slides
- 25.08.2017 Control of partial differential equations involving the fractional Laplacian, 7th workshop on Partial Differential Equations, optimal design and numerics, Benasque, Spain, PDF Slides
- 08.03.2017 Null controllability for a heat equation with a singular inverse-square potential involving the distance to the boundary function, Universidad Autónoma de Madrid, Spain.
- 24.06.2019 – 28.06.2019 Course on control problems for non-local PDE , University of Naples Slides here
- 2018/2019 Course on Mathematical Methods For Control Theory, University of Deusto.
- 2017/2018 Course on Mathematical Methods For Control Theory, University of Deusto.
IKERTRAMOS call 2019: positive evaluation of the Agencia de Calidad del Sistema Universitario Vasco (UNIBASQ) for the research activity in the 6 years period 2013-2018.