**Umberto Biccari**is a PhD. 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 research interests are related to the analysis of Partial Differential Equations, in particular from the point of view of control theory. During the years of my PhD I have been concerned with the study of controllability properties of hyperbolic (waves), parabolic (heat) and dispersive (Schrödinger) PDEs, involving non-local terms, singular inverse-square potentials, variable degenerate coefficients or dynamical boundary conditions. At the moment, I am getting interested in non-local transport problems, derived from models of collection behaviour.”

#### Education

**PhD 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.

#### PhD Thesis

*On the controllability of Partial Differential Equations involving non-local terms and singular potentials*

*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.

#### Master’s Thesis

*A free boundary problem for the neutralisation of acid waters*

*A free boundary problem for the 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.

#### Talks

**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.