Interview with Marius Tucsnak, invited speaker at ICM2022

Link to the virtual ICM 2022 talks

What is your research field?

The main part of my  work is devoted to the theory of control and optimization for systems governed by partial differential equations (PDEs). These systems appear naturally as mathematical models in numerous applications in physics, engineering, biology, and medicine. One of the main problems for this theory is to characterize the states of these systems that can be achieved by varying a function (the control) in an admissible set. The question remains open in many situations of interest. Recently, I have been interested in attainable states for systems described by the heat equation, by establishing new connections with the theory of analytic function spaces. Other systems that particularly interested me are those describing the movement of a solid within a liquid as, for example, those that model how aquatic organisms swim.

Are there places or meetings that were decisive for your career? Or findings that have profoundly affected the way you do mathematics?

Participating  (from 1990) at the emergence, under the leadership of J-L Lions, of the modern theory of the controllability of PDEs, was a key moment in my early career. The unique synthesis of the PDE methods and other fields of analysis (including harmonic, micro-local, and nonlinear) in this new context played a major role in my mathematical development.

Have you already decided what you are going to talk about at the ICM?

Yes, I’m going to explain a series of results found in the last three years of collaborative work with colleagues at the University of Bordeaux, about attainable spaces of systems defined by parabolic PDEs. First up is a complete description of the heat equation in one spatial dimension. I will then present some new properties of the heat semigroup and end with a study of the robustness of attainable states with respect to certain disturbances.

What does this conference represent for you?

To be an ICM  invited speaker is, of course, a great honour for me.