**Abstract:**

We introduce in an abstract framework the notion of controlled infinite dimensional time invariant linear system, which includes a large class of PDE systems with boundary or distributed control. We next define the fundamental notion of reachable space for this type of system and we relate its properties with various controllability types. We mainly illustrate this theory by presenting some recent advances on a problem which was considered long time as elusive: describing the reachable space for the boundary controlled heat equation. We give, in particular, a full characterization of this space when the system is described by a one dimensional heat equation.

**Biography:**

Marius Tucsnak is Professor of Mathematics of the University of Bordeaux in France and presently visiting professor at NYU Shanghai. He holds a Master's degree in mathematics from the University of Bucarest, Romania and a Ph.D. degree from the University of Orléans, France (1992). In 1995 he obtained his Habilitation pour Diriger les Recherches from the "Université Pierre et Marie Curie", Paris. In 1992 he became Associate Professor of Mathematics at the University of Versailles, France. In 1997 he became full professor of mathematics at the University of Nancy, France. He moved to University of Bordeaux in 2015. He was an invited speaker to the International Congress of Mathematicians (ICM), 2022, and since 2013 he is a Member of Institut Universitaire de France (IUF). His fields of expertise are the analysis and the control of systems governed by partial differential equations.

*Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai*

**This event is open to the NYU Shanghai community and Math community.**