Alexandros Eskenazis (CNRS, Sorbonne Université): Learning low-degree functions on the discrete hypercube

Let f be an unknown function on the n-dimensional discrete hypercube. How many values of f do we need in order to approximately reconstruct the function? In this talk we shall discuss the random query model for this fundamental problem from computational learning theory. We will explain a recently discovered connection with a family of polynomial inequalities going back to Littlewood (1930) which will in turn allow us to derive sharper estimates for the the query complexity of this model, exponentially improving those which follow from the classical Low-Degree Algorithm of Linial, Mansour and Nisan (1989), while maintaining a running time of the same order. Time permitting, we will also show a matching information-theoretic lower bound and extensions beyond the discrete hypercube. Based on joint works with Paata Ivanisvili and Lauritz Streck.

Volker Mehrmann (TU Berlin): Mathematical modeling, simulation and control of open physical systems via port-Hamiltonian systems

Most real world dynamical systems consist of subsystems from different physical domains, modelled by partial-differential equations, ordinary differential equations, and algebraic equations, combined with input and output connections. To simulate and control such complex systems, in recent years the class of dissipative port-Hamiltonian (pH) descriptor systems has emerged as a very powerful mathematical modeling paradigm. The main reasons are that the network based interconnection of pH systems is again pH, Galerkin projection in PDE discretization and model reduction preserve the pH structure. Furthermore, the physical properties are encoded in the geometric properties of the flow as well as the algebraic properties of the equations. Dissipative pH systems form a very robust representation under structured perturbations and directly indicate Lyapunov functions for stability and passivity analysis. Another advantage of energy based modeling via pH systems is that each separate model of a physical system can be a whole model catalog from which models can be chosen in an adaptive way within simulation and optimization methods. We discuss the model class of constrained pH systems and its mathematical properties. We illustrate the results with some real world examples from gas transport and district heating systems and point out emerging mathematical challenges.

Rupert Frank (Ludwig-Maximilians-Universität München):The Wehrl entropy problem: mathematical physics meets complex analysis and representation theory

The coherent state transform, under various names, appears in many fields of mathematics and physics. It is associated with representations of a group. In this talk we are concerned with the problem of minimizing the entropy of the coherent state transform and we explain how complex analysis can be used to achieve this in certain settings. We discuss various open questions.