Tri predavanja na Matematičnem kolokviju
V okviru Matematičnega kolokvija organiziramo ciklus treh predavanj uglednih matematikov:
Volker Mehrmann: Energy based network modelling, simulation, and optimization of multi-physics systems
Abstract: Most real world dynamical systems consist of subssystems from different physical domains, modelled by partial-differential equations, ordinary differential equations, algebraic equations, combined with input and output connections. To deal with such complex system, in recent years the class of dissipative port-Hamiltonian (pH) systems has emerged as a very efficient modeling methodology. 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 and the physical properties are encoded in the geometric properties of the flow as well as the algebraic properties of the equations. Furthermore, dissipative pH system form a very robust representation under structured perturbations and directly indicate Lyapunov functions for stability analysis.
We discuss dissipative pH systems and describe how many classical models can be formulated in this class. We illustrate some of the nice algebraic properties, including local canonical forms, the formulation of an associated Dirac structure, and the local invariance under space-time dependent diffeomorphisms.
Volker Mehrmann je profesor na Tehniški univerzi v Berlinu. Je predsednik Evropskega matematičnega društva.
Marija J. Esteban: Min-max characterization and computations of eigenvalues if Dirac operators in relativistic Quantum Mechanics
Maria J. Esteban je raziskovalka na inštitutu CNRS in univerzi Paris-Dauphine v Parizu. Je predsednica Mednarodnega sveta za industrijsko in uporabno matematiko.
Martin R. Bridson, FRS: Symmetries, curved universes and unsolvable problems
Abstract: No matter what sort of mathematics you study, the symmetries (automorphisms) of the objects that you encounter form a group. In this talk we'll think about how one might go about understanding the universe of all the groups that can be described with a finite amount of information. Given a group (i.e. an abstract system of symmetry), how might one go about building objects that have exactly the given type of symmetry? Fascinating new geometries emerge from the pursuit of this question.
How easy is to recognise a familiar group that is presented to us in an unfamiliar fashion? It can be "provably impossible" -- what does this mean? We'll explore and see how the ability of geometry to interpret algorithmic problems implies that some basic problems in geometry are unsolvable.
Martin R. Bridson je profesor na Univerzi v Oxfordu in predsednik Clayovega inštituta. Je član Ameriške in Kraljeve akademije znanosti.
Podrobnosti o poteku predavanj so v priponki. Vljudno vabljeni!