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MAFIA Seminar: Jonathan Rohleder (Stockholm University) - Hot spots of quantum graphs

08 Oct 2019   13:15

Srdečně vás zveme na další MAFIA Seminar v AR 2019/2020! Pozvání přijal Jonathan Rohleder (Stockholm University), který bude přednášet na téma Hot spots of quantum graphs. Seminář se koná v úterý 8. 10. 2019 od 13.15 hodin v budově FJFI Trojanova 13, Praha 2 v místnosti T112.

The Hot Spots Conjecture of J. Rauch asserts that the hottest and coldest points of an insulated body should move towards its boundary for large times, if the insulation is perfect. Via the semigroup associated with the Neumann Laplacian this reduces to proving that maximum and minimum of the eigenfunction(s)associated with the smallest positive eigenvalue are located on the boundary. This conjecture is not true in full generality but is currently open, for example, for convex domains. In this talk we will examine the corresponding question on metric graphs: for the Laplacian on a finite metric graph with standard (continuity and Kirchhoff) vertex conditions we consider the possible distribution of maxima and minima of eigenfunctions associated with the smallest nonzero eigenvalue. Among other things, we give examples to show that the usual notion of "boundary" of a metric graph, namely the set of vertices of degree one, has limited relevance for determining the "hottest" and "coldest" parts of a graph. This is joint work with James Kennedy (Lisbon).

Fakulta jaderná a fyzikálně inženýrská, Trojanova 13, Praha 2
Fakulta jaderná a fyzikálně inženýrská ČVUT v Praze
Contact person
Ing. Matěj Tušek, Ph.D., matej.tusek@fjfi.cvut.cz