Kolokviální přednáška se koná ve středu 6.prosince 2017, od 16:00 v posluchárně M1

Aleksey Kostenko (Vienna/Ljubljana)

On Infinite Quantum Graphs

Abstract:

The notion of quantum graph refers to a graph considered as a one-dimensional simplicial complex and equipped with a differential operator (“Hamiltonian”). From the mathematical point of view, quantum graphs are interesting because they are a good model to study properties of quantum systems depending on geometry and topology of the configuration space. They exhibit a mixed dimensionality being locally one-dimensional but globally multi-dimensional of many different types.
We will review basic spectral properties of infinite quantum graphs (graphs having infinitely many vertices and edges). In particular, we will discuss recently discovered fruitful connections between quantum graphs and discrete Laplacians on graphs.

Aleksey Kostenko is a renown expert in spectral theory, publishing in journals like Inventiones (2016) and his standard collaborators include Gerald Teschl of Vienna.

Kolokviální přednáška se koná ve středu 19.4.2017, od 16:00 v posluchárně M1

Phan Thanh Nam

Semiclassical analysis and Lieb-Thirring inequality

Abstract:

In 1975, Lieb and Thirring found an elegant combination of uncertainty principle and Pauli's exclusion principle in terms of a  lower bound on the kinetic energy. Their bound agrees with the semiclassical approximation used in the Thomas-Fermi theory, up to a  constant factor. It has been a long-standing conjecture that the sharp constant coincides with the semiclassical one. In the talk, I will prove a Lieb-Thirring type inequality with the sharp constant and a gradient error term which is of lower order.