Archiv kolokvií
Kolokviální přednáška - Phan Thanh Nam - Semiclassical analysis and Lieb-Thirring inequality PDF Tisk

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.

Aktualizováno Úterý, 12 Prosinec 2017 09:05
 
Záznam kolokviální přednášky - Laszlo Erdös - Universality of random matrices and log-gases PDF Tisk

Kolokviální přednáška se konala ve středu 12. října 2016, v 16:00 v posluchárně M1

Laszlo Erdös (IST, Rakousko)

Universality of random matrices and log-gases

Abstract:

The Wigner-Dyson-Mehta conjecture asserts that the local eigenvalue statistics of large real and complex Hermitian matrices with independent, identically distributed entries are universal in a  sense that  they depend only on the symmetry class of the matrix and otherwise are independent of the details of the distribution.
We present the recent solution to this half-century old conjecture. We explain how stochastic tools, such as the Dyson Brownian motion, and  PDE ideas, such as De Giorgi-Nash-Moser regularity theory, were combined in the solution.
We also show related results for log-gases that represent a  universal model for strongly correlated systems.

Záznam přednášky ZDE

Aktualizováno Úterý, 12 Prosinec 2017 09:06
 
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