Mathematical Physics at IST Austria
IST Austria is a newly founded interdisciplinary research institute and graduate school near Vienna. Three professors working in mathematical physics explain their research interests and present the opportunities for PhD studies.
Jan Maas: Spatially rough stochastic PDE
Stochastic PDEs driven by very rough noise appear naturally in many physical models.
A prime example is the Kardar-Parisi-Zhang equation, that is expected to universally describe the fluctuations of a large class of random interface growth processes. In recent years major breakthroughs have been obtained in the rigorous mathematical treatment of rough SPDE, in particular through Martin Hairer's theory of regularity structures, for which he has been awarded a Fields Medal in 2014. I will give an introduction to some of the recent results in this area.
Robert Seiringer: Quantum many-body systems and Bose-Einstein Condensation
A detailed understanding of the behaviour of many-particle systems in quantum mechanics poses a formidable challenge to mathematical physics. We will summarise some of the progress made in recent years in the case of dilute Bose gases. The topics covered include, e.g., the question of existence of Bose-Einstein condensation, as well as superfluidity and quantised vortices in rotating systems. We will describe the mathematics involved in understanding these phenomena, starting from the underlying many-body Schrödinger equation.
Laszlo Erdos: Spectral universality of random matrices.
Eugene Wigner’s revolutionary vision predicted a profound dichotomy in the local statistics of the spectrum of disordered quantum systems: localized systems have independent eigenvalues, while delocalized systems follow the celebrated Wigner-Dyson random matrix statistics. We will discuss the state of the art of the rigorous mathematical approach to this problem.
Die Vorträge beginnen um 16 Uhr im Hörsaal B 004.