Topic: 
Topological States of Matter: The Physics Nobel Prize 2016 
Date: 
26.06.17 
Time: 
16:15 
Place: 
H6 
Guest: 

Universität Bielefeld 

Abstract: 
The 2016 Nobel Prize in Physics was awarded to David J. Thouless, F. Duncan M. Haldane, and J. Michael Kosterlitz. These theoretical physicists studied exotic kinds of phase transitions. Historically, it was assumed that phase transitions of matter are usually accompanied by the breaking of some kind of symmetry. The work of Thouless, Haldane, and Kosterlitz showed, however, that completely different kinds of phase transitions can appear in nature, which are not based on symmetry breaking but instead on topological concepts. Their work had a large impact and nowadays many such topological materials have been identified and are being discovered. In this talk I will describe the conventional view of phase transitions, contrast it with the findings of Thouless, Haldane, and Kosterlitz, and discuss some of the new materials that have been discovered recently. 
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Topic: 
Random field of gradients  Critical Phenomena and Scaling limits 
Date: 
02.06.17 
Time: 
16:15 
Place: 
V2210/216 
Guest: 

University of Warwick 

Abstract: 
Random fields of gradients are families of highly correlated random variables arising in the studies of e.g. random surfaces & interfaces and discrete Gaussian Free Fields (GFFs), random geometry, field theory, and elasticity theory. Recently their study has attained a lot of attention. There are several reasons for that. On one hand, these are approximations of critical systems and natural models for a macroscopic description of elastic systems as well as, in a different setting, for fluctuating phase interfaces. In addition, over continuum, the level lines of the GFF are connected to Schramm's SLE (an active field of modern mathematics for understanding critical phenomena) and the fields are natural spacetime analog of Brownian motions and as such a simple random object of widespread application and great intrinsic beauty. Gradient fields are likely to be an universal class of models combining probability, analysis and physics in the study of critical phenomena, and these massless fields are also a starting point for many constructions in field theory. A more recent connection are mathematical models for the CauchyBorn rule of materials, i.e., a microscopic approach to nonlinear elasticity. The latter class of models requires that interaction energies are nonconvex functions of the gradients. Open problems over the last decades include unicity of Gibbs measures and strict convexity of the free energy as well as scaling limits to the Gaussian Free Field and the decay behaviour of twopoint correlation functions. After giving a broad introduction to this recently active field of research we present in the talk Gaussian decay of correlations and the scaling to the Gaussian Free Field for a class of massless fields with nonconvex interaction using a recent renormalisation group approach. 
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Topic: 
tba 
Date: 
18.07.17 
Time: 
14:15 
Place: 
D6135 
Guest: 

Argelander Institut für Astronomie, Bonn 

Abstract: 

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Topic: 
Connecting Spin Hamiltonians from DFT Calculations to Experiment 
Date: 
06.04.17 
Time: 
14:15 
Place: 
D5153 
Guest: 
Shadan Ghassemi 
TU Berlin 

Abstract: 

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Topic: 
Nonorthogonality of eigenvectors from the HaagerupLarsen theorem 
Date: 
01.06.17 
Time: 
17:00 
Place: 
D5153 
Guest: 
Wojciech Tarnowski 
Jagiellonian University Krakow 

Abstract: 
Biunitarily invariant ensembles have been thoroughly studied in recent years from the point of view of statistics of eigenvalues. An enhanced symmetry of the probability distribution function allows us to expect that all spectral properties will be determined by the singular values only. Indeed, for large matrices, a mapping between onepoint densities is known as the HaagerupLarsen theorem. Recently, this mapping has been extended to all kpoint functions (KieburgKösters). During my talk, I will present a recent extension of the HaagerupLarsen theorem, which gives a simple mapping between the radial spectral cumulative distribution function and a certain onepoint eigenvector correlation function, built out of (nonorthogonal) left and right eigenvectors. I will discuss also its relation with the stability of the spectrum. 
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Topic: 
Matrix product ensembles of Hermitetype 
Date: 
21.06.17 
Time: 
16:00 
Place: 
V3201 
Guest: 
DangZheng Liu 
Institute of Science and Technology Austria & University of Science and Technology of China 

Abstract: 
We investigate spectral properties of a Hermitised random matrix product which, contrary to previous product ensembles, allows for eigenvalues on the full real line. We find an explicit expression of the joint probability density function as a biorthogonal ensemble. As an interesting example, we focus on the product of GUE and LUE matrices and provide explicit expressions both for the biorthogonal functions and the correlation kernel. Then a new doubleside kernel is found at the origin, which is slightly different from the Bessel kernel. This talk is based on joint work with P. J. Forrester and J. R. Ipsen. 
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