Topic: 
tba 
Date: 
08.04.19 
Time: 
16:15 
Place: 
H6 
Guest: 

EPFL Lausanne 

Abstract: 

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Topic: 
On symmetryprotected topological states: from free fermions to the Haldane phase 
Date: 
01.02.19 
Time: 
16:15 
Place: 
H6 
Guest: 

University of Cologne 

Abstract: 
The NobelPrize winning Haldane phase of spin1 antiferromagnetic spin chains is a paradigm for symmetryprotected topological phases. When local charge fluctuations are allowed, there has been a debate: protection by what? My answer is that there exists an adiabatic path to a freefermion topological phase of class AIII, protected by a particlehole symmetry. To set the stage, I will review Dyson’s Threefold Way and recall the Tenfold Way of disordered fermions. 
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Topic: 
tba 
Date: 
02.04.19 
Time: 
14:15 
Place: 
D6135 
Guest: 
Masakiyo Kitazawa 
Osaka University 

Abstract: 

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Topic: 
Coupled Superconducting Qubits 
Date: 
25.01.19 
Time: 
14:15 
Place: 
D2240 
Guest: 
Timo Gahlmann 
Universität Bielefeld 

Abstract: 

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Topic: 
Rate of Convergence to the Circular Law 
Date: 
17.01.19 
Time: 
17:15 
Place: 
D5153 
Guest: 
Jonas Jalowy 
Bielefeld University 

Abstract: 
> It is well known that the (complex) empirical spectral distribution of a > nonHermitian random matrix with i.i.d. entries will converge to the > uniform distribution on the complex disc as the size of the matrix tends > to infinity. In this talk, we investigate the rate of convergence to the > Circular Law in terms of a uniform, 2dimensional Kolmogorovlike > distance. The optimal rate of convergence is determined by the Ginibre > ensemble and is given by $n^{1/2}$. I will present a smoothing > inequality for complex measures that quantitatively relates the > Kolmogorovlike distance to the concentration of logarithmic potentials. > Combining it with results from local circular laws, it is applied to > prove nearly optimal rate of convergence to the circular law with > overwhelming probability. Furthermore I will relate the result to other > distances, present an analogue for the empirical root measure of Weyl > random polynomials with independent coefficients and discuss a possible > generalization for products of independent matrices. The talk is based > on joint work with Friedrich Götze. 
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Topic: 
On Kac polynomials and truncations of random orthogonal matrices 
Date: 
30.01.19 
Time: 
16:00 
Place: 
V3201 
Guest: 
Mihail Poplavskyi 
King's College London 

Abstract: 
Zeros of random polynomials give a rise to a point process which does look similar to the ones arising in RMT but has no integrable structure. We discuss a long standing problem of finding persistence probability asymptotic behaviour for the family of Kac polynomials of even large degree. We first use imprecise connection to the model of truncations of random orthogonal matrices and calculate persistence probability by using integrability of corresponding RMT model. We then present recent progress in solving another integrable model, namely Gaussian Stationary Process with sech correlations, which was shown in 2002 [Dembo, Poonen, Shao, Zeitouni] to give a precise approximation for Kac polynomials. The talk is based on joint works with M. Gebert (QMUL/UC Davis), G. Schehr (LPTMS). 
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