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School of Mathematics

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Analytic Properties of Dispersion Relations and Spectra of Periodic Operators

2016-10-11 , Kuchment, Peter

The talk will survey some known results and unresolved problems concerning analytic properties of dispersion relations and their role in various spectral theory problems for periodic operators of mathematical physics, such as spectral structure, embedded impurity eigenvalues, Greens function asymptotics, Liouville theorems, etc.

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A Class of Asymmetric Gapped Hamiltonians on Quantum Spin Chains and its Characterization

2016-10-09 , Ogata, Yoshiko

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Honeycomb Schroedinger Operators in the Strong Binding Regime

2016-09-09 , Weinstein, Michael

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Quantum Approximate Markov Chains and the Locality of Entanglement Spectrum

2016-10-11 , Brandão, Fernando

In this talk I will show that quantum many-body states satisfying an area law for entanglement have a local entanglement spectrum, i.e. the entanglement spectrum can be approximated by the spectrum of a local model acting on the boundary of the region. The result follows from a version of the Hammersley-Clifford Theorem (which states that classical Gibbs states are equivalent to Markov networks) for quantum approximate Markov chains. In particular I'll argue that those are in one-to-one correspondence to 1D quantum Gibbs states

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Universality of Transport Coeffcients in the Haldane-Hubbard Model

2016-10-08 , Giuliani, Alessandro

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Microlocal Methods in Dynamical Systems

2016-10-10 , Zworski, Maciej

Microlocal analysis exploits mathematical manifestations of the classical/quantum (particle/wave) correspondence and has been a successful tool in spectral theory and partial differential equations. We can say that these last two fields lie on the quantum/wave side. Recently, microlocal methods have been applied to the study of classical dynamical problems, in particular of chaotic (Anosov) flows. I will illustrate this by proving that the order of vanishing of the dynamical zeta function at zero for negatively curved surfaces is given by the absolute value of the Euler characteristic (joint work with S Dyatlov).

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Emergent Pfaffian Relations in Quasi-Planar Models

2016-10-08 , Aizenman, Michael

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