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ItemAnalytic Properties of Dispersion Relations and Spectra of Periodic Operators(Georgia Institute of Technology, 2016-10-11) Kuchment, PeterThe 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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ItemQuantum Approximate Markov Chains and the Locality of Entanglement Spectrum(Georgia Institute of Technology, 2016-10-11) Brandão, FernandoIn 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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ItemMicrolocal Methods in Dynamical Systems(Georgia Institute of Technology, 2016-10-10) Zworski, MaciejMicrolocal 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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ItemA Class of Asymmetric Gapped Hamiltonians on Quantum Spin Chains and its Characterization(Georgia Institute of Technology, 2016-10-09) Ogata, Yoshiko
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ItemUniversality of Transport Coeffcients in the Haldane-Hubbard Model(Georgia Institute of Technology, 2016-10-08) Giuliani, Alessandro
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ItemEmergent Pfaffian Relations in Quasi-Planar Models(Georgia Institute of Technology, 2016-10-08) Aizenman, Michael
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ItemHoneycomb Schroedinger Operators in the Strong Binding Regime(Georgia Institute of Technology, 2016-09-09) Weinstein, Michael