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PRODID:Mathematics Seminar Calendar
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UID:20170922T041747-4103@math.msu.edu
DTSTAMP:20170922T041747Z
SUMMARY: Low-temperature localization of directed polymers
DESCRIPTION:Speaker\: Erik Bates, Stanford University\r\nOn the d-dimensional integer lattice, directed polymers can be seen as paths of a random walk in random environment, except that the environment updates at each time step. The result is a statistical mechanical system, whose qualitative behavior is governed by a temperature parameter and the law of the environment. Historically, the phase transitions of this system have been best understood by whether or not the path’s endpoint localizes. While the endpoint is no longer a Markov process as in a random walk, its quenched distribution is. The key difficulty is that the space of measures is too large for one to expect convergence results. By adapting methods recently used by Mukherjee and Varadhan, we develop a compactification theory to resolve the issue. In this talk, we will discuss this intriguing abstraction, as well as new concrete theorems it allows us to prove for directed polymers constructed from SRW or any other walk. (This talk is based on joint work with Sourav Chatterjee.)
LOCATION:C304 Wells Hall
DTSTART:20170907T150000Z
DTEND:20170907T160000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=4103
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UID:20170922T041747-4117@math.msu.edu
DTSTAMP:20170922T041747Z
SUMMARY:Reading seminar on Topological Insulators
DESCRIPTION:Speaker\: \r\nIn the study of quantum phases, the concept of topological invariant has emerged as a new paradigm beyond that of Landau theory. The relevance of topology for the classification of phases has been known since the discovery of the quantum hall effect. However, recent theoretical and experimental discoveries of new topological insulators has led to a renewed interest. The purpose of this reading group is to explore both recent and classical results for topological insulators including but not limited to (1) bulk-boundary correspondence (2) K-theoretic classification of topological insulators (3) topological invariants in the presence of disorder (4) quantization of Hall conductance in interacting systems.
LOCATION:C304 Wells Hall
DTSTART:20170912T150000Z
DTEND:20170912T160000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=4117
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UID:20170922T041747-4104@math.msu.edu
DTSTAMP:20170922T041747Z
SUMMARY:Stability of superselection sectors in infinite quantum spin systems
DESCRIPTION:Speaker\: Matthew Cha, MSU\r\nSuperselection sectors are equivalence classes of unitarily equivalent representations and can be used to label charges in a quantum system. We consider a family of superselection sectors for infinite quantum spin systems corresponding to almost localized endomorphisms. If the vacuum state is pure and satisfies certain locality conditions, we show how to recover the charge statistics. In particular, the superselection structure is that of a braided tensor category, and further, is stable against deformations by a quasi-local dynamics. We apply our results to prove stability of anyons in Kitaev's quantum double. Braided tensor categories naturally appear as the algebraic theory of anyons in topological phases of matter. Our results provide evidence that the anyonic structure is an invariant of topologically ordered states. This is work is joint with Pieter Naaijkens and Bruno Nachtergaele.\r\n
LOCATION:C304 Wells Hall
DTSTART:20170914T150000Z
DTEND:20170914T160000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=4104
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UID:20170922T041747-5133@math.msu.edu
DTSTAMP:20170922T041747Z
SUMMARY:Reading seminar on Topological Insulators
DESCRIPTION:Speaker\: Matthew Cha\r\nIn the study of quantum phases, the concept of topological invariant has emerged as a new paradigm beyond that of Landau theory. The relevance of topology for the classification of phases has been known since the discovery of the quantum hall effect. However, recent theoretical and experimental discoveries of new topological insulators has led to a renewed interest. The purpose of this reading group is to explore both recent and classical results for topological insulators including but not limited to (1) bulk-boundary correspondence (2) K-theoretic classification of topological insulators (3) topological invariants in the presence of disorder (4) quantization of Hall conductance in interacting systems.
LOCATION:C304 Wells Hall
DTSTART:20170919T150000Z
DTEND:20170919T160000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=5133
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UID:20170922T041747-4096@math.msu.edu
DTSTAMP:20170922T041747Z
SUMMARY:On the quantum and PDE models of Polaron
DESCRIPTION:Speaker\: Gang Zhou, SUNY Binghamton\r\n Polaron theory is a model of an electron in a crystal lattice.\r\nIt is studied in the framework of nonequilibrium statistic mechanics.\r\nThere are two different mathematical models: H. Frohlich proposed a\r\nquantum model in 1937; L. Landau and S. I. Pekar proposed a system of\r\nnonlinear PDEs in 1948. In this talk I will present a proof that these\r\ntwo models are equivalent to certain orders, and present some other\r\nrelated works. These are joint works with Rupert Frank.
LOCATION:C304 Wells Hall
DTSTART:20170921T150000Z
DTEND:20170921T160000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=4096
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BEGIN:VEVENT
UID:20170922T041747-4097@math.msu.edu
DTSTAMP:20170922T041747Z
SUMMARY: Localization in the droplet spectrum of the random XXZ spin chain
DESCRIPTION:Speaker\: Günter Stolz, University of Alabama Birmingham\r\nThe XXZ quantum spin chain in random exterior field is one of the models where numerics indicate the existence of a many-body localization transition. We will discuss recent joint work with Alexander Elgart and Abel Klein, which provides rigorous results on the localization side of the expected transition. We show several of the accepted manifestations of MBL at the bottom of the spectrum for the random XXZ chain in the Ising phase. In this regime spins form quasi-particles in the form of droplets (of, say, down-spins in a sea of up-spins), which become fully localized under the addition of a random field.
LOCATION:C304 Wells Hall
DTSTART:20170928T150000Z
DTEND:20170928T160000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=4097
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BEGIN:VEVENT
UID:20170922T041747-4099@math.msu.edu
DTSTAMP:20170922T041747Z
SUMMARY:BPS monopoles with non-maximal symmetry breaking and the Nahm transform
DESCRIPTION:Speaker\: Akos Nagy, Fields Institute/University of Waterloo\r\nThe notion of “broken symmetry” is central in gauge theories. For BPS monopoles, symmetry breaking can be defined in terms of the eigenvalues of the Higgs-field at infinity. The symmetry breaking is maximal if the eigenvalues are distinct. Monopoles with maximal symmetry breaking have been studied extensively by both mathematicians and physicists for decades now, but little is known about the general case.\r\nIn this talk, I will show how to produce monopoles with arbitrary symmetry breaking using the Nahm transform, and I will also outline the construction of its inverse. The inversion heavily uses first order elliptic PDE's on non-compact spaces, more concretely, the theory of Callias-type operators in 3D.\r\nThis is a joint project with Benoit Charbonneau.
LOCATION:C304 Wells Hall
DTSTART:20171003T150000Z
DTEND:20171003T160000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=4099
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UID:20170922T041747-4098@math.msu.edu
DTSTAMP:20170922T041747Z
SUMMARY:TBA
DESCRIPTION:Speaker\: Otis Chodosh\r\n
LOCATION:C304 Wells Hall
DTSTART:20171012T150000Z
DTEND:20171012T160000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=4098
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UID:20170922T041747-4100@math.msu.edu
DTSTAMP:20170922T041747Z
SUMMARY:TBA
DESCRIPTION:Speaker\: Marius Lemm, IAS\r\n
LOCATION:C304 Wells Hall
DTSTART:20171102T150000Z
DTEND:20171102T160000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=4100
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BEGIN:VEVENT
UID:20170922T041747-4101@math.msu.edu
DTSTAMP:20170922T041747Z
SUMMARY:TBA
DESCRIPTION:Speaker\: Jake Fillman, Virginia Tech\r\n
LOCATION:C304 Wells Hall
DTSTART:20171207T160000Z
DTEND:20171207T170000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=4101
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