Talk_id  Date  Speaker  Title 
4103

Thursday 9/7 11:00 AM

Erik Bates, Stanford University

Lowtemperature localization of directed polymers
 Lowtemperature localization of directed polymers
 09/07/2017
 11:00 AM  12:00 PM
 C304 Wells Hall
 Erik Bates, Stanford University
On the ddimensional 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.)

4117

Tuesday 9/12 11:00 AM


Reading seminar on Topological Insulators
 Reading seminar on Topological Insulators
 09/12/2017
 11:00 AM  12:00 PM
 C304 Wells Hall

In 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) bulkboundary correspondence (2) Ktheoretic classification of topological insulators (3) topological invariants in the presence of disorder (4) quantization of Hall conductance in interacting systems.

4104

Thursday 9/14 11:00 AM

Matthew Cha, MSU

Stability of superselection sectors in infinite quantum spin systems
 Stability of superselection sectors in infinite quantum spin systems
 09/14/2017
 11:00 AM  12:00 PM
 C304 Wells Hall
 Matthew Cha, MSU
Superselection 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 quasilocal 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.

5133

Tuesday 9/19 11:00 AM

Matthew Cha

Reading seminar on Topological Insulators
 Reading seminar on Topological Insulators
 09/19/2017
 11:00 AM  12:00 PM
 C304 Wells Hall
 Matthew Cha
In 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) bulkboundary correspondence (2) Ktheoretic classification of topological insulators (3) topological invariants in the presence of disorder (4) quantization of Hall conductance in interacting systems.

4096

Thursday 9/21 11:00 AM

Gang Zhou, SUNY Binghamton

On the quantum and PDE models of Polaron
 On the quantum and PDE models of Polaron
 09/21/2017
 11:00 AM  12:00 PM
 C304 Wells Hall
 Gang Zhou, SUNY Binghamton
Polaron theory is a model of an electron in a crystal lattice.
It is studied in the framework of nonequilibrium statistic mechanics.
There are two different mathematical models: H. Frohlich proposed a
quantum model in 1937; L. Landau and S. I. Pekar proposed a system of
nonlinear PDEs in 1948. In this talk I will present a proof that these
two models are equivalent to certain orders, and present some other
related works. These are joint works with Rupert Frank.

4097

Thursday 9/28 11:00 AM

Günter Stolz, University of Alabama Birmingham

Localization in the droplet spectrum of the random XXZ spin chain
 Localization in the droplet spectrum of the random XXZ spin chain
 09/28/2017
 11:00 AM  12:00 PM
 C304 Wells Hall
 Günter Stolz, University of Alabama Birmingham
The XXZ quantum spin chain in random exterior field is one of the models where numerics indicate the existence of a manybody 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 quasiparticles in the form of droplets (of, say, downspins in a sea of upspins), which become fully localized under the addition of a random field.

4099

Tuesday 10/3 11:00 AM

Akos Nagy, Fields Institute/University of Waterloo

BPS monopoles with nonmaximal symmetry breaking and the Nahm transform
 BPS monopoles with nonmaximal symmetry breaking and the Nahm transform
 10/03/2017
 11:00 AM  12:00 PM
 C304 Wells Hall
 Akos Nagy, Fields Institute/University of Waterloo
The notion of “broken symmetry” is central in gauge theories. For BPS monopoles, symmetry breaking can be defined in terms of the eigenvalues of the Higgsfield 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.
In 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 noncompact spaces, more concretely, the theory of Calliastype operators in 3D.
This is a joint project with Benoit Charbonneau.

4098

Thursday 10/12 11:00 AM

Otis Chodosh

TBA
 TBA
 10/12/2017
 11:00 AM  12:00 PM
 C304 Wells Hall
 Otis Chodosh
No abstract available.

4100

Thursday 11/2 11:00 AM

Marius Lemm, IAS

TBA
 TBA
 11/02/2017
 11:00 AM  12:00 PM
 C304 Wells Hall
 Marius Lemm, IAS
No abstract available.

4101

Thursday 12/7 11:00 AM

Jake Fillman, Virginia Tech

TBA
 TBA
 12/07/2017
 11:00 AM  12:00 PM
 C304 Wells Hall
 Jake Fillman, Virginia Tech
No abstract available.
