University of Virginia Mathematical Physics Seminar 2012-13

September 12	Speaker: Ajay Chandra (UVa) Title: Proving Scale Invariance of a Massless QFT over the p-adics (I) Abstract: In a sequence of talks I will show how one can leverage correlation inequalities and the theory of Gibbs measures to prove scale invariance of a measure corresponding to a certain Renormalization Group fixed point. Necessary tools include Griffiths' inequalities for ferromagnetic Ising models, a result of Aizenman, Barsky, and Fernandez on the sharpness of certain phase transitions, and techniques developed by Ruelle along with Lebowitz and Presutti for "superstable" interactions in statistical mechanics. I will give short overviews of these tools and how we apply them. This is joint work with Abdelmalek Abdesselam and Gianluca Guadagni.
September 19	Speaker: Kyle Bradford (Oregon State University) Title: The Stable Adiabatic Time - a measure of stability of a time-inhomogeneous Markov chain Abstract: In this talk I will define the Stable Adiabatic Time (S.A.T) of a specific class of time-inhomogeneous Markov chains and I will build an appropriate bound of the S.A.T. with respect to the Mixing Time, which is more commonly known. I will highlight some related theorems to place this result into a proper context and I will discuss the practicality of my result with some illustrative examples. Although I will introduce some terminology for Markov chains and I will briefly discuss the Quantum Adiabatic Theorem, a good portion of my talk should be accessible to advanced undergraduate students.
September 26	Speaker: Ajay Chandra (UVa), joint seminar with Probability Title: Proving Scale Invariance of a Massless QFT over the p-adics (II) Abstract: See talk (I) in the series.
October 3	Speaker: Ajay Chandra (UVa), joint seminar with Probability Title: Proving Scale Invariance of a Massless QFT over the p-adics (III) Abstract: See talk (I) in the series.
October 10	Speaker: Ajay Chandra (UVa), joint seminar with Probability Title: Proving Scale Invariance of a Massless QFT over the p-adics (IV) Abstract: See talk (I) in the series.
October 17	Speaker: Rajinder Mavi (UVa) Title: The percolation approach to the quantum Ising model (I) Abstract: We discuss the Feyman Kac representations of the d dimensional quantum Ising model to derive a d+1 dimensional classical model, and subsequently approach this model with Fortuin-Kastelyn percolation methods. We will be interested in the phase structure of the ferromagnetic Ising model with ergodically generated disorder.
October 24	Speaker: Rajinder Mavi (UVa) Title: The percolation approach to the quantum Ising model (II) Abstract: See talk (I) in the series.
October 31	Speaker: Rajinder Mavi (UVa) Title: The percolation approach to the quantum Ising model (III) Abstract: See talk (I) in the series.
November 16*	Speaker: Ivan Corwin (Clay Mathematics Institute, MIT and Microsoft Research), joint seminar with Probability DIFFERENT TIME AND LOCATION: Friday Nov 16, 1pm-2pm in KER 317 Title: From duality to determinants for ASEP and q-TASEP Abstract: I will show how Markov process dualities for certain integrable probabilistic systems (ASEP and q-TASEP) imply that moments solve variants of the delta Bose gas. For special initial data, these Bose gas equations can be solved explicitly via a nested contour integral ansatz originating in the theory of Macdonald processes. Taking a generating series of these moment formulas leads to Fredholm determinants characterizing one-point fluctuations in the original systems. This provides a rigorous discrete deformation of the physicist's (famously non-rigorous) polymer replica trick (for KPZ equation). This is based on joint work with Alexei Borodin and Tomohiro Sasamoto.
November 21	THANKSGIVING RECESS
November 28	Speaker: Gianluca Guadagni (UVa) Title: Cluster Expansion for almost Gaussian Models I Abstract: In equilibrium statistical mechanics it is quite common for a model to have a partition function that can be written as a Gaussian expectation of a polymer system. I will review some general results from cluster expansion and then I will prove a condition for the convergence of pressure and correlations expansions under the hypothesis that the Gaussian expectation has a finite range decomposition. This is joint work with David Brydges and Dennis Timmers at University of British Columbia.
December 5	Speaker: Gianluca Guadagni (UVa) Title: Cluster Expansion for almost Gaussian Models II Abstract: See talk (I) in the series.
December 11*	Speaker: Bernard De Saedeleer (Université Catholique de Louvain)), joint seminar with Differential Equations DIFFERENT TIME AND LOCATION: Tuesday Dec 11, 3:30pm-4:30pm in KER 317 Title: Story of an astronomical synchronisation: shall we on a whim jump to another paleoclimate history? Abstract: The mystery of 100 kyr ice ages on Earth has drawn ceaseless attention for several decades. A very widespread school of thought assumes that these paleoclimates are paced by a varying incoming solar radiation (the so-called "Milankovitch forcing" by insolation). This phenomenon is clearly related to the synchronisation phenomenon in nonlinear sciences. A persistent hypothesis in the literature is the uniqueness of the associated paleoclimate history. In this talk, we challenge that hypothesis by investigating in depth the synchronisation properties of a simple paleoclimatic toy model (a van der Pol-like relaxation oscillator). Our approach mainly relies on tools borrowed from dynamical system theory and clustering analysis. We show that, in a deterministic framework, the astronomical forcing may synchronise the ice volume to several coexisting climatic attracting trajectories, and that temporary desynchronisations may occur due to loss of local stability (positive largest local Lyapunov exponent). Additional disturbances may then cause a jump to another climate history over the last millions years of the Pleistocene, reducing the predictability of the timing of the glacial inceptions and terminations. Extensive Monte Carlo experiments confirm these results and precise them further. Such a conclusion about predictability is of major importance, because of its potential impact on the overall theory of ice ages.
December 12	Speaker: Gianluca Guadagni (UVa) Title: Cluster Expansion for almost Gaussian Models III Abstract: See talk (I) in the series.
January 30	Speaker: Gianluca Guadagni (UVa) Title: Cluster Expansion for almost Gaussian Models IV Abstract: See talk (I) in the series.
February 6	Speaker: Rajinder Mavi (UVa) Title: Localization in the tight binding model: rough quasi-periodic potentials I Abstract: We discuss some approaches to studying dynamics of the tight binding model. The Fibonacci potential and the almost Mathieu operators are interesting examples for their intermittent dynamical properties. Although RAGE-like theorems are successful at showing delocalization, localization of the entire wave is much more difficult - especially in the case of non-discrete potentials. We will discuss in particular some results which generalize these potentials, that is piecewise continuous quasi-periodic potentials satisfying local Holder continuity conditions.
February 13	Speaker: Rajinder Mavi (UVa) Title: Localization in the tight binding model: rough quasi-periodic potentials II Abstract: See talk (I) in the series.
February 20	Speaker: Rajinder Mavi (UVa) Title: Localization in the tight binding model: rough quasi-periodic potentials III Abstract: See talk (I) in the series.
February 27	Speaker: Abdelmalek Abdesselam (UVa) Title: Construction of a composite field with anomalous scaling dimension I Abstract: In this series of talks I will explain the recent rigorous nonperturbative construction of a composite field with dynamically generated anomalous dimension. This is joint work with Ajay Chandra and Gianluca Guadagni.
March 6	Seminar cancelled because of the snow.
March 20	Speaker: Abdelmalek Abdesselam (UVa) Title: Construction of a composite field with anomalous scaling dimension II Abstract: See talk (I) in the series.
March 27	Speaker: Abdelmalek Abdesselam (UVa) Title: Construction of a composite field with anomalous scaling dimension III Abstract: See talk (I) in the series.
April 3	Speaker: Abdelmalek Abdesselam (UVa) Title: Construction of a composite field with anomalous scaling dimension IV Abstract: See talk (I) in the series.
April 8*	Speaker: Annalisa Panati (McGill University) DIFFERENT TIME: Monday April 8, 2pm-3pm in KER 326 Title: Infrared (and ultraviolet) aspects of a model of QFT on a static space time. Abstract: We consider the Nelson model with variable coeffcients, which can be seen as a model describing a particle interacting with a scalar field on a static space time. We consider the problem of the existence of the ground state, showing that it depends on the decay rate of the coeffcients at infinity. We also show that it is possible to remove the ultraviolet cutoff, as it is in the flat case. We'll explain some open conjecture. (joint work with C.Gérard, F.Hiroshima, A.Suzuki)
April 17	Speaker: Abdelmalek Abdesselam (UVa) Title: Construction of a composite field with anomalous scaling dimension V Abstract: See talk (I) in the series.
April 24	Speaker: Abdelmalek Abdesselam (UVa) Title: Construction of a composite field with anomalous scaling dimension VI Abstract: See talk (I) in the series.
May 1	Speaker: Larry Thomas (UVa) Title: Scenarios for Non-equilibrium Stationary States in Statistical Mechanics. Abstract: I will sketch two simple scenarios for non-equilibrium stationary states in quantum statistical mechanics, and review the analysis of these scenarios by Jaksic and Pillet, Ruelle, Cornean, Duclos and Purice, and others.

University of Virginia Mathematical Physics Seminar 2012-13

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