September 9 |
Ira Herbst (UVa) The Navier-Stokes Equations, I : Introductory Ideas |
September 16 |
Ira Herbst (UVa) The Navier-Stokes Equations, II : Critical Spaces, Relevant Sobolev Inequalities |
September 23 |
Ira Herbst (UVa) The Navier - Stokes equations, III: Existence, analyticity |
September 30 |
Ira Herbst (UVa) The Navier - Stokes equations IV: The analyticity radius |
October 14 |
John Imbrie (UVa) Random walks, Markov chains, and Gaussian integrals. |
October 21 |
John Imbrie (UVa)
Self-avoiding walk and fermionic gaussian integrals |
October 28 |
John Imbrie (UVa)
Renormalization group for the hierarchical self-avoiding walk |
November 4 |
John Imbrie (UVa) The broken supersymmetry phase of self-avoiding walk |
November 11 |
Pierluigi Falco (IAS Princeton) The exact solution of the two dimensional Ising model Many different methods have been designed for deriving the exact solution of the 2D Ising model. I will review in details how the combinatoric approach gives us the Onsager's formula of the free energy and, time permitting, the Wu's formula of the spin-spin correlation. This method is important since, as I will discuss in the following week's talk, it allows us to find rigorous results on Ising-like models without an exact solution. [ref.: C.J. Thompson, "Mathematical Statistical Mechanics", ch.6; and T.Spencer , Phys. A 279 (2000)] |
November 18 |
Pierluigi Falco (IAS Princeton) The Kadanoff's formulas for the Eight-Vertex and the Ashkin-Teller models In 1977 Kadanoff conjectured two "extended" scaling formulas for two classical, Ising-like, planar systems: the Eight-Vertex and the Ashkin-Teller models. After introducing the models, I will discuss how the use of the Grassmann variables and the rigorous renormalization group allows us to prove one of the two. [ref.: G.Benfatto, P.Falco, V.Mastropietro , CMP 292 (2009)] |
December 2 | Ajay Chandra (UVa) Non-Gaussian fixed points for the block spin transformation on the hierarchical phi-4 model |
December 7 | Ajay Chandra (UVa)--2:30pm Monday, Note different day and time Non-Gaussian fixed points for the block spin transformation on the hierarchical phi-4 model, cont. |
December 16 | Ajay Chandra (UVa) Non-Gaussian fixed points for the block spin transformation on the hierarchical phi-4 model, cont. |
January 27 | Ajay Chandra (UVa) Non-Gaussian fixed points for the block spin transformation on the hierarchical phi-4 model, cont. |
February 3 | Ajay Chandra (UVa) Non-Gaussian fixed points for the block spin transformation on the hierarchical phi-4 model, cont. |
February 10 | Ira Herbst (UVa) Existence and non-existence of ground states in some infrared singular field theory models |
February 17 | Ira Herbst (UVa) Existence and non-existence of ground states in some infrared singular field theory models, cont. |
February 24 | Ira Herbst (UVa) Existence and non-existence of ground states in some infrared singular field theory models, cont. |
March 17 | Abdelmalek Abdesselam (UVa) Anderson localization in a supersymmetric model (after M. Disertori and T. Spencer) |
March 24 | Abdelmalek Abdesselam (UVa) Anderson localization in a supersymmetric model (after M. Disertori and T. Spencer), cont. |
March 31 | David Hasler (William and Mary) On the AC spectrum of one-dimensional random Schroedinger operators with matrix-valued potentials |
April 7 | Larry Thomas (UVa) Stability of Polarons |
April 14 | Larry Thomas (UVa) Stability of Polarons, cont. |
April 16* | Margherita Disertori (Université de Rouen)--2:00pm Friday, Note different day
A supersymmetric model for quantum diffusion in 3d We consider a lattice field model which qualitatively reflects the phenomenon of Anderson localization and delocalization for real symmetric band matrices. We prove that in three or more dimensions the model has a `diffusive' phase at low temperatures. For the same model localization at high temperatures was proved for any dimension d ≥ 1. Our analysis uses estimates on non-uniformly elliptic Green's functions and a family of Ward identities coming from internal supersymmetry (joint work with T. Spencer and M. Zirnbauer). |
April 21 | Razvan Gurau (Perimeter Institute, Waterloo)
Introduction to Group Field Theory Group field theory is the higher-dimensional generalization of random matrix models. As it has built-in scales and automatically sums over metrics and discretizations, it provides a combinatoric origin for space time. Its graphs facilitate an approach to algebraic topology which I exemplify by introducing a graph’s cellular structure and associated homology. |
April 28 | Razvan Gurau (Perimeter Institute, Waterloo)
Amplitudes in Group Field Theory In this talk I detail the relation between the Feynman amplitudes of graphs in Group Field Theory and the fundamental group. I then propose a generalization of the notion of planarity to Group Field Theory and compute the amplitude of generalized planar graphs. |
March 24 | Abdelmalek Abdesselam (UVa) Anderson localization in a supersymmetric model (after M. Disertori and T. Spencer), cont. |
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