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Mathematical Physics
2009-2010
Regular time and location:
Wednesdays, 2:00pm, 326 Kerchof Hall
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September 9
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Ira Herbst (UVa)
The Navier-Stokes Equations, I : Introductory Ideas
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September 16
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Ira Herbst (UVa)
The Navier-Stokes Equations, II : Critical Spaces, Relevant Sobolev Inequalities
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September 23
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Ira Herbst (UVa)
The Navier - Stokes equations, III: Existence, analyticity
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September 30
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Ira Herbst (UVa)
The Navier - Stokes equations IV: The analyticity radius
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October 14
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John Imbrie (UVa)
Random walks, Markov chains, and Gaussian integrals. |
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October 21
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John Imbrie (UVa)
Self-avoiding walk and fermionic gaussian integrals |
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October 28
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John Imbrie (UVa)
Renormalization group for the hierarchical self-avoiding walk |
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November 4
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John Imbrie (UVa)
The broken supersymmetry phase of self-avoiding walk |
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November 11
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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)] |
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November 18
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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 |
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*indicates different day, time, and/or location
Past Years
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