Duke Probability Seminar
A seminar for the probability community at Duke, both in and outside of the Mathematics Department.
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- Thursday, April 22, 2021, 3:15pm, Virtual, Probability Seminar
Mean-field spin glasses: beyond Parisi's formula?
J.C. Mourrat (NYU)
- Spin glasses are models of statistical mechanics encoding disordered
interactions between many simple units. One of the fundamental
quantities of interest is the free energy of the model, in the limit
when the number of units tends to infinity. For a restricted class of
models, this limit was predicted by Parisi, and later rigorously proved
by Guerra and Talagrand. I will first show how to rephrase this result
using an infinite-dimensional Hamilton-Jacobi equation. I will then
present partial results suggesting that this new point of view may allow
to understand limit free energies for a larger class of models, focusing
in particular on the case in which the units are organized over two
layers, and only interact across layers.
- Thursday, April 29, 2021, 3:15pm, Virtual, Probability Seminar
Integrability of SLE and Liouville Conformal Field Theory through Conformal Welding
Xin Sun (U. Penn)
- here are two frameworks to study quantum surfaces in Liouville quantum gravity: random planar geometry and Liouville conformal field theory (LCFT). A key feature of the first framework is the coupling with Schramm-Loewner evolution (SLE). A key feature of the second framework is the application of conformal field theoretical techniques. We report an ongoing program that unifies these two frameworks using conformal welding of quantum surfaces, which gives strong links between the integrability of SLE and LCFT. We obtain exact formulae for both SLE and LCFT which are hard to obtain from methods within their own framework. Based on a joint work with Ang and Holden, a joint work with Ang and Remy; and a series of ongoing projects with Ang.
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