Probability and Mathematical Physics Seminar
This seminar covers a wide range of topics in pure and applied probability and in mathematical physics. Unless otherwise noted, the talks take place on Fridays, 11:10am–12pm, in room WWH 1302. See directions to the Courant Institute.
To be kept informed, you can subscribe to the Probability Seminar Mailing list.
Twice every semester, we will have a joint Columbia–Courant meeting (hosted once at each institution) as the Probability and the City seminar.
Seminar Organizer(s): Eyal Lubetzky, Paul Bourgade, Klara Courteaut, and the probability group
Upcoming Events
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Friday, October 2, 202611AM, Warren Weaver Hall 1302
Soliton gases and extremal solutions of integrable nonlinear PDEs: Asymptotic analysis of deterministic and random multi-soliton solutions
Kenneth McLaughlin, Tulane UniversitySynopsis:
If all goes to plan I will explain the terminology in the title, then describe the analysis of a random Riemann-Hilbert problem, and apply the method to the study of extremal solutions and soliton gases. Convergence theorems and the overarching quest will be described. I will focus mainly on joint work with Katerina Gkogkou and Guido Mazzuca.
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Friday, October 2, 202612PM, Warren Weaver Hall 1302
Area and Perimeter Laws in Lattice Yang–Mills Theories
Ron Nissim, MITSynopsis:
Lattice Yang–Mills theory was introduced by Ken Wilson in 1974, in part to give a mathematical framework for understanding quark confinement—the physical phenomenon that quarks are not observed in isolation. Wilson proposed the area law for Wilson loop expectations as a criterion for confinement: for large rectangular loops, the expectation should decay exponentially in the area enclosed by the loop, rather than merely in its perimeter.
I will start by briefly reviewing joint work with Scott Sheffield and Sky Cao in which we substantially expanded the regime of parameters where an area law is proved. A key ingredient in this work is the center symmetry of the model. The main focus of the talk will be recent and upcoming solo work in the opposite direction: when the relevant Wilson loop is insensitive to the center of the gauge group, we prove a perimeter-law lower bound, ruling out Wilson's confinement criterion. The result holds in dimensions three and higher and, importantly, extends to the weak-coupling regime relevant to the continuum theory. I will also briefly discuss a Lean formalization of the proof and the role that AI tools played in its development.
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Friday, October 9, 202611AM, Warren Weaver Hall 1302
TBA
Yu Gu, University of Maryland, College Park -
Friday, October 9, 202612PM, Warren Weaver Hall 1302
TBA
Mostafa Sabri, NYUAD -
Friday, October 16, 202611AM, Warren Weaver Hall 1302
TBA
Patrick Lopatto, University of North Carolina at Chapel Hill -
Friday, October 23, 202611AM, Warren Weaver Hall 1302
TBA
Duncan Dauvergne, University of Toronto -
Friday, October 30, 202611AM, Warren Weaver Hall 1302
TBA
Josselin Garnier, École Polytechnique -
Friday, November 13, 202611AM, Warren Weaver Hall 1302
TBA
Eyal Lubetzky, Courant Institute, NYU