Past Events
We discuss our result on a conjecture of Talagrand, which is a fractional version of the “expectation-threshold” conjecture of Kahn and Kalai. This easily implies various difficult results in probabilistic combinatorics, e.g. thresholds for perfect hypergraph matchings (Johansson-Kahn-Vu) and…
A classical theorem of Bernstein says that entire minimal graphs over R^2 are planes. This result was extended to R^n for n < 8 in works of Fleming, De Giorgi, Almgren, and Simons. Finally, Bombieri - De Giorgi - Giusti constructed a non-flat entire minimal graph over R^8, settling the…
Consider a system of particles at a given energy, isolated from the environment, and a second identical system at thermal equilibrium with the environment. If only the energy is considered to be relevant, the maximum entropy principle provides us with two probability distributions on phase space…
Contact 3-manifolds occupy a central role in low-dimensional topology partly because of their interactions with Floer-theoretic invariants. Convex surface theory and bypasses are extremely powerful tools for analysing contact 3-manifolds, and have been successfully applied in…