4 problems

Let $\nu=\nu(\beta,q,d)$ be Potts lattice gauge theory on $\mathbb{Z}^d$. Let $\sigma_N=[0,1]^2\times\{N\}\times\{0\}$ be a plaquette, and for a plaquette $\sigma$ let…

Consider planar Sinai billiard flows whose boundary may have corner points, with the angle between the intersecting boundary pieces at each corner nonzero. Corner-point correlation…

Let $K_n$ be the upper bound on the number of smooth pieces into which the $n$th iterate of a smooth convex expanding submanifold is chopped by the billiard map. Complexity hypothe…

Optimal thermal clustering conjecture. In the massless case, the decay has the form