Past Events
How do the finite/infinite dichotomy of the Killing–Cartan classification of simple Lie groups & algebras appear in arithmetic geometry? I will explain how this Lie-theoretic dichotomy is realized in the finiteness or infinitude of positive integer solutions to certain Diophantine equations…
We will continue our study of the lace expansion and its applications.
We will give an introduction to the classification of surfaces and 2d minimal model programme with a focus on low characteristic.
The form x²+y² covers ½ of the primes, while the forms x²+y², x²+2y² cover ¾ of them. In this talk, we will show that the proportion of primes covered by the forms x²+dy², 1 ≤ d ≤ Δ, is1 - exp((α(Δ) + o(1)) √Δ / log Δ)for some 7π/12 ≤ α(Δ) ≤ 7π/12 + log 4. Furthermore, inspired by…
We study the topological components of the surface group representations into SL(2,R) and PSL(2,R). Some components correspond to geometric structures on surface, especially discrete and faithful ones to hyperbolic structures. Utilizing the signature formula established by Kim-Pansu-…
Abstract: Much is known about algebraic K theory of the integers, in particular these groups are finitely generated. There is a secondary (or categorified) K theory of a commutative ring k, replacing finite type k modules by "finite type" A_infty categories over k. I explain how to get elements…
The study of random holonomies (or Wilson loops) of the 2D Yang-Mills model goes back to the late 1980s. The law of these loop observables can be described in terms of heat kernels on Lie groups. In this talk, we start with an introductory review of these ideas. Then we discuss our new result in…