Mathematics Department Colloquium: Quantum minimal surfaces

Colloquium | October 24 | 4:10-5 p.m. | 60 Evans Hall

Maxim Kontsevich, Institut des Hautes Études Scientifiques

Department of Mathematics

Quantum analog of a minimal surface in the Euclidean space $\mathbb R^n$ is a collection of almost-commuting self-adjoint operators $X_1,\dots ,X_n$ satisfying equations $$\forall i\qquad \sum _{j=1}^n [X_j,[X_j,X_i]]=0.\qquad \qquad \qquad$$

Remarkably, the same equations appear in Yang-Mills theory for translationally-invariant connections. This story is well-known in physics, but is barely touched by mathematicians.

I will show some concrete examples, and propose many more or less precise conjectures (based on a joint work with J.Arnlind and J.Hoppe).

holtz@math.berkeley.edu