Noncommutative Geometry Seminar

Date: March 1, 2017

Time: 2:00PM - 2:50PM

Location: BLOC 628

Speaker: Yongbin Ruan , University of Michigan

Title: (Colloquium Talk) Landau-Ginzburg/Calabi-Yau correspondence

Abstract: Given quasi-homogeneous polynomial W, we can study it in two different areas of mathematics. Namely, we can set W=0 to define a hypersurface X_W of Weight projective space or we can compute its Jacobian ring C[x_1, \cdots, x_n] / \partial W. The later is the subject of singularity theory or Landau-Ginzburg model. An old theorem said that the middle cohomology of X_W can be computed using Jacobian ring. Motivated by physics, we can attach a range of invariants to X_W as well as the Landau-Ginzburg side of W. The effort to connect two subject leads to Landau-Ginzburg/Calabi-Yau correspondence, a famous duality from physics. In the talk, I will survey some of developments about this duality.