# Mathematics Colloquium Fall 2009

For further information please contact the Mathematics Department at 459-2969

**October 13, 2009 ***The Colloquium Has Been Cancelled - We will reschedule accordingly**

**Convergence of spectral decompositions of non-selfadjoint Hill operators**

**Convergence of spectral decompositions of non-selfadjoint Hill operators**

**Professor Boris Mityagin, Department of Mathematics, the Ohio State University**

I'll give a short history (from the early 20th century) of this problem in the case of ordinary differential operators. Then I'll focus on the Hill operator L = - d2/dx2 + v(x) with trigonometric polynomial potentials v(x). It happens that even in the case of such polynomials as v(x) = a exp(-2ix) + b exp(2ix) or v(x) = a exp(-2ix) + A exp(4ix) the system of eigenfunctions and associated functions (SEAF) of L with periodic boundary conditions is not a basis in L2[0, pi]. This talk is based on my joint papers with Plamen Djakov (of Sabanci University, Istanbul).

**November 19, 2009**

**Landau-Ginzburg/Calabi-Yau correspondence**

**Landau-Ginzburg/Calabi-Yau correspondence**

**Yongbin Ruan, Department of Mathematics at the University of Michigan**

For last twenty years, physics has generated many amazing predictions in mathematics. Many of them comes from powerful physical correspondence or duality which connects completely different mathematics. In this talk, we will discuss one of these powerful correspondences called Landau-Ginzburg/Calabi-Yau correspondence connecting singularity theory to Calabi-Yau geometry.