### JHU-UMD Complex Geometry Seminar Archives for Academic Year 2018

#### On the diameter rigidity of Kahler manifolds with positive bisectional curvature

When: Mon, October 8, 2018 - 4:30pm

Where: Krieger 308 (JHU)

Speaker: Yuan Yuan (Syracuse University) -

Abstract: It follows from the comparison theorem that if the Kahler

manifold has bisectional curvature at least 1, then the diameter is no

greater than the diameter of the standard complex projective space. I

will discuss a joint result with G. Liu regarding the rigidity when the

diameter reaches the maximum.

#### Universality results for zeros of random holomorphic sections

When: Tue, October 16, 2018 - 4:30pm

Where: MATH 3206

Speaker: Dan Coman (Syracuse) -

Abstract: Consider a sequence of singular Hermitian holomorphic line bundles on a compact Kaehler manifold. We prove a universality result which shows that the asymptotic distribution of zeros of random holomorphic sections is independent of the choice of probability measure on the space of holomorphic sections. We give several applications of this result, in particular to the distribution of zeros of random polynomials. The results are joint with T. Bayraktar and G. Marinescu.

#### Distinguished Lecture Series in Geometric Analysis

When: Mon, November 5, 2018 - 4:30pm

Where: MATH 1313

Speaker: Bo Berndtsson (Chalmers) -

#### On the Yau-Tian-Donaldson conjecture for singular Fano varieties

When: Tue, November 27, 2018 - 4:30pm

Where: Kirwan Hall 3206

Speaker: Chi Li (Purdue) -

Abstract: I will talk about an existence result for the Yau-Tian-Donaldson conjecture on any Q-factorial Fano variety that has a log smooth resolution of singularities such that discrepancies of all exceptional divisors are non-positive. We will show that if such a Fano variety is K-polystable, then it admits a K\â€ťahler-Einstein metric. This extends the previous existence result for Fano manifolds to this class of singular Fano varieties. The proof uses various techniques from complex geometry. This is a joint work with Gang Tian and Feng Wang.

#### Spectral asymptotics on stationary spacetimes

When: Thu, April 4, 2019 - 4:30pm

Where: Kirwan Hall 1311

Speaker: Steve Zelditch (Northwestern University) -

Abstract: Spectral asymptotics on a compact Riemannian manifold (Sigma, h) concerns the eigenvalues/eigenfunctions of its Laplacian Delta_Sigma as the eigenvalue tends to infinity. The two cornerstones of spectral asymptotics are the Weyl counting law for eigenvalues and the Gutzwiller-Duistermaat-Guillemin trace formula for the wave group. They are manifestly non-relativistic. My talk will explain how these (and virtually any) theorem of spectral asymptotics admits a generalization to globally hyperbolic, stationary spacetimes with compact Cauchy hypersurface. The eigenvalues are `quasi-normal modes' similar in spirit to the well-known ones for black hole spacetimes. Joint work with Alex Strohmaier.