JHU-UMD Complex Geometry Seminar Archives for Academic Year 2018

Pseudoconcave decompositions in complex manifolds

When: Tue, October 31, 2017 - 4:30pm
Where: Krieger 302 (JHU)
Speaker: Zbigniew Slodkowski (UIC) -
Abstract: We will discuss three situations in which pseudoconcave sets arise as obstacles to construction of strictly plurisubharmonic (psh) functions of some class. 1. Minimal kernels of weakly complete manifolds are smallest subsets in the complement of which a continuous (or smooth) psh exhaustion function can be made strictly psh. Breaking the kernel into the union of compact pseudoconcave sets shows that a weakly complete manifold is Stein iff it does not contain a compact pseudoconcave set. (Z.S. & G.Tomassini, 2004) 2. The core of a relatively pseudoconvex domain, the largest set on which the Levi form of every smooth psh defining function of the domain must be degenerate everywhere, was introduced and shown pseudoconcave by Shcherbina et al (2016/17). We prove their conjecture that the core can be decomposed into the union of pseudoconcave sets on which every psh defining function is constant. 3. Analogous phenomena will be exhibited in relation to Richberg's regularization of strongly psh functions on complex manifolds.

The Anomaly flow and the Hull-Strominger system

When: Tue, November 28, 2017 - 4:30pm
Where: Kirwan Hall 3206
Speaker: Sebastien Picard (Columbia) -
Abstract: The Anomaly flow is a geometric flow which implements the Green-Schwarz anomaly cancellation mechanism originating from superstring theory, while preserving the conformally balanced condition of Hermitian metrics. Its stationary points satisfy the Hull-Strominger system of partial differential equations. The Anomaly flow allows metrics with torsion, and we hope to use it to study non-Kahler complex geometry. I will discuss general features of this flow, and describe its behavior on certain examples. This is joint work with D.H. Phong and X.-W. Zhang.

Singular sets of plurisubharmonic functions

When: Tue, February 13, 2018 - 4:30pm
Where: JHU Gilman 186
Speaker: Slawomir Dinew (Krakow) -
Abstract: We shall discuss geometric and measure theoretic properties of mimimum sets of strictly plurisubharmonic functions. Relations to various branches of complex analysis will be investigated.

Universality for zeros of random polynomials

When: Thu, April 26, 2018 - 4:30pm
Where: Johns Hopkins, Gilman 132
Speaker: Thomas Bloom (Toronto) -
Abstract: https://www.math.umd.edu/~tdarvas/items/absuniversality.pdf

Generalized Kahler-Ricci flow in the commuting case

When: Tue, May 8, 2018 - 4:30pm
Where: Kirwan Hall 3206
Speaker: Jeff Streets (UC Irvine) -
Abstract: Generalized Kahler geometry is a particularly rich vein of Hitchin's program of ``generalized geometry," extending the notion of Kahler metric into a wider array of complex manifolds. In joint work with G. Tian I introduced an extension of Kahler-Ricci flow to this setting. In this talk I will introduce fundamental notions of generalized Kahler geometry and the generalized Kahler-Ricci flow. Then I will describe results concerning the special ``commuting'' case, where the system reduces to a non-convex fully nonlinear scalar PDE. I will descibe some global existence results and describe the remaining challenges.