Hopkins-Maryland Complex Geometry Seminar

Johns Hopkins University, University of Maryland

DATE: Tuesdays at 4:30pm.

ROOM: Gilman 186 (JHU), Math 3206 (UMD).

ORGANIZED BY:
T. Darvas,
Y. A. Rubinstein,
B. Shiffman,
R. Wentworth,
S. Wolpert,
H. Xu.

COORDINATORS: Y. A. Rubinstein, B. Shiffman.

PREVIOUS YEARS: 2012-2013, 2013-2014, 2014-2015, 2015-2016, 2016-2017.

- Oct 31 (JHU)

Zbigniew Slodkowski (UIC)

*Title: Pseudoconcave decompositions in complex manifolds*

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. - November 28 (UMD)

Sebastien Picard (Columbia)

*Title: The Anomaly flow and the Hull-Strominger system*

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. - February 13 (UMD)

Slawomir Dinew (Krakow)

*Title: Singular sets of plurisubharmonic functions*

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. - April 26 (SPECIAL LOCATION: Gilman 132 JHU)

Thomas Bloom (Toronto)

*Title: Universality for zeros of random polynomials*

Abstract: link. - May 4 (SPECIAL TIME: 11 AM and LOCATION: Math 3206)

Lei Ni (UCSD)

*Title: Metric characterizations of the projectivity*

Abstract: Recently there were several progresses on the algebraic and analytic properties of Kaehler manifolds in terms of holomorphic sectional curvature. In this talk I shall discuss some new joint results (with Fangyang Zheng) along these directions. The result either generalizes the existing one or provides a complementary coverage. The new curvature conditions also opens many questions. - May 8 (UMD)

Jeff Streets (UC Irvine)

*Title: Generalized Kahler-Ricci flow in the commuting case*

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.

Driving directions to JHU: Park in South Garage (see map) on any level (except the reserved spaces). Take a ticket when entering. The Department will provide a visitor parking pass to use when exiting.

Driving and parking directions to UMD: Park in Paint Branch Drive Visitor Lot (highlighted in yellow in the lower right corner of the second map in the previous link), or in Regents Drive Garage (highlighted in the upper right corner). If you arrive after 4pm you do not need to pay: see the instructions in the previous link.