Description: The seminar is a combination of a learning and a research seminar. The first 15 minutes or so of each talk are a "trivial notions" talk defining all basic notions, giving examples and intuition to the subject, and should be accessible to a beginning graduate student. The next 50 minutes are a regular seminar talk.
Organizers: T. DarvasJ. Martinez GarciaV.P. PingaliY.A. RubinsteinB. Shiffman, S. Wolpert
When: Tuesdays at 4:30pm
Where: Krieger Hall 300 (JHU), Kirwan Hall 1308 (UMD)
Additional Information

Archives: 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017

  • Pseudoconcave decompositions in complex manifolds

    Speaker: Zbigniew Slodkowski (UIC) -

    When: Tue, October 31, 2017 - 4:30pm
    Where: Krieger 302 (JHU)

    View Abstract

    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

    Speaker: Sebastien Picard (Columbia) -

    When: Tue, November 28, 2017 - 4:30pm
    Where: Kirwan Hall 3206

    View Abstract

    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.