The JHU-UMD Complex Geometry Seminar was founded in 2012 by Y. Rubinstein (UMD) and B. Shiffman (JHU). It serves to strengthen the ties between the historically vibrant complex geometry communities in Maryland. Starting with the academic year 2015-2016, the seminar meets once a month, alternating locations, with the purpose of discussing recent developments in both complex and convex geometry and analysis.
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.
- 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)
- April 10 (JHU)
Hamid Hezari (UC Irvine)
- April 24 (JHU)
Thomas Bloom (Toronto)
- May 8 (UMD)
Jeff Streets (UC Irvine)
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.