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.
- October 1, JHU
Jian Song (Rutgers)
Title: Compactness of Kahelr-Einstein manifolds of negative scalar curvature
Abstract: Let K(n,V) be the set of n-dimensional Kahler-Einstein manifolds (X, g) satisfying Ric(g)=-g with volume bounded above by V. We show that any sequence (X_i, g_i) in K(n,V) converge, after passing to a subsequence, in pointed Gromov-Hausdorff toplogy, to a finite union of complete Kahler-Einstein metric spaces. The limiting metric space is biholomorphic to an n-dimensional semi-log canonical model with its non log terminal locus removed. Our result is a high dimensional generalization for the compactness of constant curvature metrics on Riemann surfaces of high genus. We will also give some applications to the Weil-Petersson metric on the moduli space of canonically polarized manifolds.
- October 8, UMD
Jeffrey Case (Penn State)
Title: On global invariants of CR manifolds
Abstract: A secondary global invariant of a CR manifold is the integral of a scalar pseudohermitian invariant which is independent of the choice of pseudo-Einstein contact form. All such invariants are biholomorphic invariants of domains C^n. One example is the Burns-Epstein invariant in C^2, which gives a nice characterization of the ball. In this talk I will describe two important families of secondary global invariants. The first, the total Q-prime curvatures, give a nice analytic interpretation of the Burns-Epstein invariant. The second, the total I-prime curvatures, show that the theory of secondary global invariants is much richer than the analogous theory of global conformal invariants, and in particular disproves a conjecture of Hirachi.
- November 12, JHU
Bruce Kleiner (NYU)
Title: Ricci flow and contractibility of spaces of metrics.
Abstract: In the lecture I will discuss recent joint work with Richard Bamler, which uses Ricci flow through singularities to construct deformations of spaces of metrics on 3-manifolds. We show that the space of metrics with positive scalar on any 3-manifold is either contractible or empty; this extends earlier work by Fernando Marques, which proved path-connectedness. We also show that for any spherical space form M, the space of metrics with constant sectional curvature is contractible. This completes the proof of the Generalized Smale Conjecture, and gives a new proof of the original Smale Conjecture for S^3.
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.