Hopkins-Maryland Geometry Seminar

Johns Hopkins University, University of Maryland

DATE: Tuesdays at 4:30pm.

ROOM: Ames 234 (JHU), Math 3206 (UMD).

ORGANIZED BY:
T. Darvas,
J. Hultgren,
Y. A. Rubinstein,
B. Shiffman,
Y. Sire,
R. Wentworth,
S. Wolpert.

PREVIOUS YEARS: 2012-2013, 2013-2014, 2014-2015, 2015-2016, 2016-2017, 2017-2018, 2018-2019.

- 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.

- March 3, JHU

Felix Schulze (University of Warwick)

*Title: On the regularity of Ricci flows coming out of metric spaces*

Abstract: We consider smooth, not necessarily complete, Ricci flows, (M,g(t))_{t \in (0,T)} with Ric(g(t))\geq-1 and |Rm(g(t))|\leq c/t for all t\in(0,T) coming out of metric spaces (M,d_0) in the sense that (M,d(g(t)),x_0)->(M,d_0,x_0) as t->0 in the pointed Gromov-Hausdorff sense. In the case that B_{g(t)}(x_0,1)\Subset M for all t \in (0,T) and d_0 is generated by a smooth Riemannian metric in distance coordinates, we show using Ricci-harmonic map heat flow, that there is a corresponding smooth solution \tilde{g}(t)_{t\in (0,T)} to the \delta-Ricci-DeTurck flow on an Euclidean ball B_r(p_0)\subset R^n, which can be extended to a smooth solution defined for t\in [0,T). We further show, that this implies that the original solution g can be extended to a smooth solution on B_{d_0}(x_0,r/2) for t \in [0,T), in view of the method of Hamilton. This is joint work with Alix Deruelle and Miles Simon.

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.