CUNY Geometric Analysis Seminar
In Fall of 2017, we will meet on Thursdays, at 3pm in a room to be announced.
Room 6496. The
organizers of this seminar are Zeno Huang,
Neil Katz
and Bianca Santoro. Please
email Bianca at bsantoro(NoSpamPlease)ccny.cuny.edu to schedule a guest
speaker.
The CUNY Graduate Center is located at 365 Fifth Avenue at 34th Street, diagonally across the street
from the Empire State Building, just two blocks from Penn Station (NYC).
Fall 2017:
- Thursday, September 14: Yiming Zhao (NYU/St. Johns University)
Minkowski-type problems in convex geometry
Abstract: An overview of Minkowski-type problems will be presented. Minkowski-type problems are related to Monge-Ampere equations. Particular focus will be on the dual Minkowski problem, which is the characterization problem for a family of new geometric measures, called dual curvature measures, introduced in [Huang, Lutwak, Yang, Zhang; Acta 2016]. These are the "duals" of Federer's curvature measure. A solution to the dual Minkowski problem in the symmetric case will be demonstrated. The solution is strongly connected to measure concentration phenomenon.
- Thursday, September 21: No Seminar
Holiday
- Thursday, September 28: Klaus Kroencke (University of Hamburg)
Stability of ALE Ricci-flat manifolds under Ricci-flow
Abstract: We prove that if an ALE Ricci-flat manifold (M,g) is linearly stable and integrable, it is dynamically stable under Ricci flow, i.e. any Ricci flow starting close to g exists for all time and converges modulo diffeomorphism to an ALE Ricci-flat metric close to g. By adapting Tian's approach in the closed case, we show that integrability holds for ALE Calabi-Yau manifolds which implies that they are dynamically stable. This is joint work with Alix Deruelle
- Thursday, October 5: Xiaochun Rong (Rutgers University)
Collapsed manifolds with Ricci curvature and local rewinding volume bounded below
Abstract: I'll report some recent progress in the study of manifolds in the title. Given a number rho>0 and a point x in M, a complete n-manifold, the local rewinding volume of the rho-ball at x, B_rho(x), is the volume of the \rho-ball at \tilde xon the (incomplete) Riemannian universal cover of B_rho(x). Part of this work is joint with Hongzhi Huang, Zuohai Jiang and Shicheng Xu of Capital Normal University.
- Thursday, October 12: Hengyu Zhou (Sun Yat-Sen University)
Mean Curvature Flows in Warped Product Manifolds
Abstract: In this talk we discuss the mean curvature flow of starshaped hypersurface in warped product manifolds admitting a totally geodesic slice Sigma. With some natural conditions on the warping function and Ricci curvature, long time existences and convergences to Sigma are established. This is a joint work with Zhou Zhang (Sydney) and Zheng Huang (CUNY).
- Thursday, October 19: CUNY symposium on nonlinear problems in geometry
TBA
- Thursday, October 26: Valentino Tosatti (Northwestern University)
TBA
Abstract: TBA
- Thursday, November 2: Renato Bettiol (University of Pennsylvania)
TBA
Abstract: TBA
- Thursday, November 9: TBA
TBA
Abstract: TBA
- Thursday, November 16: Xinliang An (University of Toronto)
On Singularity Formation in General Relativity
Abstract: In the process of gravitational collapse, singularities may form, which are either covered by trapped surfaces (black holes) or visible to faraway observers (naked singularities). In this talk, with three different approaches coming from hyperbolic PDE, quasilinear elliptic PDE and dynamical system, I will provide answers for four physical questions: i) Can black holes form dynamically in vacuum? ii) To form a black hole, what is the least size of initial data? iii) Can we find the boundary of a black hole region? Can we show that a black hole region is emerging from a point? iv) For Einstein vacuum equations, could singularities other than black hole type form in gravitational collapse?
- Thursday, November 23: No seminar
Thanksgiving
- Thursday, November 30: Nan Li (New York City Tech)
TBA
Abstract: TBA
- Thursday, December 7: TBA
TBA
Abstract: TBA
Spring 2017:
- Thursday, February 16: Yusheng Wang (Beijing Normal University and Rutgers University)
Curvature>=1, diameter>=\pi/2 and rigidity (in Alexandrov geometry)
Abstract: In this talk, we will review some classical and recent rigidity results in Alexandrov geometry with curvature >=1 (including Riemannian geometry with sectional curvature
>=1) brought by distance>=\pi/2 between points or convex subsets.
- Thursday, February 23: Jorge Basilio (Graduate Center, CUNY)
Sequences of three-dimensional manifolds with positive scalar curvature
Abstract: Here we explore to what extent one may hope to preserve geometric properties of three dimensional manifolds with lower scalar curvature bounds under Gromov-Hausdorff and Intrinsic Flat limits. We introduce a new construction of three dimensional manifolds with positive scalar curvature called sewing. We produce sequences of such manifolds which converge to spaces demonstrating that almost rigidity theorems for manifolds with positive or nonnegative scalar curvature fail to hold for these limits including the Scalar Torus Rigidity Theorem and the rigidity part of the Positive Mass Theorem. Since the notion of nonnegative scalar curvature is not strong enough to persist alone, we propose that one pair a lower scalar curvature bound with a lower bound on the area of a closed minimal surface when taking sequences as this will prevent the sewing of manifolds and possibly also the existence of counter examples. This is joint work with Christina Sormani.
- Thursday, March 16: Dan Ketover (Princeton University)
Variational constructions of minimal surfaces
Abstract: I will describe how variational methods can be applied to produce many new examples of minimal surfaces with various symmetries. IÕll focus on the construction of free boundary minimal surfaces resembling a desingularization of the critical catenoid and flat disk, which were first conjectured by Fraser-Schoen.
- Thursday, March 23: Jacob Bernstein (Johns Hopkins University)
Surfaces of Low Entropy
Abstract: Following Colding and Minicozzi, we consider the entropy of (hyper)-surfaces in Euclidean space. This is a numerical measure of the geometric complexity of the surface. In addition, this quantity is intimately tied to to the singularity formation of the mean curvature flow which is a natural geometric heat flow of submanifolds. In the talk, I will discuss several results that show that closed surfaces for which the entropy is small are simple in various senses. This is all joint work with L. Wang.
- Thursday, March 30: Florentin Munch (Potsdam University)
Rigidity properties of the hypercube via discrete Ricci curvature
Abstract: We give rigidity results for discrete Bonnet-Myers diameter bound
and Lichnerowicz eigenvalue estimate. Both inequalities are sharp if
and only if the underlying graph is a hypercube. The proofs use
well-known semigoup methods as well as new direct methods which
translate curvature to combinatorial properties. The results can be
seen as first known discrete analogues of Cheng's
and Obata's rigidity theorems.
- Thursday, April 6: Ronan Conlon (Florida International University)
New examples of gradient expanding Kahler-Ricci solitons
Abstract: A complete Kahler metric g on a Kahler manifold M is a gradient expanding Kahler-Ricci soliton if there exists a smooth real-valued function f:M -> R with $\nabla^{g}f$ holomorphic such that Ric(g)-Hess(f)+g=0. I will present new examples of such metrics on the total space of certain holomorphic vector bundles. This is joint work with Alix Deruelle (Universite Paris-Sud).
- Thursday, April 27: Liming Sun (Rutgers University)
Prescribed scalar curvature plus mean curvature flows in compact manifolds with boundary of negative conformal invariant
Abstract: We study one of Yamabe problems on compact manifolds with boundary. For negative Yamabe type manifolds, we are able to prescribe scalar curvature and boundary mean curvature. Precisely, given any negative smooth functions f in M and h on the boundary $\partial M$, there exists a unique conformal metric of g_0 such that its scalar curvature equals f and mean curvature curvature equals h. One family of flow with dynamic boundary mean curvature is constructed to prove this result. At the end, I will mention some ongoing results on positive type manifold using flow approach.
- Thursday, May 4: TBA
TBA
Abstract: TBA
- Thursday, May 11: Jiayin Pan (Rutgers University)
A proof of Milnor conjecture in dimension 3
Abstract: In this talk, we present a proof of Milnor conjecture in dimension 3 based on the Cheeger-Colding theory on limit spaces of manifolds with Ricci curvature
bounded below.
Fall 2016: