In Spring 2012, we will meet on Tuesdays, either at 3:00pm in Room 3207, or at 1:30pm in Room 4214-03 (aka math thesis room). The organizers of this seminar are Dan Lee, Zheng Huang, and Marcello Lucia. Please email Dan at dan.lee(NoSpamPlease)qc.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).

Spring 2012:

Tuesday, 1/31 at 1:30 in thesis room: Tristan Collins (Columbia University)
The transverse entropy functional and the Sasaki-Ricci flow
Abstract: In this talk I will introduce the Sasaki-Ricci flow, and define a transverse entropy functional which is monotonic along the flow. I will then discuss a non-collapsing theorem for the Sasaki-Ricci flow, which is instrumental in generalizing some deep results of Perelman for the K\"ahler-Ricci flow to the Sasaki setting.
Tuesday, 2/7 at 3:00 in 3207: Ling Xiao (Johns Hopkins University)
Convex spacelike hypersurfaces of constant curvature in de Sitter space
Abstract: In this talk we are interested in finding complete spacelike (i.e. the induced metric is Riemannian) strictly locally convex immersions with constant curvature and with prescribed (compact) future asymptotic boundary.
Tuesday, 2/14: no seminar
no classes on 2/13
Tuesday, 2/21: no seminar
classes follow Monday schedule
Thursday, 2/23 in Room 4102: Recent Developments in Minimal Surfaces
Speakers are William H. Meeks III, William P. Minicozzi II, Jean-Marc Schlenker, and Michael Wolf. Click here for details.
Tuesday, 2/28: no seminar
Tuesday, 3/6: no seminar
Tuesday, 3/13 at 1:30 in thesis room: Jin-ichi Itoh (Kumamoto Univeristy)
Cut locus of Riemannian manifolds and related topics
Abstract: We will shortly review the history of study of cut locus and will discuss recent results, the cut locus of ellipsoids and cut locus structures. Moreover, as applications we will discuss about thread construction of ellipsoids, unfolding of polyhedra or continuous flattening of poyhedra.
Tuesday, 3/20 at 3:00 in 3207: Junfang Li (University of Alabama at Birmingham)
A new mean curvature type of flow and its fully nonlinear version
Abstract: (Joint with Pengfei Guan) In this talk, we will present a new type of mean curvature flow. For any closed star-shaped smooth hypersurface, this flow exists for all time t>0 and exponentially converges to a round sphere. Moreover, we will show that all the quermassintegrals evolve monotonically along this flow. Consequently, we prove a class of isoperimetric type of inequalities including the classical isoperimetric inequality on star-shaped domains. We will also present a fully non-linear analogue of this flow. More specifically, we study a fully non-linear parabolic equation of a function on the standard sphere and discuss its long-time existence and exponential convergence. As applications, we recover the well-known Alexandrov-Fenchel inequalities on bounded convex domains in Euclidean space.
Tuesday, 3/27 at 3:00 in 3207: Stephen Kleene (MIT)
Self Shrinkers for the mean curvature flow via singular perturbation
Abstract: I will discuss recent work with Niels Martin Moller and Nicos Kapouleas in which complete embedded self shrinkers are constructed via a desingularization procedure. I will also discuss future directions of this project.
Tuesday, 4/3: no seminar
Tuesday, 4/10: no seminar
Spring Break
Tuesday, 4/17 at 3:00 in 3207: Jingyi Chen (University of British Columbia)
A Bernstein type theorem for entire Willmore graphs
Abstract: We show that if the second fundamental form of an entire Willmore graph in 3-dimensional euclidean space is square integrable then it is flat. This is joint work with Tobias Lamm.
Tuesday, 4/24 at 3:00 in 3207: no seminar
Tuesday, 5/1 (TWO TALKS) at 1:30 in thesis room: Marcus Khuri (Stony Brook University)
The conformal flow of metrics and the general Penrose inequality
Abstract: Hubert Bray's conformal flow of metrics was introduced to prove the Penrose inequality in the time symmetric case. In this talk we explore ways in which it may be generalized and applied to the Penrose inequality without the time symmetric assumption.
At 3:00 in Room 3207: Christine Breiner (MIT)
A variational Characterization of the Catenoid
Abstract: We show that the catenoid is the unique surface of least area (suitably understood) within a geometrically natural class of minimal surfaces. The proof relies on a techniques involving the Weierstrass representation used by Osserman and Schiffer to show the sharp isoperimetric inequality for minimal annuli. An alternate approach that avoids the Weierstrass representation will also be discussed. This latter approach depends on a conjectural sharp eigenvalue estimate for a geometric operater and has interesting connections with spectral theory. This is joint work with J. Bernstein.
Tuesday, 5/8 at 3:00 in 3207: no seminar
Tuesday, 5/15 at 3:00 in 3207: John Head (NYU)
Mean curvature flow of two-convex hypersurfaces
Abstract: We discuss recent progress on the mean curvature evolution of smooth, closed, two-convex hypersurfaces in Euclidean space. In particular, we describe the Huisken-Sinestrari surgery program, explain how it relates to the theory of weak solutions and discuss applications to regularity theory for mean curvature flow.
Tuesday, 5/29 at 2:00 in thesis room: Andre Neves (Imperial College)
Min-max theory and the Willmore Conjecture
Abstract: In 1965, T. J. Willmore conjectured that the integral of the square of the mean curvature of any torus immersed in Euclidean three-space is at least 2 \pi^2. I will talk about my recent joint work with Fernando Marques in which we prove this conjecture using the min-max theory of minimal surfaces.