CUNY Geometric Analysis Seminar
In Spring of 2020, we will meet on Thursdays, at 3pm,
room 6495. The
organizers of this seminar are Renato Bettiol,
and Bianca Santoro. Please
email Bianca at bsantoro(NoSpamPlease)ccny.cuny.edu to schedule a guest
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).
Those participating in the Geometric Analysis seminar may also be interested in the Nonlinear Analysis and PDEs seminar which meets Thursdays in room 6496 starting at 4:15pm.
- Thursday, February 6, 3pm, Double Header: Nan Li (CUNY City Tech)
Gluing of multiple Alexandrov spaces
It was proved by Petrunin that the space glued by an intrinsic isometry between the boundaries of two Alexandrov spaces is an Alexandrov space with the same lower curvature bound. We will discuss some generalizations of this theorem, in which the partial gluing of multiple Alexandrov spaces are included.
- Thursday, February 6, 4:15pm, room 6496, Double Header: Yehuda Pinchover (The Technion - Israel Institute of Technology) . This is a joint event with the Nonlinear Analysis and PDEs seminar.
How large can Hardy-weight be?
In the first part of the talk we will discuss the existence of optimal Hardy-type inequalities with 'as large as possible' Hardy-weight for a general second-order elliptic operator defined on noncompact Riemannian manifolds and discrete graphs, while the second part of the talk will be devoted to a sharp answer to the question: "How large can Hardy-weight be?"
- Thursday, February 13: No Seminar
- Thursday, February 20, 3pm, Double Header: Marco Guaraco (University of Chicago)
Minimal surfaces and mean curvature flow in hyperbolic
We show that every quasi-Fuchsian manifold has a canonical
minimal surface bounding all incompressible minimal surfaces and one
end. We use this canonical surface to study the possibility of
parametrizing the space of quasi-Fuchsian manifolds using formal
minimal surfaces, revisiting a problem studied by K. Uhlenbeck in the
80s. In addition, as an application of the mean curvature flow with
surgery, we establish the existence of incompressible mean-convex
foliations in general three-manifolds. Combining this result with
ideas from min-max theory, we show that generic quasi-Fuchsian
manifolds admit entire foliations by smooth mean-convex surfaces.
(This is joint work with V. Lima and F. Vargas Pallete)
- Thursday, February 20, 4:15pm, room 6496, Double Header: Liming Sun (Johns Hopkins University)
Some convexity theorems of translating solitons in the mean curvature flow.
I will be talking about the translating solitons (translators) in the mean curvature flow. Convexity theorems of translators play fundamental roles in the classification of them. Spruck and Xiao proved any two dimensional mean convex translator is actually convex. Spruck and I proved a similar convex theorem for higher dimensional translators, namely the 2-convex translating solitons are actually convex. Our theorem implies 2-convex translating solitons have to be the bowl soliton. Our second theorem regards the solutions of the Dirichlet problem for translators in a bounded convex domain . We proved the solutions will be convex under appropriate conditions. This theorem implies the existence of n-2 family of locally strictly convex translators in higher dimension. In the end, we will show that our method could be used to establish a convexity theorem for constant mean curvature graph equation.
- Thursday, February 27: Jackson Goodman (U Penn)
- Thursday, March 5: TBA
- Thursday, March 12, 3pm, Double Header: Xiaowei Wang (Rutgers University)
- Thursday, March 12, 4:15pm, room 6496, Double Header: Zuoqin Wang (USTC/MIT). This is a joint event with the Nonlinear Analysis and PDEs seminar.
Semi-classical isotropic functions and applications
Rapidly oscillating functions associated with Lagrangian submanifolds play a fundamental role in semi-classical analysis. In this talk I will describe how to associate spaces of semi-classical oscillatory functions to isotropic submanifolds of phase space, and sketch their symbol calculus. As a special case we obtain the semi-classical version of the Hermite distributions of Boutet the Monvel and Guillemin. I will also discuss a couple applications of the theory. This is based on joint works with Victor Guillemin and Alejandro Uribe.
- Thursday, March 19, 4:15pm, room 6496: Jie Qing (University of California at Santa Cruz). This is a joint event with the Nonlinear Analysis and PDEs seminar.
- Thursday, March 26: Peter Smilie(Caltech)
- Thursday, April 2: Ravi Shankar (University of Oklahoma)
- Thursday, April 9 and 16: No seminar
- Thursday, April 23: CUNY symposium
Details to be announced soon!
- Thursday, April 30: Anusha Krishnan (Syracuse University)
- Thursday, May 7: Tim Buttsworth (Cornell University)
- Thursday, May 14, 3pm, Double Header: Jonathan Zhu(Princeton)
- Thursday, May 14, 4:15pm, room 6496, Double Header: Ronan Conlon (Florida International University). This is a joint event with the Nonlinear Analysis and PDEs seminar.