# CUNY Diff Geom Seminar Spring 2016

## soon to be the

**In Spring 2016, we meet on Thursdays 2:45-3:45 pm in room 6496,** unless otherwise noted. The organizers of this seminar are Professors Christina Sormani, Luis Fernandez and Neil Katz. Please email Prof Sormani to schedule a guest speaker. We expect this semester to primarily have group members present to each other rather than having outside guest speakers. We are very small with a few faculty on sabbatical. 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).

**Feb 11:** **Marcus Khuri (SUNY Stony Brook)**

Title: A mass-angular momentum-charge inequality for multiple black holes, size-angular momentum-charge inequalities for bodies, and existence of black holes

Abstract: In the first part of the talk we present a proof of the mass-angular momentum-charge inequality for multiple black holes (joint with G. Weinstein). In the second part, new inequalities relating the size and angular momentum as well as size and charge of bodies is presented. Lastly, black hole existence results due to concentration of angular momentum and charge will be discussed.

**Feb 18: No Meeting**

**Feb 25: Ling Xiao (Rutgers)**

Title: Entire downward translating solitons to the mean curvature flow in Minkowski space.

Abstract: In 2005, Mark A. S. Aarons conjectured that if $u$ is a downward translating solution to the mean curvature flow with forcing term in Minkowski space, then it has to be rotationally symmetric or flat. In this talk, we will discuss some classical results related to this topic and also our results and proof. This is a joint work with J. Spruck.

**Mar 3:** **Mehdi Lejme (BCC)**

Title: Hypercomplex manifolds of dimension 8.

Abstract: The goal of the talk is to prove a quaternionic analog of the well-known fact that a compact complex surface is Kähler if and only if its first Betti number is even. More precisely, we prove that a compact 8-dimensional SL(2,H) manifold admits an hyperkähler with torsion metric if and only if its Hodge number h^{0,1} is even. This is a joint work with Gueo Grantcharov and Misha Verbitsky.

**Mar 10:** **Sylvester Eriksson-Bique**

Title: Quantitative Bi-Lipschitz embeddings of bounded curvature manifolds

and orbifolds

Abstract: In this talk we will outline a multi-scale method for constructing bi-Lipschitz embeddings for bounded curvature manifolds and

orbifolds. The results heavily rely on ideas from collapsing theory. We outline two proofs; one based solely on collapsing theory and a more

algebraic proof. The algebraic approach leads to a more quantitative collapsing theory for certain model spaces, and thus permits us to

give some explicit bounds for the bi-Lipschitz constants.

**Mar 17: St. Patrick's Day**

**Mar 24: Chen-Yun Lin (Toronto)**

Title: Local embedding of Riemannian manifolds and its application to image denoising.

Abstract: Data sets often have certain nonlinear structures. Modeling/Approximating the nonlinear structures by the manifold model is attracting more and more attention in data science nowadays. A natural question is to find coordinate charts for data sets, i.e., manifolds. In this talk, I will discuss local embedding of manifolds via eigen-vector fields of the connection Laplacian. For data sets, the eigen-vector fields can be computed by the graph connection Laplacian (GCL). I will also discuss the mathematical framework of image denoising via the GCL.

**Mar 31:** **Marcel Schmidt (Friedrich Schiller University Jena)**

Title: Does diffusion determine the geometry?

Abstract: Can one hear the shape of a drum? In mathematical terms this famous question of M. Kac asks whether two unitarily equivalent Laplacians live on the same geometric object. It is now known, that the answer to this question is negative in general. Following an idea of Wolfgang Arendt, we replace the unitary transformation intertwining the Laplacians by an order preserving one and then ask how much of the geometry is preserved. In this situation the associated semigroups, which encode diffusion, are equivalent up to an order isomorphism. Therefore, our question becomes as stated in the title and we try to give an answer. In particular, we discuss the situation for graph Laplacians. (this is joint work with Matthias Keller, Daniel Lenz and Melchior Wirth)

**Apr 7:** No meeting (Eleanora DiNezza at Columbia) **(****Geometry Festival ****this weekend)**

**Apr 14: ** No meeting (Sormani out of town) (Jian Song at Columbia)

**Apr 21: **No Meeting (Simon Brendle at Columbia)

**Apr 28: No Meeting (Spring break)**

**May 5: Rafael Montezuma Pinheiro Cabral (Princeton University)**

Title: Min-max minimal hypersurfaces in noncompact manifolds

Abstract: I will discuss the existence of embedded closed minimal hypersurfaces in complete noncompact manifolds containing a bounded open subset with smooth and strictly mean-concave boundary and a natural behavior on the geometry at infinity. For doing this, we develop a modified min-max theory for the area functional following Almgren-Pitts' setting, to produce minimal hypersurfaces with intersecting properties.

**May 12: Samuel Weiner (UNICAMP)**

Title: Dirac Equation and Isometric Immersions

Abstract: In a famous paper, Thomas Friedrich (1998) showed how the Weiestrass representation of minimal surfaces can be understood in terms of the appropriate Dirac equation. In addition, it is also proved that this kind of result can be generalized to certain isometric immersions of surfaces. Following this article, a series of authors extended this result to a few particular dimensions. The aim of this talk is to present a bit of my Ph. D. project: the generalization of Friedrich's result to arbitrary dimensions.

**CUNY Differential Geometry Seminar**s

Spring 2011, Fall 2010, Spring 2010, Fall 2009, Spring-Summer 2009, Fall 2008, Spring 2008, Fall 2007, Spring-Summer 2007, Fall 2006, Spring-Summer 2006, Fall 2005, Spring 2005, Fall 2004, Spring 2004, Fall 2003, Spring 2003,Fall 2002, Spring 2002, Fall 2001, Spring 2001.