Seminars Sorted by Series

Abstract: Given a class of conformally compact Einstein manifolds with boundary, we are interested to study the compactness of the class under some local and non-local boundary constraints. I will report some joint work with Yuxin Ge and Jie Qing...

Abstract: We discuss singularities of Teichmueller harmonic map flow, which is a geometric flow that changes maps from surfaces into branched minimal immersions, and explain in particular how winding singularities of the map component can lead to...

Abstract: Colding-Minicozzi introduced a natural entropy for hypersurfaces in euclidean space that is non-increasing under the mean curvature flow (MCF) and is a natural measure of the hypersurface's geometric complexity. In particular...

Abstract: After recalling the gluing construction for Kaehler constant scalar curvature and extremal (`a la Calabi) metrics starting from a compact or ALE orbifolds with isolated singularities, I will show how to compute the Futaki invariant of the...

Abstract : What are the possible limits of smooth curvatures with uniformly bounded $L^p$ norms ?We shall see that the attempts to give a satisfying answer to this natural question from the calculus of variation of gauge theory brings us to numerous...

Abstract: The spacetime positive mass theorem says that an asymptotically flat initial data set with the dominant energy condition must have a timelike energy-momentum vector, unless the initial data set is in the Minkowski spacetime. We will review...

Abstract: I will talk about periodic geodesics, geodesic loops, and geodesic nets on Riemannian manifolds. More specifically, I will discuss some curvature-free upper bounds for compact manifolds and the existence results for non-compact manifolds...

Abstract: Functional Determinants are quantities constructed out of spectra of conformally covariant operators, and are explicit in dimension two and four, due to formulas by Polyakov and Branson-Oersted. Extremizing them in a conformal class...

Abstract: Finding non-constant harmonic 3-spheres for a closed target manifold N is a prototype of a super-critical variational problem. In fact, the
direct method fails, as the infimum of the Dirichlet energy in any homotopy class of maps from the...

Abstract: Let M be a compact Riemannian manifold. Morse theory for the energy function on the free loopspace LM of M gives a link between geometry and topology, between the growth of the index of the iterates of closed geodesics on M, and the...

Abstract: It is a basic open question in geometric measure theory to understand regularity of a stationary integral varifold. Even a.e. regularity remains an open question. The central issue is analyzing the varifold near a point Z with a tangent...

Abstract: For a given finite subset S of a compact Riemannian manifold (M; g) whose Schouten curvature tensor belongs to a given cone, we establish a necessary and
sufficient condition for the existence and uniqueness of a conformal metric on $M...

Abstract : It is a joint work with G. Courtois, S. Gallot and A.Sambusetti. We prove a compactness theorem for metric spaces with anupper bound on the entropy and other conditions that will be discussed.Several finiteness results will be drawn. It...

Abstract: We present new-curvature one-cycle sweepout estimates in Riemannian geometry, both on surfaces and in higher dimension. More precisely, we derive upper bounds on the length of one-parameter families of one-cycles sweeping out essential...

Abstract: For surfaces immersed into a compact Riemannian manifold, we consider the curvature functional given by the $L^2$ integral of the second fundamental form. We discuss an an area bound in terms of that functional, with application to the...

Abstract: Uryson k-width of a metric space X measures how close X is to being k-dimensional. Several years ago Larry Guth proved that if M is a closed n-dimensional manifold, and the volume of each ball of radius 1 in M does not exceed a certain...