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For Zoom URL please contact Laura Keller

Spring Semester 2016

Date / Time Speaker Title Location
1 March 2016
15:15-16:15 		Dr. Luca Spolaor
Max Plank, Leipzig
Event Details

Analysis Seminar

Title "Regularity results for semicalibrated currents"
Speaker, Affiliation Dr. Luca Spolaor, Max Plank, Leipzig
Date, Time 1 March 2016, 15:15-16:15
Location HG G 43
Abstract In this talk I will introduce the notion of semicalibrated currents and give some examples. After that I will present some regularity results, which are analogous to the ones for area minimizing currents. Finally I will try to give an idea of the proof of the following fact: the singular set of a two dimensional semicalibrated current is locally finite. In particular I will explain what are the center manifold and the frequency function, and try to explain their roles in the proof.
"Regularity results for semicalibrated currents"read_more
HG G 43
8 March 2016
15:15-16:15 		Prof. Dr. Andrea Malchioldi
SNS, Pisa
Event Details

Analysis Seminar

Title A positive mass theorem in CR geometry
Speaker, Affiliation Prof. Dr. Andrea Malchioldi, SNS, Pisa
Date, Time 8 March 2016, 15:15-16:15
Location HG G 43
Abstract We consider a class of CR manifolds which are defined as asymptotically Heisenberg, and for these we give a notion of mass. From the solvability of the $\Box_b$ equation in a certain weighted class, we prove positivity of the mass under the condition that the Webster curvature is positive and that the manifold is embeddable. We apply this result to the Yamabe problem for compact CR manifolds, and we discuss the properties of Sobolev-type quotients. This is joint work with J.H.Cheng and P.Yang.
A positive mass theorem in CR geometryread_more
HG G 43
22 March 2016
15:15-16:15 		Prof. Dr. Jean-Claude Saut
Université Orsay
Event Details

Analysis Seminar

Title "Long time existence for some water waves systems”
Speaker, Affiliation Prof. Dr. Jean-Claude Saut, Université Orsay
Date, Time 22 March 2016, 15:15-16:15
Location HG G 43
"Long time existence for some water waves systems”
HG G 43
5 April 2016
15:15-16:15 		Prof. Dr. Bernard Dacorogna
Université de Lausanne
Event Details

Analysis Seminar

Title "Symplectic decomposition, Darboux theorem and ellipticity"
Speaker, Affiliation Prof. Dr. Bernard Dacorogna, Université de Lausanne
Date, Time 5 April 2016, 15:15-16:15
Location HG G 43
"Symplectic decomposition, Darboux theorem and ellipticity"
HG G 43
12 April 2016
14:15-15:15 		Dr. Costante Bellettini
University of Cambridge
Event Details

Analysis Seminar

Title Regularity of stable CMC hypersurfaces
Speaker, Affiliation Dr. Costante Bellettini, University of Cambridge
Date, Time 12 April 2016, 14:15-15:15
Location HG G 43
Abstract In a joint work with N. Wickramasekera (Cambridge) we develop a regularity and compactness theory for a class of codimension-1 integral n-varifolds with generalised mean curvature in L^{p}_{loc} for some p > n. Subject to suitable variational hypotheses on the regular part (namely criticality and stability for the area functional with respect to variations that preserve the "enclosed volume") and two necessary structural assumptions, we show that the varifolds under consideration are "smooth" (and have constant mean curvature) away from a closed singular set of codimension 7. In the case that the mean curvature is non-zero, the smoothness is to be understood in a generalised sense, i.e. also allowing the tangential touching of two smooth CMC hypersurfaces (e.g. two spheres touching).
Regularity of stable CMC hypersurfacesread_more
HG G 43
12 April 2016
15:30-16:30 		Dr. Francesca De Marchis
University "La Sapienza" of Rome
Event Details

Analysis Seminar

Title The singular Nirenberg problem
Speaker, Affiliation Dr. Francesca De Marchis, University "La Sapienza" of Rome
Date, Time 12 April 2016, 15:30-16:30
Location HG G 43
Abstract I will consider the problem of prescribing the Gaussian curvature (under pointwise conformal change of the metric) on surfaces with conical singularities. This question has been first raised by Troyanov and it is a generalization of the Kazdan-Warner problem for regular surfaces, known as the Nirenberg problem on the sphere. Answer this question amounts to solve a singular differential problem on the surface. This equation has been studied first in the case K > 0, where K denotes the curvature we want prescribe. I will present some new results (obtained in collaboration with R. Lopez-Soriano) in the case K sign-changing. When the surface is the sphere, under some mild conditions on the nodal set of K we derived some sufficient conditions on K and on the conical singularities for the existence of solutions of (1). Even if we do not expect these conditions to be necessary, I will explain why they are somehow sharp.
Assets https://math.ethz.ch/ndb/00006/08316/AbstractZurigo.pdffile_download
The singular Nirenberg problemread_more
HG G 43
19 April 2016
15:15-16:15 		Prof. Dr. Karl-Theodor Sturm
Universität Bonn
Event Details

Analysis Seminar

Title Super-Ricci Flows for Metric Measure Spaces
Speaker, Affiliation Prof. Dr. Karl-Theodor Sturm , Universität Bonn
Date, Time 19 April 2016, 15:15-16:15
Location HG G 43
Abstract A time-dependent family of Riemannian manifolds is a super-Ricci flow if 2 Ric + \partial_t g \ge 0. This includes all static manifolds of nonnegative Ricci curvature as well as all solutions to the Ricci flow equation. We extend this concept of super-Ricci flows to time-dependent metric measure spaces. In particular, we present characterizations in terms of dynamical convexity of the Boltzmann entropy on the Wasserstein space as well in terms of Wasserstein contraction bounds and gradient estimates. And we prove stability and compactness of super-Ricci flows under mGH-limits.
Super-Ricci Flows for Metric Measure Spacesread_more
HG G 43
26 April 2016
15:15-16:15 		Prof. Dr. Xiuxiong Chen
SUNY Stony Brook
Event Details

Analysis Seminar

Title On the Kähler Ricci flow
Speaker, Affiliation Prof. Dr. Xiuxiong Chen, SUNY Stony Brook
Date, Time 26 April 2016, 15:15-16:15
Location HG G 43
On the Kähler Ricci flow
HG G 43
24 May 2016
15:15-16:15 		Prof. Dr. Benjamin Sharp
Imperial College London
Event Details

Analysis Seminar

Title Morse index and Betti numbers of minimal hypersurfaces
Speaker, Affiliation Prof. Dr. Benjamin Sharp, Imperial College London
Date, Time 24 May 2016, 15:15-16:15
Location HG G 43
Abstract Abstract: As critical points of the area functional, minimal hypersurfaces of Riemannian manifolds have a well-defined Morse index. In general, a minimal hypersurface with bounded index and area is also qualitatively controlled in terms of both geometry and topology (Buzano - Sharp 2016 preprint). However, in the case where the ambient manifold has positive curvature it is expected that control on the index alone is enough to conclude quantitative linear bounds on the first Betti number of the minimal hypersurface - a conjecture of Schoen and Marques-Neves. In this talk, we will show that under certain conditions on the ambient manifold, the index of a minimal hypersurfaces grows linearly with their first Betti numbers. The hypotheses on the ambient manifold are flexible enough to include all compact symmetric spaces of rank one and small graphical perturbations of the round sphere, for example. Thus we verify the Schoen, Marques-Neves conjecture in these cases. This is a joint work with L. Ambrozio and A. Carlotto.
Morse index and Betti numbers of minimal hypersurfacesread_more
HG G 43

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Organizers: Francesca Da Lio, Tom Ilmanen, Thomas Kappeler, Tristan Rivière, Michael Struwe

Archive: SS 24 AS 23 SS 23 AS 22 SS 22 AS 21 SS 21 AS 20 SS 20 AS 19 SS 19 AS 18 SS 18 AS 17 SS 17 AS 16 SS 16 AS 15 SS 15 AS 14 SS 14 AS 13 SS 13 AS 12 SS 12 AS 11 SS 11 AS 10 SS 10 AS 09

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