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Seminars winter 2014/15

There are several research seminars in the Potsdam-Berlin area which are closely related to Geometric Analysis:

  • Usually biweekly during term, on Thursdays, the joint seminar "Topics in Geometric Analysis" taking place in turns at the University of Potsdam (UP), the Albert Einstein Institute (AEI) and the Free University Berlin (FU). It is organised by Theodora Bourni (FU), Ulrich Menne (AEI), and Jan Metzger (UP). The dates are Oct 23 (UP), Nov 6 (FU), Dec 4 (UP), Jan 15 (FU) and Jan 29 (AEI).
  • In the weeks where there is no "Topics in Geometric Analysis" seminar there will usually be a reading seminar on "Geometric Measure Theory" at the Albert Einstein Institute (AEI). It will take place on Oct 16, Oct 30, Nov 13, Nov 27, Dec 11, Jan 8, Jan 22, and Feb 5. Details see below.
Timetable of seminars
DatesTypePlaceSpeakerTopic
Oct 16th, 2014, 10:00-11:30 GMT reading seminar Albert Einstein Institute, Room 0.01, Am Mühlenberg 1, 14476 Potsdam Ananda Lahiri (AEI) Frank Duzaar and Giuseppe Mingione, "Second order parabolic systems, optimal regularity, and singular sets of solutions", 2005.
Oct 16th, 2014, 12:30-14:00 GMT reading seminar Albert Einstein Institute, Room 0.01, Am Mühlenberg 1, 14476 Potsdam Ananda Lahiri (AEI) Frank Duzaar and Giuseppe Mingione, "Second order parabolic systems, optimal regularity, and singular sets of solutions", 2005.
Oct 23th, 2014, 11:00-12:30 GMT reading seminar Albert Einstein Institute, Room 0.63, Am Mühlenberg 1, 14476 Potsdam Ananda Lahiri (AEI) Frank Duzaar and Giuseppe Mingione, "Second order parabolic systems, optimal regularity, and singular sets of solutions", 2005.
Oct 23th, 2014, 13:30-15:00 GMT reading seminar Albert Einstein Institute, Room 0.63, Am Mühlenberg 1, 14476 Potsdam Ananda Lahiri (AEI) Frank Duzaar and Giuseppe Mingione, "Second order parabolic systems, optimal regularity, and singular sets of solutions", 2005.
Oct 30th, 2014, 14:15-15:15 Topics in Geometric Analysis FU Berlin, Room 140, Arnimallee 5, 14195 Berlin André Arroja Neves (Imperial College London)
Minimal hypersurfaces in manifolds with positive Ricci curvature

I will show that manifolds with positive Ricci curvature have infinitely many minimal smooth embedded hypersurfaces. This is joint work with Fernando Marques.

Oct 30th, 2014, 15:45-16:45 Topics in Geometric Analysis FU Berlin, Room 140, Arnimallee 5, 14195 Berlin Andrea Marchese (MIS Leipzig)
Differentiability of Lipschitz functions with respect to measures in the Euclidean space

Rademacher theorem states that every Lipschitz function on the Euclidean space is differentiable almost everywhere, with respect to the Lebesgue measure. I will discuss an extension of this theorem where the Lebesgue measure is replaced by an arbitrary measure. Time permitting, in the last part of the talk, I will show some applications of this result about the theory of currents. This is joint work with Giovanni Alberti.

Nov 6th, 2014, 16:15-17:15 Topics in Geometric Analysis University of Potsdam, Room 1.14, Building 9, Am Neues Palais 10, 14469 Potsdam Matthew Randall (University of Hannover)
Generalised Ricci Solitons in 2 dimensions

We introduce a class of overdetermined systems of partial differential equations of on (pseudo)-Riemannian manifolds that we call the generalised Ricci soliton equations. These equations depend on three real parameters. For special values of the parameters they specialise to various important classes of equations in differential geometry. Among them there are: the Ricci soliton equations, the vacuum near-horizon geometry equations in general relativity, special cases of Einstein-Weyl equations and their projective counterparts, equations for homotheties and Killing's equation. We provide explicit examples of generalised Ricci solitons in 2 dimensions, some of them obtained using techniques developed by J. Jezierski. This is joint work with Pawel Nurowski available at arXiv:1409.4179.

Nov 6th, 2014, 17:45-18:45 Topics in Geometric Analysis University of Potsdam, Room 1.14, Building 9, Am Neues Palais 10, 14469 Potsdam Anna Sakovich (AEI)
On the positive mass theorem for asymptotically hyperbolic initial data

In this talk, we will discuss asymptotically hyperbolic initial data for the Einstein equations modeling asymptotically null slices in asymptotically Minkowski spacetimes. Such initial data consists of a Riemannian manifold (M,g) whose geometry at infinity approaches that of hyperbolic space, and a symmetric 2-tensor K representing the second fundamental form of the embedding into spacetime, such that K approaches g at infinity.

Just like in the asymptotically Euclidean setting, positive mass conjecture for asymptotically hyperbolic initial data can be proven by spin techniques in all dimensions. However, without spin assumption only partial results are available, even in the important particular case K=g, where the conjecture merely states that an asymptotically hyperbolic manifold whose scalar curvature is greater than or equal to the scalar curvature of hyperbolic space must have positive mass unless it is hyperbolic space.

Having reviewed the available results, we will present a non-spinor proof of positive mass theorem for asymptotically hyperbolic initial data sets in dimension 3. The argument uses the Jang equation to reduce the proof to the application of the celebrated Riemannian positive mass theorem for asymptotically Euclidean manifolds and can potentially be extended to all dimensions less than 8.

Nov 13th, 2014, 09:45-11:30 GMT reading seminar Albert Einstein Institute, Room 0.01, Am Mühlenberg 1, 14476 Potsdam Ananda Lahiri (AEI) Frank Duzaar and Giuseppe Mingione, "Second order parabolic systems, optimal regularity, and singular sets of solutions", 2005.
Nov 13th, 2014, 12:30-13:45 GMT reading seminar Albert Einstein Institute, Room 0.01, Am Mühlenberg 1, 14476 Potsdam Ananda Lahiri (AEI) Frank Duzaar and Giuseppe Mingione, "Second order parabolic systems, optimal regularity, and singular sets of solutions", 2005.
Nov 20th, 2014, 09:45-11:30 GMT reading seminar Albert Einstein Institute, Room 0.01, Am Mühlenberg 1, 14476 Potsdam Ananda Lahiri (AEI) Frank Duzaar and Giuseppe Mingione, "Second order parabolic systems, optimal regularity, and singular sets of solutions", 2005.
Nov 20th, 2014, 12:30-13:45 GMT reading seminar Albert Einstein Institute, Room 0.01, Am Mühlenberg 1, 14476 Potsdam Ananda Lahiri (AEI) Frank Duzaar and Giuseppe Mingione, "Second order parabolic systems, optimal regularity, and singular sets of solutions", 2005.
Nov 27th, 2014, 09:45-11:30 GMT reading seminar Albert Einstein Institute, Room 0.01, Am Mühlenberg 1, 14476 Potsdam Ananda Lahiri (AEI) Frank Duzaar and Giuseppe Mingione, "Second order parabolic systems, optimal regularity, and singular sets of solutions", 2005.
Nov 27th, 2014, 12:30-13:45 GMT reading seminar Albert Einstein Institute, Room 0.01, Am Mühlenberg 1, 14476 Potsdam Ananda Lahiri (AEI) Frank Duzaar and Giuseppe Mingione, "Second order parabolic systems, optimal regularity, and singular sets of solutions", 2005.
Dec 4th, 2014, 16:15-17:15 Topics in Geometric Analysis University of Potsdam, Room 1.14, Building 9, Am Neues Palais 10, 14469 Potsdam Costante Bellettini (University of Cambridge)
Regularity questions for semi-calibrated integral cycles

Semi-calibrated currents naturally appear when dealing with several geometric questions, some aspects of which require a deep understanding of regularity properties of semi-calibrated currents. We will focus mostly on the case of dimension $2$, where it turns out that semi-calibrated cycles are actually pseudo holomorphic. By using an analysis implementation of the algebro-geometric blowing up of a point we study the regularity of semi-calibrated $2$-cycles from the point of view of uniqueness of tangent cones and of local smoothness.

Dec 4th, 2014, 17:45-18:45 Topics in Geometric Analysis University of Potsdam, Room 1.14, Building 9, Am Neues Palais 10, 14469 Potsdam Esther Cabezas-Rivas (University of Frankfurt) “Whatever”-preserving mean curvature flows: what's new?

Constrained versions of the mean curvature flow have shown their unfriendliness due to the global nature of the equation, which makes the usual techniques in extrinsic flows either fail (like comparison principle, preservation of embeddedness,…) or become more subtle. Despite the difficulties, such flows (specially those preserving area or enclosed volume) are still quite appealing because they are specially well suited for applications to the isoperimetric problem.

This is an overview talk of the current situation of the study of such flows; we will review what has been done and which are the perspectives for the future. This will finish with the presentation of two counterexamples for the preservation of mean convexity (which has been claimed to be preserved in a couple of papers) and positivity of the scalar curvature, resp. This ends the hope of doing a singularity analysis à la Huisken-Sinestrari for such constrained flows.

Dec 11th, 2014, 09:45-11:30 GMT reading seminar Albert Einstein Institute, Room 0.01, Am Mühlenberg 1, 14476 Potsdam Sławomir Kolasiński (AEI) Richard Schoen and Leon Simon, "Regularity of Stable Minimal Hypersurfaces", 1981.
Dec 11th, 2014, 12:30-13:45 GMT reading seminar Albert Einstein Institute, Room 0.01, Am Mühlenberg 1, 14476 Potsdam Sławomir Kolasiński (AEI) Richard Schoen and Leon Simon, "Regularity of Stable Minimal Hypersurfaces", 1981.
Jan 8th, 2015, 09:45-11:30 GMT reading seminar Albert Einstein Institute, Room 0.01, Am Mühlenberg 1, 14476 Potsdam Sławomir Kolasiński (AEI) Richard Schoen and Leon Simon, "Regularity of Stable Minimal Hypersurfaces", 1981.
Jan 8th, 2015, 12:30-13:45 GMT reading seminar Albert Einstein Institute, Room 0.01, Am Mühlenberg 1, 14476 Potsdam Sławomir Kolasiński (AEI) Richard Schoen and Leon Simon, "Regularity of Stable Minimal Hypersurfaces", 1981.
Jan 15th, 2015, 16:15-17:15 Topics in Geometric Analysis FU Berlin, Room E31, Arnimallee 7, 14195 Berlin Heiko von der Mosel (RWTH Aachen)
On minimal surfaces in Finsler spaces (joint work with P. Overath)

In contrast to classic minimal surface theory relatively little seems to be known about minimal surfaces in Finsler manifolds. We explore a connection between the Busemann-Hausdorff volume in Finsler spaces and Cartan functionals to prove new results in that direction, such as Bernstein theorems, a uniqueness result, and removability of singularities for Finsler-minimal graphs, isoperimetric inequalities and enclosure theorems for minimal immersions in Finsler space, and we treat the Plateau problem in Finsler $3$-space.

Jan 15th, 2015, 17:45-18:45 Topics in Geometric Analysis FU Berlin, Room E31, Arnimallee 7, 14195 Berlin Joseph Grotowski (University of Queensland) Geometric Evolution Equations in critical dimensions

We consider the 4-D Yang Mills heat flow and the 2-D harmonic map heat flow. In these dimensions, the associated energy functional is (locally) conformally invariant, that is, the dimension is critical. We discuss some similarities and differences between the two flows, in particular in the equivariant setting.

Jan 22th, 2015, 09:45-11:30 GMT reading seminar Albert Einstein Institute, Room 0.01, Am Mühlenberg 1, 14476 Potsdam Sławomir Kolasiński (AEI)
Richard Schoen and Leon Simon, "Regularity of Stable Minimal Hypersurfaces", 1981.
Jan 22th, 2015, 12:30-13:45 GMT reading seminar Albert Einstein Institute, Room 0.01, Am Mühlenberg 1, 14476 Potsdam Theodora Bourni (FU Berlin) Richard Schoen and Leon Simon, "Regularity of Stable Minimal Hypersurfaces", 1981.
Jan 29th, 2015, 16:15-17:15 Topics in Geometric Analysis Albert Einstein Institute, Room 0.01, Am Mühlenberg 1, 14476 Potsdam Guofang Wang (University of Freiburg)
A generalized mass and its related geometric inequalities

In this talk I will first introduce a generalized mass by using the Gauss-Bonnet-Chern curvature and then discuss related geometric inequalities.

Jan 29th, 2015, 17:45-18:45 Topics in Geometric Analysis Albert Einstein Institute, Room 0.01, Am Mühlenberg 1, 14476 Potsdam Anestis Fotiadis (Aristotle University of Thessaloniki) Harmonic extensions of quasi-symmetric maps

In this talk we study harmonic maps between hyperbolic spaces. In particular, we focus on a famous conjecture due to Rick Schoen. According to this conjecture every quasi-symmetric map φ : S1 → S1 can be uniquely extended to a quasi-conformal harmonic diffeomorphism u : D2 → D2 , where here D2 stands for the unit open disk of R2 equipped with the hyperbolic metric. The uniqueness has been settled by Li and Tam. However, the existence part remains still open. We shall confirm affirmatively the conjecture if we impose some additional conditions on the initial data.

Feb 5th, 2015, 09:45-11:30 GMT reading seminar Albert Einstein Institute, Room 0.01, Am Mühlenberg 1, 14476 Potsdam Theodora Bourni (FU Berlin) Richard Schoen and Leon Simon, "Regularity of Stable Minimal Hypersurfaces", 1981.
Feb 5th, 2015, 12:30-13:45 GMT reading seminar Albert Einstein Institute, Room 0.01, Am Mühlenberg 1, 14476 Potsdam Theodora Bourni (FU Berlin) Richard Schoen and Leon Simon, "Regularity of Stable Minimal Hypersurfaces", 1981.