Oberseminar Differentialgeometrie

(O): Regular talks of the Oberseminar (For internal talks, see the webpage of our Research Seminar.)

(S): Talks that additionally are part of the "Seminar on Differential Geometry and Analysis", co-organized by Hans-Christoph Grunau, Miles Simon (Otto-von-Guericke Universität Magdeburg) and Roger Bielawski, Knut Smoczyk (Leibniz Universität Hannover). 

All talks take place at LUH in Seminarraum 016, Callinstraße 23 (Gebäude 3110), except those talks marked (M).

(M): Meetings that take place in Magdeburg.


Winter semester 2023/2024

15 Uhr (s.t.)

Prof. Dr. Benoit Charbonneau (University of Waterloo)

Title: Symmetric Instantons

Abstract: With Spencer Whitehead, we developed a systematic framework to study instantons on R^4 that are invariant under groups of isometries. In this presentation, I will describe this framework and some results obtained using it.


Unusual Day and Location: Welfengarten 1 (Hauptgebäude), G005

17:00-18:00 Prof. Dr. Niels Martin Møller (University of Copenhagen) Title: Rigidity of the grim reaper cylinder as a collapsed self-translating soliton

Abstract: Mean curvature flow self-translating solitons are minimal hypersurfaces for a certain incomplete conformal background metric, and are among the possible singularity models for the flow. In the collapsed case, they are confined to slabs in space. The simplest non-trivial such example, the grim reaper curve $\Gamma$ in $\mathbb{R}^2$, has been known since 1956, as an explicit ODE-solution, which also easily gave its uniqueness.

We consider here the case of surfaces, where the rigidity result for $\Gamma\times\mathbb{R}$ that we'll show is:
The grim reaper cylinder is the unique (up to rigid motions) finite entropy unit speed self-translating surface which has width equal to $\pi$ and is bounded from below. (Joint with Impera & Rimoldi.)

Time permitting, we'll also discuss recent uniqueness results in the collapsed simply-connected low entropy case (w/ E.S. Gama & F. Martín), using Morse theory and nodal set techniques, which extend Chini's classification.
07.12.2023 (S) 16:30-17:30

Dr. Enno Keßler (Max-Planck-Institut für Mathematik in den Naturwissenschaften Leipzig)

Title: Super J-holomorphic curves

Abstract: J-holomorphic curves or pseudoholomorphic curves are maps from Riemann
surfaces to almost Kähler manifolds satisfying the Cauchy-Riemann equations.
J-holomorphic curves are of great interest because they allow to construct
invariants of symplectic manifolds and those invariants are deeply related to
topological superstring theory. A crucial step towards Gromov–Witten
invariants is the compactification of the moduli space of J-holomorphic curves
via stable maps.

In this talk, I want to report on a supergeometric generalization of J-
holomorphic curves and stable maps where the domain is a super Riemann
surface. Super Riemann surfaces have first appeared in superstring theory as
generalizations of Riemann surfaces with an additional anti-commutative
variable. Super J-holomorphic curves are solutions to a system of partial
differential equations on the underlying Riemann surface coupling the Cauchy-
Riemann equation with a Dirac equation for spinors. I will explain how to
construct moduli spaces of super J-holomorphic curves, their compactification
via super stable maps in genus zero and hint at a possible generalization of
Gromov-Witten invariants.

07.12.2023 (S) 15:00-16:00  Prof. Dr. Francisco Martin (University of Granada) Title: Semi-graphical Translators of the Mean Curvature Flow

Abstract: A soliton is a special solution to a partial differential equation that maintains its shape and moves at a constant velocity. In the context of mean curvature flow, a translating soliton is a solution to the mean curvature flow equation that moves by a constant velocity in the direction of a vector. Translating solitons are particularly interesting because they provide insights into the behavior of evolving surfaces. On the other hand, we say that a surface is semi-graphical if when we remove a discrete set of vertical lines, then the resulting surface is the graph of a smooth function. We are going to provide a classification of all the semi-graphical translator in Euclidean 3-space. First, we will describe a comprehensive zoo of all examples of this type of translators, and then we will focus on classification arguments. We will conclude with some open problems. This talk summarizes various joint works with D. Hoffman and B. White, on one hand, and with M. Saez and R. Tsiamis, on the other.
18.01.2024 16:30-17:30 Prof. Dr. Hans-Joachim Hein (Universität Münster)

Title: A gluing construction for complex surfaces with hyperbolic cusps

Abstract: We will describe an example of a degeneration of degree 6 algebraic surfaces in CP^3 with only ordinary triple point singularities on its central fiber. Then we will show how the unique negative Kähler-Einstein metrics on the smooth fibers, which exist by the Aubin-Yau theorem, disintegrate into three distinct geometric pieces on approach to the central fiber: (1) Kobayashi's complete Kähler-Einstein metric on the complement of the triple points, (2) long thin neck regions, and (3) Tian-Yau's complete Ricci-flat Kähler metrics in small neighborhoods of the vanishing cycles. Joint work with Xin Fu and Xumin Jiang.

18.01.2024 15:00-16:00 Prof. Dr. Jason D. Lotay (University of Oxford)

Title: Translators in Lagrangian mean curvature flow

Abstract: Lagrangian mean curvature flow is potentially a powerful tool in solving problems in symplectic topology.  One of the key challenges is the understanding of formation of singularities, which is conjectured to have links to J-holomorphic curves, stability conditions and the Fukaya category.   Unlike the usual mean curvature flow for hypersurfaces, here one is expected to have to tackle singularities modelled on translating solutions to the flow.   I will describe joint work with Felix Schulze and Gabor Szekelyhidi which allows one to recognize a singularity model in Lagrangian mean curvature flow as a translator - this is the first such result in any form of mean curvature flow beyond curves.


Sommer semester 2023

16:30-17:30  Prof. Dr. Ernst Kuwert (Freiburg)

Title: Curvature varifolds with orthogonal boundary.

Abstract: We consider surfaces in a domain with orthogonal boundary condition. The problem to obtain mass bounds in terms of curvature bounds leads to a varifold setting (joint work with Marius Mueller).


Prof. Dr. Oliver Schnürer (Konstanz

Title: Unbounded solutions to mean curvature flow

Abstract:We discuss several aspects of complete noncompact solutions to graphical mean curvature flow in Euclidean space in codimension one:  
1) different variants of stability and instability and 
2) beauty and the beast in mean curvature flow without singularities corresponding to nice and pathological solutions that are graphical over proper subsets of Euclidean space.

15:00-17:30  Special guests on Research Seminar Please attempt to our special guests in the Research Seminar page!


Winter semester 2022 / 2023


Prof. Tobias Lamm

(KIT Karlsruhe)

Title: Index estimates for sequences of harmonic maps
Abstract: We study the limiting behavior of the index and the nullity of sequences of harmonic maps from a two-dimensional Riemann surface into a general target manifold. We show upper and lower bounds for the index of the sequence in terms of the index of the so called bubble limit.
This is a joint work with Jonas Hirsch (Leipzig).

Dr. Athanasios Chatzikaleas

(Uni Münster)

Title:  Non-linear periodic waves in the Anti-de Sitter spacetime and islands of stability.

Abstract:  In 2006, Dafermos-Holzegel conjectured that the Anti-de Sitter spacetime is an unstable solution to the Einstein equations under reflective boundary conditions for general initial data. Rostworowski-Maliborski enhanced this conjecture by proving numerical evidence that indicate the existence of "special" initial data leading to time-periodic solutions for the Einstein-Klein-Gordon system which are in fact stable. Motivated by these, we construct families of arbitrary small time-periodic solutions to several toy models on the fixed Anti-de Sitter background providing a rigorous proof of the numerical constructions above in a simpler setting. The models we consider include the conformal cubic wave equation and the spherically-symmetric Yang-Mills equations on the fixed Anti-de Sitter spacetime and our proof relies on the modifications of a theorem of Bambursi-Paleari for which the main assumption is the existence of a seed solution, given by a non-degenerate zero of a non-linear operator associated with the resonant system.



Prof. Umberto Hryniewicz

(RWTH Aachen)

Title:  A Poincaré-Birkhoff Theorem for 3-Dimensional Energy Levels

Abstract:  In subcritical energy levels of the planar circular restricted 3-body problem (PCR3BP) Poincaré encountered special periodic orbits that span an annular global section for the flow. This motivated the formulation of what is known today as the Poincaré-Birkhoff theorem, from where Poincaré derived beautiful applications to the PCR3BP. In this talk I would like to explain how the action functional from classical mechanics can be used to prove analogous statements for more general systems. This is based on joint work with Al Momin and Pedro Salomão (NYU-Shanghai).
14:15-15:15  Prof. Alberto Abbondandolo
(Universität Bochum)

Systolic inequalities in Metric Symplectic Geometry

Abstract: The prototypical question of metric systolic geometry is to give upper bounds on the length of the shortest closed geodesics on a closed Riemannian manifold in terms of its volume. Systolic questions have a natural generalization to conservative dynamical systems, in which closed geodesics are replaced by periodic orbits, length by period and volume by phase space volume. This generalization turns out to be quite fruitful: on the one hand, symplectic methods allow us to solve some long standing questions in metric systolic geometry, on the other hand many interesting new questions arise. These new questions are related to challenging open problems in symplectic and in convex geometry. This talk is based on joint works with Gabriele Benedetti, Barney Bramham, Umberto Hryniewicz and Pedro Salomão.

16:00-17:00  Prof. Patrick Dondl
(Universität Freiburg)

Phase field models with connectedness constrains


15:00-16:00  Prof. Klaus Kröncke
(KTH Stockholm )

Local and Global Scalar curvature rigidity of Einstein Manifolds


Summer semester 2022

14:15-15:15  Elena Mäder-Baumdicker
Compactification of Minimal flowers and their Morse Index
14:15-15:15 Christian Rose
Compact manifolds with Kato-bounded Ricci curvature
14:15-15:15 Mario Schulz
Free boundary minimal surfaces in the unit ball


Winter semester 2021 / 2022

14:15-15:15  Hartmut Weiß
Parabolic Higgs bundles and gravitational instantons
14:15-15:15 Gianmichele di Matteo
Double bubbles with high constant mean curvature in closed manifolds
14:15-15:15  Leandro Pessoa
Stochastic half-space theorems for minimal surfaces of R³ and 1-surfaces of H³
14:15-15:15  Andreas Savas-Halilaj
(University of Ioannina)
Graphical mean curvature flow in codimension 2


Winter semester 2019 / 2020

15:00-16:00 Massimiliano Morini
Nonlinear stability results for nonlocal gradient flows (txt-Datei)
16:30-17:30 Ovidiu Munteanu
(Storrs, Connecticut)
Green's function estimates and the Poisson equation (txt-Datei)
15:00-16:00 Jonas Hirsch
(Universität Leipzig)
Nonclassical minimizing surfaces with smooth boundary
16:30-17:30 Vladimir Matveev
(Universität Jena)
Nijenhuis Geometry: singularities and global issues
15:00-16:00 Gilles Carron
(Université de Nantes)
Volume growth estimates on complete Riemannian manifolds
16:30-17:30 Carla Cederbaum
(Universität Tübingen)
On CMC-foliations of asymptotically flat manifolds


Summer semester 2019

15:00-16:00             Matteo Novaga
(Università di Pisa)
Anisotropic and crystalline mean curvature flow


16:30-17:30 Alix Deruelle
(Sorbonne Université Paris)
Classification of asymptotically conical 2D shrinking gradient Kähler-Ricci solitons
06.06.2019 15:00-16:00 Karin Melnick
(University of Maryland)
A D'Ambra Theorem in conformal Lorentzian geometry
06.06.2019 16:30-17:30 Volker Branding
(Universität Wien)
Higher order generalizations of harmonic maps
15:00-16:00 Tobias Weth
(Goethe-Universität Frankfurt)
Critical domains for the first nonzero Neumann eigenvalue in Riemannian manifolds
16:30-17:30 Boris Vertman
(Carl von Ossietzky Universität Oldenburg)
Perelman Entropies on Singular spaces