The "Topics in General Relativity" seminar is the seminar of the Holzegel group at Mathematics Münster. It takes place every Tuesday at 12:00 at the Westfälische Wilhelms-Universität. For further details/to receive e-mails concerning this seminar, feel free to contact Allen Juntao Fang, the current organiser of the seminar. The page for previous semesters may be found here: Summer 2022, Winter 2022-2023, Summer 2023, Winter 2023-2024, , Summer 2024, and Winter 2024-2025 .
The "PDE colloquium" takes places Tuesdays at 14:15 at the Westfälische Wilhelms-Universität, in Room SRZ 203 (unless otherwise announced) of the Seminarraumzentrum building (Orléans-Ring 12). If you want to be on the mailing list, please send an email to pde.colloquium@uni-muenster.de. The seminar's webpage for further details may be found here.
Ludovic Souêtre (21 April 2026, room MA 503)
Topics in General RelativityTitle: The homogeneous Robin boundary conditions for asymptotically Anti-de Sitter spaces
Abstract: Modelled on the Anti-de Sitter space, asymptotically Anti-de Sitter spaces can be defined as Lorentzian manifolds that possess a timelike conformal boundary. Due to their lack of global hyperbolicity, finding asymptotically Anti-de Sitter solutions to the Einstein equations (necessarily with a negative cosmological constant) through the Cauchy problem requires tackling the latter as an initial boundary value problem. In this talk, I will present the two known types of geometric boundary conditions leading to the local existence and uniqueness of solutions in dimension 4: the Dirichlet boundary conditions, which were introduced by Friedrich in 1995, and the homogeneous Robin boundary conditions, which I introduced in a recent work.
Filippo Riva (5 May 2026, room SRZ 203)
PDE ColloquiumTitle: Existence of gradient flows via trajectory-minimization in spaces of measures
Abstract: We present a novel global-in-time variational approach to gradient flows and doubly nonlinear equations in (reflexive) Banach spaces. It is based on the De Giorgi's principle, which states that solving a gradient flow is equivalent to being a null-minimizer of a suitable energy functional among all trajectories sharing the same initial position. As for the similar Brezis-Ekeland-Nayroles (BEN) principle (which applies only to a convex framework), finding a minimizer for such functional is not difficult in general, but proving that the minimum is zero poses a real challenge. In the BEN formulation, the task has been accomplished by Ghoussoub, resorting to the tool of self-dual Lagrangians. Our approach allows to extend the analysis to nonconvex energies, directly dealing with the De Giorgi's functional, and it relies on a convexification of the problem in spaces of measures exploiting the so-called superposition principle. The validity of the null-minimization is then recovered by a careful application of the Von Neumann minimax theorem, and by employing the "backward boundedness" property of the dual Hamilton-Jacobi equation. The talk is based on a joint work with A. Pinzi and G. Savaré.
Nikolas Eptaminitakis (12 May 2026, room MA 503)
Topics in General RelativityTitle: Tensor Tomography on Asymptotically Hyperbolic Surfaces
Abstract: Given a Riemannian manifold, the geodesic X-ray transform of a symmetric tensor field is defined by the line integrals of the latter over geodesics, and it is a central object in geometric inverse problems. Broadly speaking, one is interested in recovering information about the unknown tensor field from its X-ray transform, and the extent to which this is possible depends heavily on the underlying geometry. In this talk, we focus on the geodesic X-ray transform in the geometric setting of two-dimensional asymptotically hyperbolic manifolds, which are non-constant curvature generalizations of hyperbolic space. This setting is interesting in part due to its connections to theoretical physics, specifically the AdS-CFT Correspondence. The geodesic X-ray transform on symmetric tensor fields of positive rank has a natural nullspace, implying that such a tensor field cannot be uniquely recovered from its X-ray transform. On asymptotically hyperbolic surfaces we propose gauge representatives modulo the nullspace of the transform to be reconstructed from the data, by proving a ``transverse traceless-conformal-potential'' decomposition. We then use our tensor decompositions to provide range characterizations of the geodesic X-ray transform in the special case of 2-dimensional hyperbolic space, as well as to develop reconstruction procedures. Based on joint work with François Monard and Yuzhou Zou.
Jan Bohr (9 June 2026, room MA 503)
Topics in General RelativityTitle: Zoll magnetic systems and ruled surfaces
Abstract: On an oriented surface M, the dynamics of a charged particle in a magnetic field is governed by a pair (g,\lambda) that consists of a Riemannian metric g together with a smooth function \lambda modelling the magnetic field. If every unit speed particle moves on a closed orbit (and the minimal period depends continuously on the orbit), we call (g,\lambda) a Zoll magnetic system. We show that there is a plethora of such systems on every closed oriented surface, essentially one for every closed 1-form on M. In negative Euler characteristic these are the first examples beyond the trivial case (constant curvature and large constant magnetic field). The construction of Zoll magnetic systems is based on so-called transport twistor spaces and holomorphic blow-down maps into ruled surfaces. Based on joint work with Gabriel P. Paternain..
Tony Salvi (16 June 2026, room MA 503)
Topics in General RelativityTitle: TBA
Abstract: TBA.
Oskar Schiller (7 July 2026, room MA 503)
Topics in General RelativityTitle: TBA
Abstract: TBA.