Institut
Allgemeine Informationen über das Institut wie z.B. Leitbild, Organisationsstruktur, Mitarbeiterverzeichnis, Geschichte, Anfahrtsbeschreibung usw.

Mehr anzeigen
Forschung
Wissenschaftliches Profil mit allen Forschungsgruppen, Themen, Projekten sowie weiteren Forschungsrubriken des Instituts.

Mehr anzeigen
News
Nachrichten und Pressemitteilungen des Instituts, sowie ein Pressearchiv.

Mehr anzeigen
Veranstaltungen
Übersicht über alle Veranstaltungen rund um das Institut, wie Vorträge, Seminare, Vorlesungen, Workshops, Konferenzen und öffentliche Veranstaltungen.

Mehr anzeigen
Publikationen
Übersicht über alle wissenschaftlichen Veröffentlichungen des Instituts sowie über unsere Preprint- und Software-Archive.

Mehr anzeigen
Karriere
Informationen zu Stellenangeboten am Institut, Karriere Benefits, dem Graduiertenkolleg und der Betreuung von Postdocs.

Mehr anzeigen

Intranet

Veranstaltungen
Workshop on Infinite-Dimensional Geometry

Black text on a green, yellow, orange gradient: ‘Conference - Workshop on Infinite-Dimensional Geometry’

MPI für Mathematik in den Naturwissenschaften Leipzig

E1 05 (Leibniz-Saal)

conference

01.06.26 03.06.26

Workshop on Infinite-Dimensional Geometry

conference

01.06.26 03.06.26

Workshop on Infinite-Dimensional Geometry

The Max Planck Institute for Mathematics in the Sciences (Leipzig) will host a workshop on geometry in infinite dimension. The workshop aims to bring together researchers interested in geometric phenomena that arise in infinite dimension, with particular emphasis on structures and methods from differential geometry, functional analysis and related areas. Topics of interest include infinite-dimensional symmetric spaces, notions of positivity and large-scale geometry, the use of functional-analytic tools to study infinite-dimensional geometric objects, as well as the non-abelian Hodge correspondence.

Confirmed speakers (as of April 10, 2026):

George Domat (University of Michigan)
Bruno Duchesne (Université Paris-Saclay)
Paula Heim (MPI MiS)
Georgios Kydonakis (University of Patras)
Yusen Long (Université Paris-Est Crétail)
Pierre Py (CNRS/Université Grenoble Alpes)
Gonzalo Ruiz Stolowicz (UCLouvain)
Federico Viola (EPFL)

WARNING: Please be wary if a company directly contacts you regarding payment for accommodation in Leipzig: this is fraud / phishing.

Program

08:45 - 09:00	Welcome Coffee and Registration
09:00 - 10:30	Georgios Kydonakis (University of Patras, Greece) A Hitchin component for the group $\mathrm{SL}(\infty, \mathbb{R})$, after Hitchin, Biquard Following the works of Hitchin and Biquard, we will study in this talk the solutions to the self-duality equations for the group $\mathrm{SU}(\infty)$. This group can be interpreted as the group of Hamiltonian diffeomorphisms of the 2-sphere $\mathbb{S}^2$, and its Lie algebra consists of the smooth functions on $S^2$ modulo the constant functions. Then, a solution to the self-duality equations is equivalent to a folded hyperk\"{a}hler metric, that is, a hyperk\"{a}hler metric on the total space of an $S^2$-bundle with a fold singularity on the equator of each $\mathbb{S}^2$-fiber. A conjectural picture suggests that an appropriate solution of these equations can provide a flat symplectic connection on a symplectic $\mathbb{S}^1 \times \mathbb{R}$-bundle over a negatively curved surface whose holonomy lies in the proper subgroup $\mathrm{Sp}(\infty, \mathbb{R})$ of Hamiltonian diffeomorphisms commuting with the involution given by reversing the orientation of an oriented geodesic.
10:30 - 11:00	Coffee & Tea
11:00 - 12:00	Pierre PY (CNRS / Université Grenoble Alpes, France) Exotic representations of $\mathrm{PO}(n,1)$ and kernels of hyperbolic type: a survey We will survey our (old) joint work with Monod on the construction and study of exotic actions of the group $\mathrm{PO}(n,1)$ on the infinite dimensional real hyperbolic space, as well as some more recent developments. Along the way, we will recall the notion of kernels of hyperbolic type, which turns out to be useful to study group actions on real hyperbolic spaces.
12:00 - 14:00	Lunch Break
14:00 - 15:30	Gonzalo Emiliano Ruiz Stolowicz (ICMAT-Madrid, Spain) Kernels of Möbius type Given a Möbius structure or cross-ratio defined on a set, we will be provide necessary and sufficient conditions for this cross-ratio to be induced by an embedding in the visual boundary of a real or complex hyperbolic space. This is not the first effort in this direction. The idea of studying hyperbolic representations through kernels (of hyperbolic type) is largely based on the work of Pierre Py and Nicolas Monod.The kernels of hyperbolic type "model" the maps of a set into a real or complex hyperbolic space. In their equivariant version those kernels can be used to study the hyperbolic representations through the orbit maps of points contained in the hyperbolic space. With the kernels of Möbius type, introduced in this talk, and their equivariant version, the study of hyperbolic representations is done by looking at the induced action by Möbius transformations on the visual boundary of the hyperbolic spaces. This presents some advantages due to the dynamic properties of such actions. With the language of the kernels of Möbius type at hand, one can give necessary and sufficient conditions for two irreducible representations of a group on a real or complex hyperbolic space to be equivalent. Kim, developing on techniques by Otal, showed that in the locally compact case, the marked length of an irreducible representation is a complete invariant.Using the kernels of Möbius type is straightforward to generalize that result for any hyperbolic representation, possibly on an infinite-dimensional hyperbolic space.
15:30 - 16:00	Coffee & Tea
16:00 - 17:00	Discussion Session

08:45 - 09:00	Welcome Coffee
09:00 - 10:30	Yusen Long (Université Paris-Est Créteil, France) A hyperbolic model for finite and infinite dimensional convex bodies By studying the continuous self-representations of the Möbius group, Monod-Py introduced the notion of kernel of real hyperbolic type, which serve as hyperbolic analogues to classical positive-definite kernels. In the domain of integral geometry, the classical Alexandrov-Fenchel inequality for mixed volumes of n-dimensional convex bodies can be intepretated as a reversed Cauchy-Schwarz inequality, naturally giving rise to a hyperbolic kernel. Building upon this foundation, Debin and Fillastre developed a hyperbolic model for the homothety classes of finite-dimensional convex bodies. In this talk, we review this construction and present a generalisation to the infinite-dimensional setting. As an application, we utilise the 2-dimensional model to construct an irreducible representation of $\mathrm{PSL}(2,\mathrm{R})$ in $\mathrm{PO}(1,\infty)$. This work is joint with François Fillastre and David Xu.
10:30 - 11:00	Coffee & Tea
11:00 - 12:00	Bruno Duchesne (Université Paris-Saclay (Orsay), France) Infinite dimensional symmetric spaces of finite rank In this talk, I will survey results about non-positively curved symmetric spaces of infinite dimension and their isometry groups. I will start form their definition and classifications, explain why there is a demarcation line between the real and complex infinite dimensional hyperbolic spaces and all the others, and show what are the consequences for character varieties with these groups as targets.
12:00 - 14:00	Lunch Break
14:00 - 15:30	Federico Viola (EPFL (Lausanne), Switzerland) A fixed point theorem for higher rank p-adic groups acting on infinite-dimensional symmetric spaces We discuss isometric actions of linear algebraic groups over local fields on simply connected non-positively curved symmetric spaces of infinite dimension and finite rank. The study of these spaces, which was first suggested by Gromov, has largely been carried out by Duchesne; their isometry groups can be characterized as groups of projective transformations of a Hilbert space preserving a nondegenerate sesquilinear form of finite index. We give an overview of some known results, then we present a new result stating that, for most linear higher rank simple algebraic groups over non-archimedean local fields, every continuous isometric action on a simply connected non-positively curved symmetric space of infinite dimension and finite rank has a fixed point.
15:30 - 16:00	Coffee & Tea
16:00 - 17:00	Discussion Session

08:45 - 09:00	Welcome Coffee
09:00 - 10:30	George Domat (University of Michigan (Ann Arbor), USA) Asymptotically Conformal Deformation Spaces and Surface Houghton Groups I will introduce a type of "medium" mapping class groups: Surface Houghton groups. As the name suggests, these were first introduced as a surface analog of the classical Houghton groups and were shown to exhibit certain finiteness properties. They arise as asymptotically rigid subgroups of mapping class groups of infinite-type surfaces. They are finitely generated, but also still dense inside of big mapping class groups, hence "medium." This talk will be on current work in progress relating these groups to asymptotically conformal deformation spaces of Riemann surfaces. Under certain geometric conditions we will see that asymptotically conformal modular groups are virtually surface Houghton groups. All of this is joint work with Javier Aramayona and Chris Leininger.
10:30 - 11:00	Coffee & Tea
11:00 - 12:00	Paula Heim (MPI MiS (Leipzig), Germany) Quasiisometries of infinite-dimensional rank-one symmetric spaces Quasiisometries of finite-dimensional rank-one symmetric spaces behave very differently in different families of symmetric spaces. While real and complex hyperbolic spaces admit many nontrivial quasiisometries, the quaternionic hyperbolic spaces and the octonionic hyperbolic plane exhibit a strong rigidity phenomenon: every self-quasiisometry is bounded distance away from an isometry, this is a theorem of Pansu. It is natural to ask if this divide survives in infinite dimensions. In this talk we discuss this question and explore potential ways of extending Pansu's proof strategy to the infinite-dimensional case.
12:00 - 14:00	Lunch Break
14:00 - 15:45	Discussion Session with Coffee & Tea

Participants

Irina Bobrova

TU Berlin, Germany

Samuel Bronstein

MPI-MIS, Germany

George Domat

University of Michigan, USA

Bruno Duchesne

Université Paris-Saclay, France

Adnan Fazil

University of L'Aquila, Italy

Paula Heim

MPI MiS, Germany

Patrick Heslin

MPI Leipzig, Germany

Vincenzo Antonio Isoldi

Max Planck Institute for Mathematics in the Sciences, Germany

Magali Jay

Max Planck Institute, Germany

Nat Kendal-Freedman

MPI MiS, Germany

Clarence Kineider

Max Planck Institute for Mathematics in the Sciences, Germany

Georgios Kydonakis

University of Patras, Greece

Laura Lankers

MPI MiS Leipzig, Germany

Yusen Long

Université Paris-Est Créteil, France

Raphaël Maurette

ENS Paris, France

Pierre PY

CNRS / Université Grenoble Alpes, France

Max Riestenberg

MPI MiS, Germany

Eugen Rogozinnikov

Korea Institute for Advanced Study - KIAS, South Korea

Thomas Rolland

Université Paris-Saclay, France

Gonzalo Emiliano Ruiz Stolowicz

ICMAT-Madrid, Spain

Nimra Sheikh

Freie Universität Berlin, Germany

Jiajun Shi

MPI MiS, Germany

Roméo Troubat

Institut des Hautes Etudes Scientifiques, France

Federico Viola

EPFL, Switzerland

Anna Wienhard

Max Planck Institute for Mathematics in the Sciences, Germany

David Xu

Korea Institute for Advanced Study - KIAS, South Korea

Organizers

Clarence Kineider

Max Planck Institute for Mathematics in the Sciences

Eugen Rogozinnikov

Korea Institute for Advanced Study - KIAS

David Xu

Korea Institute for Advanced Study - KIAS

Administrative Contact

Antje Vandenberg

Max Planck Institute for Mathematics in the Sciences Contact via Mail