September 7 - December 18, 2026

Organizers: Shreya Arya (UPenn), Karen Habermann (Warwick), Stephan Huckemann (Göttingen), Ezra Miller (Duke), Yvo Pokern (UCL), Wilderich Tuschmann (KIT), Zhigang Yao (Singapore)

Description: The community around geometric statistics – its theory, application, and computation – is growing both in numbers and in breadth.  This ranges from increasing interaction with related research communities such as manifold statistics, topological data analysis, and geometric machine learning to fertilization of the applied sciences such as biostructure and biomedical modeling and imaging. 

This dual trimester program will foster and expand interactions among the above disciplines within the mathematical sciences.  The focus will be on the following six topics:

1. Geometric structure of data objects and suitable spaces,
2. Stochastic analysis on manifolds and singular spaces,
3. Statistical behavior and geometry,
4. Applied topology,
5. Non-Euclidean learning,
6. Computational methods for all of the topics listed above.

The dual trimester program will include a

• Introductory School: Geometric Statistics (Sept. 14 – 18)
• Workshop I: Stochastic Analysis, Statistics, and Computation on Manifolds and Singular Spaces (Oct. 12 – 16)
• Workshop II: Geometry, Topology, and Learning on Smooth and Singular Spaces (Nov. 9 - 13)
• Conference: Interactions of Statistics and Geometry III [ISAG III] (Dec. 7 – 11)

The application deadline to attend the Conference has been extended to August 2, 2026, 11:59 pm (CEST). For more information, see the Conference section below.

In case of questions concerning services and administration, please contact Emma Seggewiss.

Global Mobility Fellowships

Our Global Mobility Fellowships offer fully-funded and fully-organized visits to the Trimester Programs of the Hausdorff Research Institute for Mathematics and participation spots for the Special Topic Schools of the Hausdorff School for Mathematics for selected researchers and PhD students from countries of the Global South. With this program we aim to reduce economic and practical barriers to participation in some of the core initiatives of HCM and to welcome researchers from around the world to our programs and events!

Click here for further information.

In case of questions, please contact Magdalena Balcerak Jackson or Emma Seggewiss.

September 14 - 18, 2026

Venue: HIM lecture hall, Poppelsdorfer Allee 45, Bonn

Lecture series by: 

• Fernando Galaz-Garcia (Durham University, UK)
• Elton Hsu (Northwestern University, Evanston, US)
• Xavier Pennec (INRIA, Université Côte d’Azur, FR)
• Amy Willis (University of Washington, US)

Description: Geometric statistics focuses on statistical methods that recognize and exploit the geometric structure of data sets, data objects, and parameters. Its importance arises from an increasing amount of modern data naturally living on curved, constrained, or stratified spaces rather than flat Euclidean spaces. Notable examples of these data objects include shapes, networks, covariance matrices, trees, or configuration spaces. On such objects or spaces parametrizing them, traditional statistical methods may fail or not apply. New mathematics to deal with these issues often yield surprising results and high relevance for complex applications in fields such as structural biology, physical chemistry, medical imaging, robotics, and forensics.

The Introductory School will provide a set of foundational mini courses designed to equip participants, especially young researchers and newcomers, with an overview of pertinent background in geometry, topology, probability, statistics, and computation specific to statistics and data analysis in settings that are non-Euclidean. In particular, mini courses will cover foundations of geometric statistics, asymptotics of Fréchet means on manifolds and stratified spaces, SDEs on manifolds, and Alexandrov and RCD spaces. Together, these mini courses aim to establish a shared scientific language for participants entering the broader program in geometric statistics.

The call for participation for this Introductory School is now closed. Click here to access the registration platform.

The School is aimed at PhD students and early-career researchers, typically within six years of completing their PhD.

Trimester Program guests, who were invited and have confirmed to be at HIM during the period of this workshop, are eligible to attend this event. Beyond this, researchers from the HCM, in particular, early-career researchers, are welcome upon request.

October 12 - 16, 2026

Venue: HIM lecture hall, Poppelsdorfer Allee 45, Bonn

Organizers: Karen Habermann, Yvo Pokern

External speaker thus far: 

• Fabrice Baudoin (Aarhus University)
• Marcelo Hartmann (University of Helsinki)
• Yuga Iguchi (Lancaster University)
• Naotaka Kajino (Kyoto University)
• Alexander Lewis (Chalmers University of Technology/ University of Gothenburg)
• Radomyra Shevchenko (École Centrale Méditerranée and Université Côte d'Azur)
• Anja Sturm (University of Göttingen)
• Frank van der Meulen (Vrije Universiteit Amsterdam)
• Max von Renesse (Leipzig University)
• Olivier Zahm (Inria)

Description: An increasing amount of modern data naturally lives on curved, constrained, or stratified spaces, including spaces with singularities. Classical statistical methodology often falls short when faced with curvature effects, non‑smooth structure, or singular behaviour. Deepening our understanding of stochastic processes on both smooth and singular spaces and adapting statistical methodology for such processes are therefore paramount for capturing modern data’s geometric variability and for advancing the theoretical foundations of geometric statistics. 
This workshop aims to bring together researchers working at the interface of stochastic analysis, geometric statistics, and computation on manifolds and singular spaces. The central focus of the workshop is the study of stochastic processes on manifolds and, crucially, on singular spaces, where standard techniques and standard statistical methodology may break down yet many real‑world datasets naturally live in. By improving our understanding of stochastic processes and statistical models in these settings, we aim to enable more robust statistical methods capable of handling complex geometric variability. Such developments will drive progress in geometric statistics, with applications in shape analysis, computational anatomy, topological data analysis, and machine learning on structured domains.

Trimester Program guests, who were invited and have confirmed to be at HIM during the period of this workshop, are eligible to attend this event. Beyond this, researchers from the HCM, in particular, early-career researchers, are welcome upon request.

November 9 - 13, 2026

Venue: HIM lecture hall, Poppelsdorfer Allee 45, Bonn

Organizers: Shreya Arya, Stephan Huckemann, Wilderich Tuschmann, Emil Saucan, Kelin Xia 

External speakers thus far:

• Ginestra Bianconi (Queen Mary University of London)
• Frédéric Chazal (Inria and Université Paris-Saclay)
• Ian Dryden (University of Nottingham)
• David Xianfeng Gu (State University of New York at Stony Brook) - via Zoom
• Heather Harrington (Max Planck Institute of Molecular Cell Biology and Genetics)
• Adam Jaffe (Columbia University)
• Jürgen Jost (Max Planck Society)
• Christof Schötz (Technical University Munich)
• Theo Sturm (University of Bonn)
• Yu Guang Wang (Monash University)
• Giulio Zucal (Max Planck Institute of Cell Biology and Genetics)

Description: Our workshop focuses on the integration of geometric and topological methodologies into modern statistical learning, with particular emphasis on data defined over both smooth and singular spaces. By combining tools from geometric data analysis--such as Ricci curvature, Riemannian and sub-Riemannian structures, Laplacians, optimal transport, and information geometry--with techniques from topological data analysis, including persistent homology and Hodge theory, the program aims to develop richer data representations that capture both local geometric features and global structural properties. A central theme is the extension of statistical and learning frameworks from smooth manifolds to singular and stratified spaces, such as graphs, simplicial complexes, and other higher-order networks, which naturally arise in modern data analysis. This unified perspective enables geometric and topological methods to effectively model complex, non-Euclidean data across multiple scales and irregular domains. Moving beyond traditional linear assumptions, the workshop highlights advances in non-Euclidean statistics and probability ranging from manifolds to singular settings. Emphasis is placed on both theoretical foundations and computational frameworks, fostering scalable, robust, and interpretable models. Overall, the workshop aims to promote a synergistic paradigm in which geometry, topology, and learning on smooth and singular spaces jointly drive innovation in statistics and data science. 

Trimester Program guests, who were invited and have confirmed to be at HIM during the period of this workshop, are eligible to attend this event. Beyond this, researchers from the HCM, in particular, early-career researchers, are welcome upon request.

December 7 - 11, 2026

Venue: Lipschitz-Saal, Endenicher Allee 60, Bonn
- The conference will begin on Monday morning and end before 1 p.m. on Friday -

Organizers: Ezra Miller, Wilderich Tuschmann, Zhigang Yao

Speakers:

• Eddie Aamari (CNRS - ENS PSL)
• Fernando Galaz-Garcia (Durham University)
• Thomas Hamelryck (University of Copenhagen)
• Erik Jansson (University of Cambridge)
• John Kent (University of Leeds)
• Stephan Klaus (Mathematisches Forschungsinstitut Oberwolfach)
• Alice Le Brigant (University Paris 1)
• Clement Levrard
• Alexander Lytchak (KIT)
• Rong Ma (Harvard University)
• Kanti Mardia (University of Leeds) - via Zoom
• Steve Marron (University of North Carolina)
• Susovan Pal (Vrije Universiteit Brussel)
• Jaesung Park (Seoul National University/Institute for Data Innovation in Science)
• Wanli Qiao (George Mason University)
• Wolfgang Stummer (Friedrich-Alexander-Universität Erlangen-Nürnberg)
• Anne van Delft
• Christoph von Tycowicz (Zuse Institute Berlin)

Description: The world is witnessing an explosion in abundance of "complicated data" with geometric structure and a growing need for its statistical analysis. In the last century, substantial progress had largely focused on suitably linearizing such data and subjecting it to classical statistical methods. With the advent of increased computational power, more elaborate novel intrinsic methodology has been developed. This has led, on the one hand, to design of highly sophisticated new statistical descriptors (e.g. in persistenthomology) and, on the other hand, to discovery of non-Euclidean limiting behaviors of such descriptors. These have linked geometry and statistics in an unanticipated and quite unprecedented way. This currently evolving new field "Statistics of Data with Geometric Structure" requires intense collaboration across mathematical disciplines that have been traditionally remote: statistics, probability, optimization, and machine learning on one side, and combinatorics, topology, and geometry on the other side. This conference brings together specialists from the disciplines of this trimester program to discuss fundamental questions raised by the program and looking toward the future.  This meeting is the third in the ISAG series, following ISAGI and ISAG II.

The call for participation for the Conference is now open until August 2, 2026, 11:59 pm (CEST). Click here to access the application platform.

Trimester Program guests, who were invited and have confirmed to be at HIM during the period of this workshop, are eligible to attend this event. Beyond this, researchers from the HCM, in particular, early-career researchers, are welcome upon request.