The aim of the project is to reinforce the collaboration between scientists from Austrian research institutions and international institutions around the topic of infinite dimensional geometry. Direct applications of the theoretical aspects of infinite dimensional geometry to shape analysis and medical imaging are part of the program.

The programme will last five 5 weeks, each devoted to different topic ranging from abstract theoretical questions to very concrete applications (e.g. medical).

Each week mini-courses lecturers and keynote speakers will share their understanding on particular topics. Short talks from the participants will complete the programme.

• Week 1: Geometric structures and infinite-dimensional manifolds
• Week 2: Dynamical systems and infinite-dimensional manifolds
• Week 3: Homeomorphisms of S^1 and Groups in infinite-dimensions
• Week 4: Shape Analysis and Geometry
• Week 5: Shape Analysis and Medical Applications

Detailed schedule together with the list of speakers will be announced at a later date. The following researchers agreed to contribute to the programme (please note that the list is not final yet):

Week 1: Geometric structures and infinite-dimensional manifolds

• Mini-courses
  • Eduardo Chiumiento (Instituto Argentino de Matemática and Universidad de La Plata), Operator ideals and infinite-dimensional geometry
  • Madeleine Jotz  (University of Würzburg), Lie algebroid cohomology and ideals in Lie algebroids
  • Aneta Slizewska (University of Białystok), Banach-Lie groupoids
• Keynote talks:
  • Anton Alekseev (University of Geneva), Loop group Hamiltonian actions: a review
  • Esteban Andruchow (Instituto Argentino de Matemática and Universidad Nacional de General Sarmiento, Buenos Aires), On pairs of subspaces with or without a common complement
  • Daniel Beltiţă (Institute of Mathematics of the Romanian Academy, Bucharest), Leaf spaces in Lie theory
  • Chiara Esposito (University of Salerno), Global Homotopies for HKR Theorems in Differential Geometry
  • Karl-Hermann Neeb (Friedrich-Alexander-Universität Erlangen-Nürnberg), Covariant projective representations of Hilbert-Lie groups
• Tutorials:
  • Alice Barbara Tumpach (WPI, TU Wien and Lille University), Nahm's equations and hyperkaehler structures
  • Cornelia Vizman (WU Timisoara), Decorated vs augmented nonlinear Grassmannians (Prequantizable coadjoint orbits of diffeomorphism groups)

Week 2: Dynamical systems and infinite-dimensional manifolds

• Mini-courses
  • Annalisa Calini (College of Charleston), Finite-gap solutions of integrable geometric curve flows
  • Katarzyna Grabowska (University of Warsaw), Geometric Mechanics – Tulczyjew Triples, Algebroids, and Dirac Structures
  • Anton Izosimov (University of Arizona), Infinite-dimensional geometry and integrable PDEs
• Keynote talks:
  • François Gay-Balmaz (Nanyang Technological University, Singapore), On Two Extensions of Arnold's Geometric Fluid Dynamics
  • Stefan Haller (University of Vienna), Augmented nonlinear Grassmannians as coadjoint orbits of classical diffeomorphism groups
  • Eva Miranda (Universitat Politecnica de Catalunya), Euler flows as universal models for dynamical systems
  • Stephen Preston (City University of New York), Geometry and curvature of diffeomorphism groups
  • Keti Tenenblat (University of Brazilia), Classes of nonlinear PDEs related to metrics of constant curvature
• Tutorials:
  • Alice Barbara Tumpach (WPI, TU Wien and Lille University), Banach Poisson-Lie groups
  • Cornelia Vizman (WU Timisoara), Vortex dynamics

Week 3: Homeomorphisms of S^1 and Groups in infinite-dimensions

• Mini-courses
  • Tobias Diez (Shanghai Jiao Tong University), Infinite-dimensional Symplectic Geometry
  • Laszlo Feher (University of Szeged), Integrable Hamiltonian systems from Poisson reductions of doubles of compact Lie groups
  • Anastasia Molchanova (TU Wien), Sobolev homeomorphisms and their weak limits
• Keynote talks:
  • Olga Bernardi (University of Padova) Studying symplectic billiards: an overview and recent rigidity results
  • Anna Florio (Universite Paris Dauphine-PSL), Genericity of transverse homoclinic points for analytic convex billiards
  • Peter Michor (University of Vienna) Remarks on Infinite dimensional symplectic and
    Poisson geometry
  • Yurii Neretin (Univ. Vienna & Pauli Institut), Unitary representations of the group of diffeomorphisms of the circle
  • Tudor Ratiu (Shanghai Jiao Tong University)

• Tutorials:
  • Alice Barbara Tumpach (WPI, TU Wien and Lille University), The Universal Teichmüller space
  • Cornelia Vizman (WU Timisoara), Central extensions in infinite dimension

Week 4: Shape Analysis and Geometry

• Mini-courses
  • Blanche Buet (Universite Paris-Saclay), Varifolds: variational manifolds.
  • Elena Celledoni (Norwegian University of Science and Technology), Shape analysis, structure preservation and deep learning
  • Klas Modin (Chalmers University), Information geometry of diffeomorphism groups
• Keynote talks:
  • Martin Bauer (Florida State University), Infinite dimensional Riemannian geometry and geometric data science
  • Rita Fioresi (University of Bologna), Learning Manifold and dimensionality reduction in Deep and Geometric Learning
  • Alice Le Brigant (Sorbonne University), The $L^p$-Fisher-Rao metrics and alpha-connections
  • Fabian Rupp (University of Vienna), Conformally constrained minimization of total curvature
  • Alain Trouvé (ENS Cachan)
• Special Guest: 
  • Guillaume Charpiat (INRIA Saclay)
  • Nguyen Tien Zung (Torus AI)

• Tutorials:
  • Alice Barbara Tumpach (WPI, TU Wien and Lille University), Gauge invariant structures

Week 5: Shape Analysis and Medical Applications

• Mini-courses
  • Pooran Memari (Ecole Polytechnique), Circle Patterns: Geometry, Analysis, and Applications
  • Xavier Pennec (INRIA Sophia-Antipolis), Geometric Statistics with applications in
    Computational anatomy
• Keynote talks:
  • Ivona Brandic (Vienna University of Technology)
  • Remco Duits (CASA, University of Eindhoven), Geometric Learning via data-efficient PDE-G-CNNs: Training of Association Fields
  • Georg Langs (Medical University of Vienna)
  • Nina Miolane (UC Santa Barbara)
  • Stefan Ohrhallinger (Vienna University of Technology), The Sampling - Reconstruction Dual
• Special Guests  
  • Frédéric Barbaresco (Thales), Transverse Symplectic Foliation Structure for Thermodynamics-Informed Neural Network and Lie-Groups Machine Learning
  • Frank Nielsen (Sony Computer Sciences Laboratories)
  • Peter Kán (TU Wien), Reconstruction of Illumination in 3D Scenes
• Software Tutorials:
  • Jean Feydy (INRIA Paris), Creating good-looking 3D figures with PyVista
  • Jean Feydy (INRIA Paris), Shape metrics with scikit-shapes
  • Anton François (ENS Paris-Saclay), Python library Demeter Metamorphosis https://github.com/antonfrancois/Demeter_metamorphosis.
  • Elodie Maignant (Zuse Institute Berlin) and Luis F. Peirera (UC Santa Barbara): Geomstat
• Tutorials:
  • Alice Barbara Tumpach (WPI, TU Wien and Lille University), Poisson structures and isospectral matrices