Infinite-Dimensional Geometry - Theory and Applications

Erwin Schrödinger International Institute for Mathematics and Physics (ESI) via YouTube

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Explore infinite-dimensional geometry through this comprehensive 5-week conference program featuring theoretical foundations and practical applications in shape analysis and medical imaging. Delve into geometric structures on infinite-dimensional manifolds, dynamical systems, homeomorphisms of S^1, and groups in infinite dimensions during the first three weeks. Progress to shape analysis and geometry in week four, culminating with medical applications in the final week. Attend mini-courses and keynote presentations covering topics from abstract theoretical questions to concrete medical applications, including brain development reconstruction, minimal surfaces, circle patterns, geometric learning via PDE-G-CNNs, and neural network growth for frugal AI. Learn from experts presenting on Banach-Lie groupoids, operator ideals, Poisson-Lie groups, integrable PDEs, symplectic geometry, and diffeomorphism groups. Engage with cutting-edge research spanning geometric mechanics, quantum dynamics, magnetic geodesic flows, optimal transport, and information geometry, while exploring applications in neuroimaging, 3D scene reconstruction, and single-cell trajectory analysis.

Syllabus

Georg Langs - From Brain Development and Reorganization to Reconstructing 77 Million Years of...
Najma Mosadegh - Investigation on Minimal Surfaces, Biharmonic Submanifolds, and their App...
Pooran Memari - Circle Patterns: Geometry, Analysis, and Applications, Part 1
Pooran Memari - Circle Patterns: Geometry, Analysis, and Applications, Part 2
Pooran Memari - Circle Patterns: Geometry, Analysis, and Applications, Part 3
Anton Francois - Python library Demeter Metamorphosis
Stefan Ohrhallinger - The Sampling - Reconstruction Dual
Remco Duits - Geometric Learning via data-efficient PDE-G-CNNs: Training of Association Fields
Elodie Maignant - Geometry of single-cell trajectories
Frédéric Barbaresco - Transverse Symplectic Foliation Structure for Thermodynamics-Informed Neural..
Alice Barbara Tumpach - Poisson structures and isospectral matrices
Peter Kán - Reconstruction of Illumination in 3D Scenes
Olivier Bisson - Differentiable Structures on Correlation Matrices with Applications in Neuroimaging
Mao Nishino - Path constrained unbalanced optimal transport
Tom Szwagier - The curse of isotropy: from principal components to principal subspaces
Emmanuel Hartman - Parameterization Invariant Representations for Efficient Shape Learning
Guillaume Charpiat - Neural Network Growth for Frugal AI : a functional analysis viewpoint
Martin Bauer - Infinite dimensional Riemannian geometry and geometric data science
Fabian Rupp - Conformally constrained minimization of total curvature
Minh Ha Quang - An information geometric and optimal transport framework for Gaussian processes
Karen Habermann - Geodesic and stochastic completeness for landmark space
Alice Le Brigant - The Lp-Fisher-Rao metrics and alpha-connections
Guillaume Serieys - On the metric geometry of general Lebesgue spaces and metrics accounting...
Theo Rudkiewicz - Tensor decomposition in frugal neural networks
Klas Modin - Information geometry of diffeomorphism groups, Part 3
Manon Verbockhaven - Growing Tiny Networks: Spotting Expressivity Bottlenecks and Fixing Them Opt...
Styliani Douka - Growing arbitrary DAG networks: method and strategies
Klas Modin - Information geometry of diffeomorphism groups, Part 2
Thomas Pierron - Extended LDDMM and applications to multi-scale matching problems
Rayane Mouhli - Decorrelation of vector fields with speed of varifolds
Klas Modin - Information geometry of diffeomorphism groups, Part 1
Tom Needham - Gromov-Wasserstein Distance and Applications to Shape Graphs
Anna Florio - Genericity of transverse homoclinic points for analytic convex billiards
Farid Diaf - Vector fields on the hyperbolic plane and surfaces in half-pipe space
Sadashige Ishida - More symplectic structures on the space of space curves
Lina Deschamps - On a hyperkähler view of the magnetic geodesic flow on CP^n.
Alice Barbara Tumpach - Infinite-dimensional hyperkaehler quotients, Nahm's equations and coad...
Tobias Diez - Infinite-dimensional Symplectic Geometry, Part 3
Laszlo Feher - Integrable Hamiltonian systems from Poisson reductions of doubles..., Part 3
Alice Barbara Tumpach - The Universal Teichmüller space
Yurii Neretin - Unitary representations of the group of diffeomorphisms of the circle
Tobias Diez - Infinite-dimensional Symplectic Geometry, Part 2
Laszlo Feher - Integrable Hamiltonian systems from Poisson reductions of doubles..., Part 2
Tobias Diez - Infinite-dimensional Symplectic Geometry, Part 1
Laszlo Feher - Integrable Hamiltonian systems from Poisson reductions of doubles..., Part 1
Zofia Grochulska - Approximately differentiable homeomorphisms: derivatives and Jacobians, Part 1
Baptiste Coquinot - Tracking Dissipative Dynamics with Geometry
Alina Dobrogowska - A new look at Lie algebras
Janusz Grabowski - Geometry of quantum dynamics in infinite-dimensions
Stephen Preston - Geometry and curvature of diffeomorphism groups
Stefan Haller - Augmented nonlinear Grassmannians as coadjoint orbits of classical diffeomorphism...
Levin Maier - On Mañé's Critical Value, the Magnetic Hunter-Saxton System, and an Infinite-Dim...
Tilmann Wurzbacher - Geometric prequantisation of two-pectic manifolds
Keti Tenenblat - Classes of nonlinear PDEs related to metrics of constant curvature
Anton Izosimov - Infinite-dimensional geometry and integrable PDEs, Part 3
Katarzyna Grabowska-Geometric Mechanics – Tulczyjew Triples, Algebroids, and Dirac Structures, Part3
Eva Miranda - Euler flows as universal models for dynamical systems
Gabriel Larotonda - Connections in Grassmann manifolds
Bas Janssens - Central extensions of the group of exact volume preserving diffeomorphisms
Katarzyna Grabowska-Geometric Mechanics – Tulczyjew Triples, Algebroids, and Dirac Structures, Part2
Anton Izosimov - Infinite-dimensional geometry and integrable PDEs, Part 2
Ali Suri - Conjugate points along spherical harmonics and quasi-geostrophic motion
Tomasz Goliński - Banach manifolds and integrable systems around them
Oscar Cosserat - Hamiltonian dynamics on Poisson manifolds and symplectic groupoids
Katarzyna Grabowska-Geometric Mechanics – Tulczyjew Triples, Algebroids, and Dirac Structures, Part1
Anton Izosimov - Infinite-dimensional geometry and integrable PDEs, Part 1
Esteban Andruchow - Subspaces with or without a common complement
Damaris Meier - Uniformization of metric surfaces
David Miyamoto - Lie algebras of diffeomorphism groups of non-compact manifolds, Part 2
Christian Blohmann - Lie algebras of diffeomorphism groups of non-compact manifolds, Part 1
Eduardo Chiumiento - Operator ideals and infinite-dimensional geometry, Part 3
Aneta Sliżewska - Banach-Lie groupoids, Part 3
Praful Rahangdale- Correspondence between infinite-dimensional Poisson-Lie groups and Lie bialgebras
Madeleine Jotz - Lie algebroid cohomology and ideals in Lie algebroids, Part 3
Alice Barbara Tumpach - Banach Poisson-Lie groups
Chiara Esposito - Global Homotopies for HKR Theorems in Differential Geometry
Daniel Beltita - Leaf spaces in Lie theory
Karl-Hermann Neeb - Covariant projective representations of Hilbert--Lie groups
Milan Niestijl - Holomorphic induction of unitary representations of BCH Fréchet-Lie groups
Anton Alekseev - Loop group Hamiltonian actions: a review
Eduardo Chiumiento - Operator ideals and infinite-dimensional geometry, Part 2
Cornelia Vizman - Central extensions in infinite dimensions
Aneta Sliżewska - Banach-Lie groupoids, Part 2
Madeleine Jotz - Lie algebroid cohomology and ideals in Lie algebroids, Part 2
Eduardo Chiumiento - Operator ideals and infinite-dimensional geometry, Part 1
Aneta Sliżewska - Banach-Lie groupoids, Part 1
Francesco Cattafi - PB-groupoids vs VB-groupoids
Madeleine Jotz - Lie algebroid cohomology and ideals in Lie algebroids, Part 1