Synthetic Curvature Bounds for Non-Smooth Spaces: Beyond Finite Dimension
It is the intended goal of the workshop to bring together experts in the field of analysis and geometry on metric measure spaces, and discuss the current state of the art of the general theory together with its recent developments and some major open problems. These include in particular the study of:
► extended metric spaces with non-Radon measures (i.e. for which the distance can attain the value +∞ and/or the measure is not Radon);
► sub-Riemannian, Lorentzian and other geometries, for which the standard definitions of curvature-dimension condition do not hold and new ones have recently been proposed;
► discrete and semi-discrete geometry for which several possibly inequivalent theories are available.
May 21, 2024
May 22, 2024
May 23, 2024
May 24, 2024
09:00 — 09:30
Registration & Welcome
09:30 — 10:15
Karl-Theodor Sturm (U Bonn)
Bakry–Émery, Hardy, and Spectral Gap Estimates on Manifolds with Conical Singularities
Bakry–Émery, Hardy, and Spectral Gap Estimates on Manifolds with Conical Singularities
10:20 — 10:50
Coffee Break
10:50 — 11:35
Nageswari Shanmugalingam (U of Cincinnati)
Discrete approximations of metric measure spaces and nonlocal energies
Discrete approximations of metric measure spaces and nonlocal energies
11:40 — 12:25
Nicola Gigli (SISSA, Trieste)
Trading linearity for ellipticity - a novel approach to global Lorentzian geometry
Trading linearity for ellipticity - a novel approach to global Lorentzian geometry
12:30 — 14:00
Lunch Break
14:00 — 14:45
Shouhei Honda (Tohoku U)
Gromov-Hausdorff stability of tori under Ricci and integral scalar curvature bounds
Gromov-Hausdorff stability of tori under Ricci and integral scalar curvature bounds
14:50 — 15:35
Eva Kopfer (HCM, Bonn)
Homogenisation of discrete dynamical optimal trans- port
Homogenisation of discrete dynamical optimal trans- port
15:40 — 16:10
Coffee Break
16:10 — 16:55
Raquel Perales (CIMAT, Guanajuato)
Rigidity of mass-preserving 1-Lipschitz maps from integral current spaces into Euclidean space
Rigidity of mass-preserving 1-Lipschitz maps from integral current spaces into Euclidean space
09:00 — 09:45
Andrea Pinamonti (U of Trento)
The Bernstein problem in Sub-Riermannian Heisenberg groups: Origins and new developments
The Bernstein problem in Sub-Riermannian Heisenberg groups: Origins and new developments
09:50 — 10:20
Coffee Break
10:20 — 11:05
11:10 — 11:55
Maria (Masha) Gordina (U of Connecticut)
Dimension-independent functional inequalities on sub-Riemannian manifolds
Dimension-independent functional inequalities on sub-Riemannian manifolds
12:00 — 13:30
Lunch Break
13:30 — 14:15
Shin-ichi Ohta (U Osaka)
Integral Varadhan formula for nonlinear heat flow
Integral Varadhan formula for nonlinear heat flow
14:20 — 15:05
15:10 — 15:40
Coffee Break
15:40 — 16:25
Clemens Sämann (U Oxford)
Non-regular spacetime geometry via metric (measure) geometry
Non-regular spacetime geometry via metric (measure) geometry
18:30 — 22:00
Conference Dinner
09:00 — 09:45
Giuseppe Savaré (U Bocconi, Milano)
Sobolev spaces in extended metric-topological measure spaces
Sobolev spaces in extended metric-topological measure spaces
09:50 — 10:20
Coffee Break
10:20 — 11:05
Giorgio Stefani (SISSA, Trieste)
Sub-Riemannian manifolds are not CD
Sub-Riemannian manifolds are not CD
11:10 — 11:55
Kazuhiro Kuwae (Fukuoka U)
Riesz transforms for Dirichlet spaces tamed by distributional curvature lower bounds
Riesz transforms for Dirichlet spaces tamed by distributional curvature lower bounds
12:00 — 13:30
Lunch Break
13:30 — 14:15
Fernando Galaz-García (Durham U)
Metric geometry of spaces of persistence diagrams
Metric geometry of spaces of persistence diagrams
14:20 — 15:05
David Tewodrose (Vrije U Brussels)
Kato meets Bakry-Émery
Kato meets Bakry-Émery
15:10 — 15:40
Coffee Break
15:40 — 16:25
Kohei Suzuki (Durham U)
Dyson Brownian Motion as a Wasserstein Gradient Flow
Dyson Brownian Motion as a Wasserstein Gradient Flow
09:00 — 09:45
Patricia Alonso Ruiz (TAMU, College Station)
Looking for p-energy forms in Cheeger spaces.
Looking for p-energy forms in Cheeger spaces.
09:50 — 10:20
Coffee Break
10:20 — 11:05
Florentin Münch (MPI MIS, Leipzig)
Markov chain curvature and mixing
Markov chain curvature and mixing
11:10 — 11:55
Daniele Semola (ETH Zurich)
Sharp concavity of the isoperimetric profile under lower Ricci bounds: recent results and open questions
Sharp concavity of the isoperimetric profile under lower Ricci bounds: recent results and open questions
12:00 — 13:30
Lunch Break
13:30 — 14:15
Qin Deng (MIT, Cambridge)
Maximal boundary volume rigidity for Alexandrov spaces
Maximal boundary volume rigidity for Alexandrov spaces
14:20 — 15:05
Danka Lučić (JYU, Jyväskylä)
Plans, derivations, and currents in metric measure spaces
Plans, derivations, and currents in metric measure spaces
15:10 — 15:40
Coffee Break
15:40 — 16:25
Mattia Magnabosco (U Oxford)
Failure of the curvature-dimension condition in sub-Finsler manifolds
Failure of the curvature-dimension condition in sub-Finsler manifolds
Organizers
| Name | Affiliation |
|---|---|
| Lorenzo Dello Schiavo | Institute of Science and Technology Austria |
| Christian Ketterer | Albert Ludwigs U Freiburg |
| Chiara Rigoni | University of Vienna |
Attendees
| Name | Affiliation |
|---|---|
| Mohammad Alattar | Durham University |
| Patricia Alonso Ruiz | Texas A & M University |
| Davide Barilari | Università di Padova |
| Samuel Borza | SISSA |
| Giovanni Brigati | Institute of Science and Technology Austria |
| Matteo Calisti | University of Vienna |
| Mauricio Che | Durham University |
| Nicolò Cont | Vrije Universiteit Brussel |
| Qin Deng | MIT |
| Marco Flaim | Hausdorff Center for Mathematics, University of Bonn |
| Valerie Freund | University of Leipzig |
| Fernando Galaz-García | Durham University |
| Luca Gennaioli | SISSA |
| Nicola Gigli | SISSA |
| Maria (Masha) Gordina | University of Connecticut |
| Wojciech Gorny | University of Vienna |
| Shouhei Honda | Tohoku University |
| Eva Kopfer | Hausdorff Center for Mathematics, University of Bonn |
| Kazuhiro Kuwae | Fukuoka University |
| Tri Minh Le | TU Wien |
| Ruowei Li | Max Planck Institute for Mathematics in the Sciences |
| Danka Lučić | University of Jyväskylä |
| Jan Maas | Institute of Science and Technology Austria |
| Mattia Magnabosco | University of Oxford |
| Davide Manini | Technion Haifa |
| Andrea Mondino | University of Oxford |
| Florentin Münch | Max Planck Institute for Mathematics in the Sciences |
| Argam Ohanyan | University of Vienna |
| Shin-ichi Ohta | Osaka University |
| Raquel Perales | Centro de Investigacion en Matematicas |
| Andrea Pinamonti | University of Trento |
| Renata Possobon | Max Planck Institute for Mathematics in the Sciences |
| Filippo Quattrocchi | Institute of Science and Technology Austria |
| Felix Rott | SISSA |
| Clemens Sämann | University of Oxford |
| Giuseppe Savaré | Università Commerciale Luigi Bocconi |
| Daniele Semola | ETH Zürich |
| Nageswari Shanmugalingam | University of Cincinnati |
| Giacomo Enrico Sodini | University of Vienna |
| Ulisse Stefanelli | University of Vienna |
| Giorgio Stefani | SISSA |
| Karl-Theodor Sturm | University of Bonn |
| Kohei Suzuki | Durham University |
| David Tewodrose | Vrije Universiteit Brussel |
| Alessio Vardabasso | University of Vienna |
| Simone Vincini | SISSA |
| Melchior Wirth | Institute of Science and Technology Austria |
| Sergio Zamora Barrera | Max Planck Institute for Mathematics |
| Matteo Zanardini | SISSA |
| Xin Zhang | University of Vienna |
| Xingyu Zhu | Universität Bonn |
Nicola Gigli (SISSA, Trieste): Trading linearity for ellipticity - a novel approach to global Lorentzian geometry
May 21, 2024 11:40 — 12:25
May 21, 2024 11:40 — 12:25
Raquel Perales (CIMAT, Guanajuato): Rigidity of mass-preserving 1-Lipschitz maps from integral current spaces into Euclidean space
May 21, 2024 16:10 — 16:55
May 21, 2024 16:10 — 16:55
Davide Barilari (UP): Unified synthetic Ricci curvature lower bounds for Riemannian and sub-Riemannian structures
May 22, 2024 10:20 — 11:05
May 22, 2024 10:20 — 11:05
Maria (Masha) Gordina (U of Connecticut): Dimension-independent functional inequalities on sub-Riemannian manifolds
May 22, 2024 11:10 — 11:55
May 22, 2024 11:10 — 11:55
Shin-ichi Ohta (U Osaka): Integral Varadhan formula for nonlinear heat flow
May 22, 2024 13:30 — 14:15
May 22, 2024 13:30 — 14:15
Andrea Mondino (U Oxford): A sharp isoperimetric-type inequality for Lorentzian spaces satisfying time-like Ricci lower bounds
May 22, 2024 14:20 — 15:05
May 22, 2024 14:20 — 15:05
Andrea Mondino (U Oxford): A sharp isoperimetric-type inequality for Lorentzian spaces satisfying time-like Ricci lower bounds
May 22, 2024 14:20 — 15:05
May 22, 2024 14:20 — 15:05
Clemens Sämann (U Oxford): Non-regular spacetime geometry via metric (measure) geometry
May 22, 2024 15:40 — 16:25
May 22, 2024 15:40 — 16:25
Giuseppe Savaré (U Bocconi, Milano): Sobolev spaces in extended metric-topological measure spaces
May 23, 2024 09:00 — 09:45
May 23, 2024 09:00 — 09:45
Kazuhiro Kuwae (Fukuoka U): Riesz transforms for Dirichlet spaces tamed by distributional curvature lower bounds
May 23, 2024 11:10 — 11:55
May 23, 2024 11:10 — 11:55
Fernando Galaz-García (Durham U): Metric geometry of spaces of persistence diagrams
May 23, 2024 13:30 — 14:15
May 23, 2024 13:30 — 14:15
Patricia Alonso Ruiz (TAMU, College Station): Looking for p-energy forms in Cheeger spaces.
May 24, 2024 09:00 — 09:45
May 24, 2024 09:00 — 09:45
Daniele Semola (ETH Zurich): Sharp concavity of the isoperimetric profile under lower Ricci bounds: recent results and open questions
May 24, 2024 11:10 — 11:55
May 24, 2024 11:10 — 11:55
Danka Lučić (JYU, Jyväskylä): Plans, derivations, and currents in metric measure spaces
May 24, 2024 14:20 — 15:05
May 24, 2024 14:20 — 15:05
Mattia Magnabosco (U Oxford): Failure of the curvature-dimension condition in sub-Finsler manifolds
May 24, 2024 15:40 — 16:25
May 24, 2024 15:40 — 16:25
At a glance
- Type:
- Workshop
- When:
- May 21, 2024 — May 24, 2024
- Where:
- ESI Boltzmann Lecture Hall
- Organizer(s):
-
Lorenzo Dello Schiavo (ISTA, Klosterneuburg)
Christian Ketterer (ALU Freiburg)
Chiara Rigoni (U of Vienna)