Geometry beyond Riemann: Curvature and Rigidity
The programme centers around recent developments on generalized curvature, convexity, and rigidity. The objects of study include Riemannian and Lorentzian cone-manifolds, Hilbert and Finsler metrics, path metric spaces. Among the questions are deformations of geometric structures and their rigidity, approximation and convergence.
A school will take place from September 18 - 22, 2023 with the following mini-courses:
Peter Aichelburg and Piotr Chrusciel (University of Vienna): Elements of general relativity
Andreas Bernig (University of Frankfurt): Curvature tensors and measures of singular spaces Lecture notes
Mohammad Ghomi (Georgia Institute of Technology): Geometric inequalities in spaces of nonpositive curvature Lecture notes 1-2 Lecture notes 3-4
Feng Luo (Rutgers University): Discrete conformal geometry of polyhedral surfaces
Vladimir Matveev (University of Jena): Nijenhuis geometry Slides
Andrea Seppi (University of Grenoble): Anti-de Sitter geometry and applications to hyperbolic surfaces. https://arxiv.org/abs/2004.14414
A conference will take place from October 16 - 20, 2023.
Sept. 18, 2023
Sept. 19, 2023
Sept. 20, 2023
Sept. 21, 2023
Sept. 22, 2023
Oct. 16, 2023
Oct. 17, 2023
Oct. 18, 2023
Oct. 19, 2023
Oct. 20, 2023
09:00 — 09:30
Registration ＆Welcome
09:30 — 10:20
Andreas Bernig (Goethe U Frankfurt)
Curvature tensors and measures of singular spaces I
Curvature tensors and measures of singular spaces I
10:20 — 10:40
Coffee break
10:40 — 11:30
Andrea Seppi (U Grenoble Alpes)
Anti-de Sitter geometry and applications to hyperbolic surfaces I
Anti-de Sitter geometry and applications to hyperbolic surfaces I
11:30 — 12:20
Peter C. Aichelburg (U of Vienna), Piotr T. Chruściel (U of Vienna)
Elements of general relativity I
Elements of general relativity I
Lectures by Prof. Aichelburg are unfortunately not publicly available due to copy right restrictions.
12:20 — 14:00
Lunch break
14:00 — 14:50
Peter C. Aichelburg (U of Vienna), Piotr T. Chruściel (U of Vienna)
Elements of general relativity II
Elements of general relativity II
14:50 — 15:10
Coffee break
15:10 — 16:00
Mohammad Ghomi (GATECH, Atlanta)
Geometric inequalities in space of nonpositive curvature I
Geometric inequalities in space of nonpositive curvature I
16:00 — 16:50
Vladimir Matveev (U of Jena)
Nijenhuis geometry I
Nijenhuis geometry I
17:00 — 19:00
Reception
09:00 — 09:50
Andreas Bernig (Goethe U Frankfurt)
Curvature tensors and measures of singular spaces II
Curvature tensors and measures of singular spaces II
09:50 — 10:10
Coffee break
10:10 — 11:00
Andrea Seppi (U Grenoble Alpes)
Anti-de Sitter geometry and applications to hyperbolic surfaces II
Anti-de Sitter geometry and applications to hyperbolic surfaces II
11:00 — 11:50
Peter C. Aichelburg (U of Vienna), Piotr T. Chruściel (U of Vienna)
Elements of general relativity III
Elements of general relativity III
12:00 — 14:00
Lunch break
14:00 — 14:50
Feng Luo (Rutgers U)
Discrete conformal geometry of polyhedral surfaces I
Discrete conformal geometry of polyhedral surfaces I
14:50 — 15:10
Coffee break
15:10 — 16:00
Mohammad Ghomi (GATECH, Atlanta)
Geometric inequalities in space of nonpositive curvature II
Geometric inequalities in space of nonpositive curvature II
16:00 — 16:50
Vladimir Matveev (U of Jena)
Nijenhuis geometry II
Nijenhuis geometry II
09:00 — 09:50
Peter C. Aichelburg (U of Vienna), Piotr T. Chruściel (U of Vienna)
Elements of general relativity IV
Elements of general relativity IV
09:50 — 10:10
Coffee break
10:10 — 11:00
Andrea Seppi (U Grenoble Alpes)
Anti-de Sitter geometry and applications to hyperbolic surfaces III
Anti-de Sitter geometry and applications to hyperbolic surfaces III
11:00 — 11:50
Feng Luo (Rutgers U)
Discrete conformal geometry of polyhedral surfaces II
Discrete conformal geometry of polyhedral surfaces II
19:00
Dinner
09:00 — 09:50
Andreas Bernig (Goethe U Frankfurt)
Curvature tensors and measures of singular spaces III
Curvature tensors and measures of singular spaces III
09:50 — 10:10
Coffee break
10:10 — 11:00
Andrea Seppi (U Grenoble Alpes)
Anti-de Sitter geometry and applications to hyperbolic surfaces IV
Anti-de Sitter geometry and applications to hyperbolic surfaces IV
11:00 — 11:50
Peter C. Aichelburg (U of Vienna), Piotr T. Chruściel (U of Vienna)
Elements of general relativity V
Elements of general relativity V
12:00 — 14:00
Lunch break
14:00 — 14:50
Feng Luo (Rutgers U)
Discrete conformal geometry of polyhedral surfaces III
Discrete conformal geometry of polyhedral surfaces III
14:50 — 15:10
Coffee break
15:10 — 16:00
Mohammad Ghomi (GATECH, Atlanta)
Geometric inequalities in space of nonpositive curvature III
Geometric inequalities in space of nonpositive curvature III
16:00 — 16:50
Vladimir Matveev (U of Jena)
Nijenhuis geometry III
Nijenhuis geometry III
09:00 — 09:50
Andreas Bernig (Goethe U Frankfurt)
Curvature tensors and measures of singular spaces IV
Curvature tensors and measures of singular spaces IV
09:50 — 10:10
Coffee break
10:10 — 11:00
Peter C. Aichelburg (U of Vienna), Piotr T. Chruściel (U of Vienna)
Elements of general relativity VI
Elements of general relativity VI
Lectures by Prof. Aichelburg are unfortunately not publicly available due to copy right restrictions.
11:00 — 11:50
Vladimir Matveev (U of Jena)
Nijenhuis geometry IV
Nijenhuis geometry IV
12:00 — 14:00
Lunch break
14:00 — 14:50
Mohammad Ghomi (GATECH, Atlanta)
Geometric inequalities in space of nonpositive curvature IV
Geometric inequalities in space of nonpositive curvature IV
14:50 — 15:40
Feng Luo (Rutgers U)
Discrete conformal geometry of polyhedral surfaces IV
Discrete conformal geometry of polyhedral surfaces IV
15:40
Coffee
09:00 — 09:30
Registration & Welcome
09:30 — 10:20
Francesco Bonsante (U of Pavia)
Projective rigidity of circle packings
Projective rigidity of circle packings
10:20 — 10:40
Coffee Break
10:40 — 11:30
Roman Prosanov (U of Vienna)
On hyperbolic 3-manifolds with polyhedral boundary
On hyperbolic 3-manifolds with polyhedral boundary
11:30 — 12:20
Jean-Marc Schlenker (U of Luxembourg)
Understanding convex hyperbolic manifolds from their boundary
Understanding convex hyperbolic manifolds from their boundary
12:20 — 14:00
Lunch Break
14:00 — 14:50
Andrea Seppi (U Grenoble Alpes)
On the (non-)uniqueness of minimal surfaces in hyperbolic three-space
On the (non-)uniqueness of minimal surfaces in hyperbolic three-space
14:50 — 15:20
Coffee Break
15:20 — 16:10
Alexander Lytchak (KIT, Karlsruhe)
Conformal planes of bounded area
Conformal planes of bounded area
16:30 — 19:00
Welcome Reception
09:00 — 09:50
Dmitry Faifman (Tel Aviv U)
The Funk metric in and around convex geometry
The Funk metric in and around convex geometry
09:50 — 10:20
Coffee Break
10:20 — 11:10
Ken'ichi Ohshika (Gakushuin U, Tokyo)
The bounded image theorem, the original argument and a new proof
The bounded image theorem, the original argument and a new proof
11:10 — 12:00
Yurii Neretin (U of Graz & HSM MIPT)
"Rational" maps of Bruhat--Tits buildings.
"Rational" maps of Bruhat--Tits buildings.
12:00 — 14:00
Lunch Break
14:00 — 14:50
Sergiu Moroianu (IMAR, Bucharest)
Gauss-Bonnet formulae on noncompact manifolds
Gauss-Bonnet formulae on noncompact manifolds
14:50 — 15:20
Coffee Break
15:20 — 16:10
Mohammad Ivaki (TU Vienna)
Firey's worn stones are round
Firey's worn stones are round
09:00 — 09:50
Gérard Besson (U de Grenoble)
Bishop-Gromov's Inequality: a central tool in Geometry.
Bishop-Gromov's Inequality: a central tool in Geometry.
09:50 — 10:20
Coffee Break
10:20 — 11:10
Anders Karlsson (UNIGE, Geneve)
A fixed point theorem for isometries of metric spaces
A fixed point theorem for isometries of metric spaces
11:10 — 12:00
Hiroyasu Izeki (Keio U)
Harmonic maps and random walks on countable groups
Harmonic maps and random walks on countable groups
19:00 — 22:00
Conference Dinner at Heurigen
09:00 — 09:50
Tatiana Nagnibeda (U of Geneva)
On spectra of Laplacians on infinite graphs
On spectra of Laplacians on infinite graphs
09:50 — 10:20
Coffee Break
10:20 — 11:10
Ayato Mitsuishi (U Fukuoka)
Quantitative Lipschitz homotopy convergence of Alexandrov spaces.
Quantitative Lipschitz homotopy convergence of Alexandrov spaces.
11:10 — 12:00
Irina Markina (U of Bergen)
A unified approach to extremal curves on Stiefel manifolds
A unified approach to extremal curves on Stiefel manifolds
12:00 — 14:00
Lunch Break
14:00 — 14:50
Michael Kunzinger (U of Vienna)
Lorentzian length spaces
Lorentzian length spaces
14:50 — 15:20
Coffee Break
15:20 — 16:10
Christian Müller (TU Vienna)
Tensegrities and Koenigs nets
Tensegrities and Koenigs nets
09:00 — 09:50
Francois Fillastre (U Montpellier)
Flat surfaces, cellulations of hyperbolic surfaces and convex polyhedra
Flat surfaces, cellulations of hyperbolic surfaces and convex polyhedra
09:50 — 10:20
Coffee Break
10:20 — 11:10
Ingrid Irmer (SUSTech, Shenzhen)
Schmutz-Thurston duality
Schmutz-Thurston duality
11:10 — 12:00
Daniel Massart (Université de Montpellier)
Algebraic intersection on surfaces
Algebraic intersection on surfaces
12:00 — 14:00
Lunch Break
14:00 — 14:50
Joan Porti (UA de Barcelona)
A local approach to Anosov groups
A local approach to Anosov groups
14:50 — 15:20
Coffee Break
15:20 — 16:10
Nicolas Tholozan (ENS Paris)
Globally hyperbolic anti-de Sitter manifolds and compact Clifford-Klein forms
Globally hyperbolic anti-de Sitter manifolds and compact Clifford-Klein forms
This event has no subevents associated to it.
Organizers
| Name | Affiliation |
|---|---|
| Ivan Izmestiev | Technical University of Vienna |
| Athanase Papadopoulos | Institut de Recherche Mathématique Avancée |
| Marc Troyanov | École Polytechnique Fédéral de Lausanne |
| Sumio Yamada | Gakushuin University |
Attendees
| Name | Affiliation |
|---|---|
| Antoine Ablondi | ENS de Lyon |
| Norbert A'Campo | University of Basel |
| Annette A'Campo-Neuen | University of Basel |
| Peter C. Aichelburg | University of Vienna |
| Alisher Aikyn | King Abdullah University of Science and Technology |
| Mohammad Alattar | Durham University |
| Tobias Beran | University of Vienna |
| Andreas Bernig | Goethe University Frankfurt |
| Silvan Bernklau | University of Jena |
| Gérard Besson | Université de Grenoble |
| Alexey Bolsinov | Loughborough University |
| Francesco Bonsante | University of Pavia |
| Samuel Bronstein | École Normale Supérieure |
| Matteo Calisti | University of Vienna |
| Javier Casado | Universidad Autonoma de Madrid |
| Christopher Cashen | University of Vienna |
| Nicola Cavallucci | École Polytechnique Fédéral de Lausanne |
| Charalampos Charitos | Agricultural University of Athens |
| Piotr T. Chruściel | University of Vienna |
| Manuel Cuerno | Universidad Autonoma de Madrid |
| Farid Diaf | Université Grenoble Alpes |
| Abraham Dorsaz | École Polytechnique Fédéral de Lausanne |
| Dmitry Faifman | Tel Aviv University |
| Francois Fillastre | University of Montpellier |
| Valerie Freund | University of Leipzig |
| Christoph Fritz | Université de Bretagne Occidentale, Brest |
| Mohammad Ghomi | Georgia Institute of Technology |
| Tomasz Goliński | University of Białystok |
| François Guéritaud | University of Strasbourg |
| Sachiko Hamano | Kyoto Sangyo University |
| Joseph Hoisington | Max Planck Institute for Mathematics |
| Yingxiang Hu | Technical University of Vienna |
| Yi Huang | Yau Mathematical Sciences Center, Tsinghua University |
| Ingrid Irmer | Southern University of Science and Technology |
| Mohammad Ivaki | Technical University of Vienna |
| Hiroyasu Izeki | Keio University |
| Anders Karlsson | Universite de Geneve |
| Michael Kunzinger | University of Vienna |
| Wai Yeung Lam | University of Luxembourg |
| René Langøen | University of Bergen |
| Jihye Lee | University of California, Santa Barbara |
| Feng Luo | Rutgers University |
| Alexander Lytchak | Karlsruhe Institute of Technology |
| Irina Markina | University of Bergen |
| Daniel Massart | Université de Montpellier |
| Leo Mathis | Goethe University Frankfurt |
| Vladimir Matveev | University of Jena |
| Thomas Mieling | University of Vienna |
| Ayato Mitsuishi | University of Fukuoka |
| Hideki Miyachi | Kanazawa University |
| Sergiu Moroianu | Simion Stoilow Institute of Mathematics of the Romanian Academy |
| Thiziri Moulla | University of Montpellier |
| Christian Müller | Technical University of Vienna |
| Tatiana Nagnibeda | University of Geneva |
| Stylianos Negrepontis | National and Technical University of Athens |
| Yurii Neretin | University of Graz & HSM MIPT |
| Argam Ohanyan | University of Vienna |
| Ken'ichi Ohshika | Gakushuin University |
| Alan Pinoy | KTH Stockholm |
| Denis Polly | Technical University of Vienna |
| Joan Porti | Universitat Autònoma de Barcelona |
| Roman Prosanov | University of Vienna |
| Manuel Quaschner | University of Jena |
| Matteo Raffaelli | Technical University of Vienna |
| Nicholas Rungi | SISSA |
| Jaime Santos Rodríguez | Universidad Politécnica de Madrid |
| Jean-Marc Schlenker | University of Luxembourg |
| Andrea Seppi | Université Grenoble Alpes |
| Rym Smai | Institut de Recherche Mathématique Avancée |
| Alexey Sossinsky | University of Strasbourg |
| Roland Steinbauer | University of Vienna |
| Darya Sukhorebska | National Academy of Science Ukraine |
| Gudrun Szewieczek | Technical University of Munich |
| Susumu Tanabe | Galatasaray University |
| Nicolas Tholozan | Ecole Normale Superieure |
| Enrico Trebeschi | University of Pavia |
| Alice Barbara Tumpach | Wolfgang Pauli Institut |
| Raphaela Wutte | Arizona State University |
Andreas Bernig (Goethe U Frankfurt): Curvature tensors and measures of singular spaces I
Sept. 18, 2023 09:30 — 10:20
Sept. 18, 2023 09:30 — 10:20
Andrea Seppi (U Grenoble Alpes): Anti-de Sitter geometry and applications to hyperbolic surfaces I
Sept. 18, 2023 10:40 — 11:30
Sept. 18, 2023 10:40 — 11:30
Peter C. Aichelburg (U of Vienna), Piotr T. Chruściel (U of Vienna): Elements of general relativity II
Sept. 18, 2023 14:00 — 14:50
Sept. 18, 2023 14:00 — 14:50
Mohammad Ghomi (GATECH, Atlanta): Geometric inequalities in space of nonpositive curvature I
Sept. 18, 2023 15:10 — 16:00
Sept. 18, 2023 15:10 — 16:00
Andreas Bernig (Goethe U Frankfurt): Curvature tensors and measures of singular spaces II
Sept. 19, 2023 09:00 — 09:50
Sept. 19, 2023 09:00 — 09:50
Andrea Seppi (U Grenoble Alpes): Anti-de Sitter geometry and applications to hyperbolic surfaces II
Sept. 19, 2023 10:10 — 11:00
Sept. 19, 2023 10:10 — 11:00
Peter C. Aichelburg (U of Vienna), Piotr T. Chruściel (U of Vienna): Elements of general relativity III
Sept. 19, 2023 11:00 — 11:50
Sept. 19, 2023 11:00 — 11:50
Feng Luo (Rutgers U): Discrete conformal geometry of polyhedral surfaces I
Sept. 19, 2023 14:00 — 14:50
Sept. 19, 2023 14:00 — 14:50
Mohammad Ghomi (GATECH, Atlanta): Geometric inequalities in space of nonpositive curvature II
Sept. 19, 2023 15:10 — 16:00
Sept. 19, 2023 15:10 — 16:00
Peter C. Aichelburg (U of Vienna), Piotr T. Chruściel (U of Vienna): Elements of general relativity IV
Sept. 20, 2023 09:00 — 09:50
Sept. 20, 2023 09:00 — 09:50
Andrea Seppi (U Grenoble Alpes): Anti-de Sitter geometry and applications to hyperbolic surfaces III
Sept. 20, 2023 10:10 — 11:00
Sept. 20, 2023 10:10 — 11:00
Feng Luo (Rutgers U): Discrete conformal geometry of polyhedral surfaces II
Sept. 20, 2023 11:00 — 11:50
Sept. 20, 2023 11:00 — 11:50
Andreas Bernig (Goethe U Frankfurt): Curvature tensors and measures of singular spaces III
Sept. 21, 2023 09:00 — 09:50
Sept. 21, 2023 09:00 — 09:50
Andrea Seppi (U Grenoble Alpes): Anti-de Sitter geometry and applications to hyperbolic surfaces IV
Sept. 21, 2023 10:10 — 11:00
Sept. 21, 2023 10:10 — 11:00
Peter C. Aichelburg (U of Vienna), Piotr T. Chruściel (U of Vienna): Elements of general relativity V
Sept. 21, 2023 11:00 — 11:50
Sept. 21, 2023 11:00 — 11:50
Feng Luo (Rutgers U): Discrete conformal geometry of polyhedral surfaces III
Sept. 21, 2023 14:00 — 14:50
Sept. 21, 2023 14:00 — 14:50
Mohammad Ghomi (GATECH, Atlanta): Geometric inequalities in space of nonpositive curvature III
Sept. 21, 2023 15:10 — 16:00
Sept. 21, 2023 15:10 — 16:00
Andreas Bernig (Goethe U Frankfurt): Curvature tensors and measures of singular spaces IV
Sept. 22, 2023 09:00 — 09:50
Sept. 22, 2023 09:00 — 09:50
Mohammad Ghomi (GATECH, Atlanta): Geometric inequalities in space of nonpositive curvature IV
Sept. 22, 2023 14:00 — 14:50
Sept. 22, 2023 14:00 — 14:50
Feng Luo (Rutgers U): Discrete conformal geometry of polyhedral surfaces IV
Sept. 22, 2023 14:50 — 15:40
Sept. 22, 2023 14:50 — 15:40
Roman Prosanov (U of Vienna): On hyperbolic 3-manifolds with polyhedral boundary
Oct. 16, 2023 10:40 — 11:30
Oct. 16, 2023 10:40 — 11:30
Jean-Marc Schlenker (U of Luxembourg): Understanding convex hyperbolic manifolds from their boundary
Oct. 16, 2023 11:30 — 12:20
Oct. 16, 2023 11:30 — 12:20
Andrea Seppi (U Grenoble Alpes): On the (non-)uniqueness of minimal surfaces in hyperbolic three-space
Oct. 16, 2023 14:00 — 14:50
Oct. 16, 2023 14:00 — 14:50
Dmitry Faifman (Tel Aviv U): The Funk metric in and around convex geometry
Oct. 17, 2023 09:00 — 09:50
Oct. 17, 2023 09:00 — 09:50
Ken'ichi Ohshika (Gakushuin U, Tokyo): The bounded image theorem, the original argument and a new proof
Oct. 17, 2023 10:20 — 11:10
Oct. 17, 2023 10:20 — 11:10
Yurii Neretin (U of Graz & HSM MIPT): "Rational" maps of Bruhat--Tits buildings.
Oct. 17, 2023 11:10 — 12:00
Oct. 17, 2023 11:10 — 12:00
Sergiu Moroianu (IMAR, Bucharest): Gauss-Bonnet formulae on noncompact manifolds
Oct. 17, 2023 14:00 — 14:50
Oct. 17, 2023 14:00 — 14:50
Gérard Besson (U de Grenoble): Bishop-Gromov's Inequality: a central tool in Geometry.
Oct. 18, 2023 09:00 — 09:50
Oct. 18, 2023 09:00 — 09:50
Anders Karlsson (UNIGE, Geneve): A fixed point theorem for isometries of metric spaces
Oct. 18, 2023 10:20 — 11:10
Oct. 18, 2023 10:20 — 11:10
Hiroyasu Izeki (Keio U): Harmonic maps and random walks on countable groups
Oct. 18, 2023 11:10 — 12:00
Oct. 18, 2023 11:10 — 12:00
Irina Markina (U of Bergen): A unified approach to extremal curves on Stiefel manifolds
Oct. 19, 2023 11:10 — 12:00
Oct. 19, 2023 11:10 — 12:00
Daniel Massart (Université de Montpellier): Algebraic intersection on surfaces
Oct. 20, 2023 11:10 — 12:00
Oct. 20, 2023 11:10 — 12:00
Nicolas Tholozan (ENS Paris): Globally hyperbolic anti-de Sitter manifolds and compact Clifford-Klein forms
Oct. 20, 2023 15:20 — 16:10
Oct. 20, 2023 15:20 — 16:10
At a glance
- Type:
- Thematic Programme
- When:
- Sept. 11, 2023 — Nov. 3, 2023
- Where:
- ESI Boltzmann Lecture Hall
- Organizer(s):
-
Ivan Izmestiev (TU Vienna)
Athanase Papadopoulos (IRMA, Strasbourg)
Marc Troyanov (EPFL, Lausanne)
Sumio Yamada (Gakushuin U, Tokyo)