Spectral Theory and Mathematical Relativity
Since the discovery of quantum theory we know that spectral theory of linear operators in Hilbert spaces is fundamental in our description of nature. Apart from its significance in the formulation of quantum mechanics, spectral theory has also been very influential in other areas of pure and applied mathematics. The proposed programme is broadly about novel applications of spectral methods in general relativity such as "Spectral Theory of Stationary Spacetimes", "Stability questions in General Relativity", and "The Mathematics of QFT and Hawking Radiation".
Introductory Workshop: June 19 - 23, 2023
Main Conference: July 10 -14, 2023
The main conference can be followed live online via the streaming a link.
Calendar for the talks:
https://calendar.google.com/calendar/embed?src=geometryandrelativity%40gmail.com&ctz=Europe%2FVienna
June 7, 2023
June 12, 2023
June 13, 2023
June 14, 2023
June 15, 2023
June 16, 2023
June 19, 2023
June 20, 2023
June 21, 2023
June 22, 2023
June 23, 2023
June 26, 2023
June 27, 2023
June 28, 2023
June 29, 2023
June 30, 2023
July 3, 2023
July 4, 2023
July 5, 2023
July 6, 2023
July 7, 2023
July 10, 2023
July 11, 2023
July 12, 2023
July 13, 2023
July 14, 2023
July 17, 2023
July 18, 2023
July 19, 2023
July 20, 2023
July 21, 2023
14:00 — 15:30
Discussion session of current research topics in PDEs
This is an information session where current participants of the program give short talks presenting their current research topics. Others are also welcome.
Location: Schrödinger Lecture Hall
15:00 — 15:50
Håkan Andréasson (Chalmers U of Technology, Gothenburg)
The weak cosmic censorship conjecture and the Hoop conjecture in the case of the axially symmetric Einstein-Vlasov system
The weak cosmic censorship conjecture and the Hoop conjecture in the case of the axially symmetric Einstein-Vlasov system
15:00 — 15:50
Clotilde Fermanian Kammerer (UPEC)
Semi-classical approximation for time-dependent systems
Semi-classical approximation for time-dependent systems
15:00 — 15:50
Jonathan Glöckle (U Regensburg)
Initial data rigidity via Dirac-Witten operators
Initial data rigidity via Dirac-Witten operators
15:00 — 15:50
Ethan Sussman (MIT, Cambridge)
Massive waves gravitationally bound to static bodies
Massive waves gravitationally bound to static bodies
14:00 — 14:50
Amir Vig (U of Michigan, Ann Arbor)
Cancellations in the wave trace
Cancellations in the wave trace
09:30 — 10:00
Registration & Welcome
10:00 — 10:30
Coffee break
10:30 — 11:30
Birgit Schörkhuber (U of Innsbruck)
Singularity formation, stability and spectral analysis I
Singularity formation, stability and spectral analysis I
11:30 — 13:30
Lunch break
13:30 — 14:30
14:30 — 15:00
Coffee break
15:30 — 16:30
Birgit Schörkhuber (U of Innsbruck)
Singularity formation, stability and spectral analysis II
Singularity formation, stability and spectral analysis II
16:30 — 17:00
Discussions
09:00 — 10:00
Birgit Schörkhuber (U of Innsbruck)
Singularity formation, stability and spectral analysis III
Singularity formation, stability and spectral analysis III
10:00 — 10:30
Coffee break
10:30 — 11:30
Alexander Strohmaier (U Leeds)
Spectral theory of stationary spacetimes I: Normally hyperbolic operators on spacetimes and solution theory
Spectral theory of stationary spacetimes I: Normally hyperbolic operators on spacetimes and solution theory
11:30 — 13:00
Lunch break
13:00 — 14:00
Birgit Schörkhuber (U of Innsbruck)
Singularity formation, stability and spectral analysis IV
Singularity formation, stability and spectral analysis IV
14:00 — 14:30
Coffee break
14:30 — 15:30
Maciej Zworski (UC, Berkeley)
Microlocal methods for operators with analytic coefficients II: Microlocal elliptic regularity
Microlocal methods for operators with analytic coefficients II: Microlocal elliptic regularity
15:40 — 16:20
Oana Ivanovici (Sorbonne U, Paris)
Geometry and analysis of waves on domains
Geometry and analysis of waves on domains
16:20 — 17:00
Discussions
09:00 — 10:00
Dietrich Häfner (U Grenoble Alpes)
Dirac fields on Kerr spacetime and the Hawking radiation, I: The Kerr spacetime
Dirac fields on Kerr spacetime and the Hawking radiation, I: The Kerr spacetime
10:00 — 10:30
Coffee break
10:30 — 11:30
Alexander Strohmaier (U Leeds)
Spectral theory of stationary spacetimes II: Fourier integral operators and microlocal theory
Spectral theory of stationary spacetimes II: Fourier integral operators and microlocal theory
11:30 — 14:00
Lunch break
14:00 — 17:00
Free afternoon & discussions
18:00 — 22:00
Workshop Dinner
09:00 — 10:00
Maciej Zworski (UC, Berkeley)
Microlocal methods for operators with analytic coefficients III: Kashiwara's watermelon theorem
Microlocal methods for operators with analytic coefficients III: Kashiwara's watermelon theorem
10:00 — 10:30
Coffee break
10:30 — 11:30
Dietrich Häfner (U Grenoble Alpes)
Dirac fields on Kerr spacetime and the Hawking radiation, II: Scattering theory
Dirac fields on Kerr spacetime and the Hawking radiation, II: Scattering theory
11:30 — 13:30
Lunch break
13:30 — 14:30
Alexander Strohmaier (U Leeds)
Spectral theory of stationary spacetimes III: Trace formulas
Spectral theory of stationary spacetimes III: Trace formulas
14:30 — 15:00
Coffee break
15:00 — 16:00
Dietrich Häfner (U Grenoble Alpes)
Dirac fields on Kerr spacetime and the Hawking radiation, III: The Unruh state for fermions
Dirac fields on Kerr spacetime and the Hawking radiation, III: The Unruh state for fermions
16:00 — 17:00
Discussions
09:00 — 10:00
Alexander Strohmaier (U Leeds)
Spectral theory of stationary spacetimes IV: Spectral asymptotics
Spectral theory of stationary spacetimes IV: Spectral asymptotics
10:00 — 10:30
Coffee break
10:30 — 11:30
Maciej Zworski (UC, Berkeley)
Microlocal methods for operators with analytic coefficients IV: Applications to unique continuation
Microlocal methods for operators with analytic coefficients IV: Applications to unique continuation
11:30 — 13:30
Lunch break
13:30 — 14:30
Dietrich Häfner (U Grenoble Alpes)
Dirac fields on Kerr spacetime and the Hawking radiation, IV: The Hawking effect
Dirac fields on Kerr spacetime and the Hawking radiation, IV: The Hawking effect
14:30 — 15:00
Coffee break
15:00 — 15:50
Maciej Zworski (UC, Berkeley)
Classically forbidden regions and analytic hypoellipticity
Classically forbidden regions and analytic hypoellipticity
15:00 — 15:50
Maciej Maliborski (U of Vienna)
Instability of scalar field in a reflective cavity
Instability of scalar field in a reflective cavity
15:00 — 15:50
Allen Juntao Fang (Princeton U)
Nonlinear stability of Kerr-de Sitter
Nonlinear stability of Kerr-de Sitter
15:00 — 15:50
Oliver Petersen (KTH Stockholm)
Wave equations in Kerr-de Sitter spacetimes: the full subextremal range
Wave equations in Kerr-de Sitter spacetimes: the full subextremal range
15:00 — 15:50
Onirban Islam (U of Potsdam)
Feynman propagators on curved spacetime.
Feynman propagators on curved spacetime.
14:00 — 14:50
Gautam Satishchandran (Princeton U)
Infrared Finite Scattering Theory in QFT and Quantum Gravity
Infrared Finite Scattering Theory in QFT and Quantum Gravity
15:00 — 15:50
Alden Waters (U Leeds)
The relative trace formula in electromagnetic scattering
The relative trace formula in electromagnetic scattering
14:00 — 14:50
Florian Johne (Columbia U, New York)
Intermediate curvature and a generalization of Geroch's conjecture
Intermediate curvature and a generalization of Geroch's conjecture
15:00 — 15:50
Pascal Millet (U Grenoble Alpes)
Leading-order term expansion for the Teukolsky equation on subextremal Kerr black holes
Leading-order term expansion for the Teukolsky equation on subextremal Kerr black holes
15:00 — 15:50
Lionel Mason (U Oxford)
Gravity from holomorphic discs and celestial Lw1+∞ symmetries
Gravity from holomorphic discs and celestial Lw1+∞ symmetries
15:00 — 15:50
Simone Murro (U Genova)
Hadamard states for Maxwell fields via complete gauge fixing
Hadamard states for Maxwell fields via complete gauge fixing
14:00 — 14:50
Andrea Nützi (ETH Zurich)
Maurer-Cartan perturbation theory and scattering amplitudes in general relativity
Maurer-Cartan perturbation theory and scattering amplitudes in general relativity
09:30 — 10:00
Registration and Welcome
10:00 — 10:50
Kasia Rejzner (U of York)
New proposal for renormalisation group equations on curved spacetimes
New proposal for renormalisation group equations on curved spacetimes
11:00 — 11:50
Robert Wald (U of Chicago)
Quantum Field Theory in Curved Spacetime
Quantum Field Theory in Curved Spacetime
12:00 — 14:00
Lunch break
14:00 — 14:50
Michał Wrochna (Cergy Paris U.)
Low-energy obstructions to quantizing linearized gravity
Low-energy obstructions to quantizing linearized gravity
14:50 — 15:30
Coffee break
15:30 — 16:20
Dean Baskin (TAMU, College Station)
The Feynman propagator for the wave equation with an inverse square potential
The Feynman propagator for the wave equation with an inverse square potential
09:00 — 09:50
András Vasy (Stanford U)
The Feynman propagator and self-adjointness
The Feynman propagator and self-adjointness
09:50 — 10:20
Coffee break
10:20 — 11:10
Semyon Dyatlov (MIT, Cambridge)
Microlocal analysis of internal waves in 2D aquaria
Microlocal analysis of internal waves in 2D aquaria
11:20 — 12:10
Jeremy Louis Marzuola (U of North Carolina, Chapel Hill)
Spectral minimal partitions, nodal deficiency and the Dirichlet-to-Neumann map
Spectral minimal partitions, nodal deficiency and the Dirichlet-to-Neumann map
12:20 — 14:00
Lunch break
14:00 — 14:50
Georgios Moschidis (EPFL, Lausanne)
Weak turbulence on Schwarzschild-AdS spacetime
Weak turbulence on Schwarzschild-AdS spacetime
14:50 — 15:30
Coffee break
15:30 — 16:20
Jonathan Luk (Stanford U)
Late time tail of waves on dynamic asymptotically flat spacetimes of odd space dimensions
Late time tail of waves on dynamic asymptotically flat spacetimes of odd space dimensions
09:00 — 09:50
Christian Bär (U of Potsdam)
Survey on Index Theory on Lorentzian Manifolds
Survey on Index Theory on Lorentzian Manifolds
09:50 — 10:20
Coffee break
10:20 — 11:10
Stefan Czimek (U Leipzig)
Obstruction-free gluing for the Einstein equations
Obstruction-free gluing for the Einstein equations
11:20 — 12:10
Christoph Kehle (ETH Zurich)
A small divisors instability at the Kerr-AdS Cauchy horizon
A small divisors instability at the Kerr-AdS Cauchy horizon
Free afternoon
09:00 — 09:50
Rita Teixeira da Costa (U of Cambridge)
The Teukolsky equation on Kerr in the full subextremal range |a|<M
The Teukolsky equation on Kerr in the full subextremal range |a|<M
09:50 — 10:20
Coffee break
10:20 — 11:10
Claude Warnick (U of Cambridge)
Quasinormal modes of (near) extremal black holes
Quasinormal modes of (near) extremal black holes
11:20 — 12:10
Zoe Wyatt (U of Cambridge)
Global Stability of Spacetimes with Supersymmetric Compactifications
Global Stability of Spacetimes with Supersymmetric Compactifications
12:20 — 14:00
Lunch break
14:00 — 14:50
14:50 — 15:30
Coffee break
15:30 — 16:20
Jared Wunsch (Northwestern U Evanston)
Wave propagation on rotating cosmic string backgrounds
Wave propagation on rotating cosmic string backgrounds
09:30 — 10:20
Tanya Christiansen (U of Missouri, Columbia)
Resolvent at low energy in two dimensions
Resolvent at low energy in two dimensions
10:20 — 11:00
Coffee break
11:00 — 11:50
Colin Guillarmou (U Paris-Saclay)
Virasoro semi-groups and conformal blocks
Virasoro semi-groups and conformal blocks
12:00 — 14:00
Lunch break
14:00 — 14:50
Stefan Hollands (U Leipzig)
Semi-classical analysis of strong cosmic censorship
Semi-classical analysis of strong cosmic censorship
14:50 — 15:30
Coffee break
15:30 — 16:20
Michael Eichmair (U of Vienna)
On the canonical geometric structure of initial data for the Einstein equations
On the canonical geometric structure of initial data for the Einstein equations
09:30 — 10:20
Shi-Zhuo Looi (CalTech)
Asymptotics of non-linear and linear waves on asymptotically flat spacetimes
Asymptotics of non-linear and linear waves on asymptotically flat spacetimes
09:30 — 10:20
Zhongkai Tao (UC, Berkeley)
Solution operators for the Einstein constraint equation
Solution operators for the Einstein constraint equation
Schrödinger Lecture Hall
15:00 — 15:50
Dietrich Häfner (U Grenoble Alpes)
On the linear stability of Kerr black holes
On the linear stability of Kerr black holes
Boltzmann Lecture Hall
09:30 — 10:20
Moritz Doll (U Melbourne)
Microlocal Analysis of the Klein-Gordon equation with spatial potentials
Microlocal Analysis of the Klein-Gordon equation with spatial potentials
Schrödinger Lecture Hall
09:30 — 10:20
Rudrajit Banerjee (Okinawa IST)
Wick rotating the heat kernel
Wick rotating the heat kernel
Schrödinger Lecture Hall
This event has no subevents associated to it.
Organizers
| Name | Affiliation |
|---|---|
| Piotr T. Chruściel | University of Vienna |
| Peter Hintz | ETH Zurich |
| Alexander Strohmaier | University of Leeds |
| Steven Morris Zelditch † | Northwestern University Evanston |
Attendees
| Name | Affiliation |
|---|---|
| Peter C. Aichelburg | University of Vienna |
| Selim Amar | Stanford University |
| Håkan Andréasson | Chalmers University of Technology |
| Rudrajit Banerjee | Okinawa Institute of Science and Technology |
| Christian Bär | University of Potsdam |
| Dean Baskin | Texas A & M University |
| Robert Beig | University of Vienna |
| Anxo Biasi | École Normale Supérieure |
| Andras Bonk | University of Vienna |
| Tanya Christiansen | University of Missouri |
| Wan Cong | University of Vienna |
| Stefan Czimek | University of Leipzig |
| Daine Danielson | University of Chicago |
| Claudio Dappiaggi | University of Pavia |
| Pedro del Real Lavergne | University of Vienna |
| Moritz Doll | University of Melbourne |
| Roland Donninger | University of Vienna |
| Semyon Dyatlov | Massachusetts Institute of Technology |
| Michael Eichmair | University of Vienna |
| David Fajman | University of Vienna |
| Allen Juntao Fang | Princeton University |
| Clotilde Fermanian Kammerer | Université Paris Est - Créteil Val-de-Marne |
| Filip Ficek | University of Vienna |
| Stefano Galanda | Università di Genova |
| Jonathan Glöckle | Universität Regensburg |
| Juan Manuel González Brantes | Pontificial Catholic University of Chile |
| Finnian Gray | University of Vienna |
| Colin Guillarmou | Université Paris-Saclay |
| Dietrich Häfner | Université Grenoble Alpes |
| Stefan Hollands | University of Leipzig |
| Gemma Hood | Imperial College London |
| Albert Huber | University of Applied Sciences Vienna |
| Onirban Islam | University of Potsdam |
| Oana Ivanovici | Sorbonne University |
| Jose-Luis Jaramillo | Université de Bourgogne |
| Florian Johne | Columbia University |
| Istvan Kadar | University of Cambridge |
| Christopher Kauffman | University of Münster |
| Christoph Kehle | ETH Zürich |
| Christiane Klein | University of Leipzig |
| Michael Kunzinger | University of Vienna |
| Rubens Longhi | University of Potsdam |
| Shi-Zhuo Looi | California Institute of Technology |
| Jonathan Luk | Stanford University |
| Maciej Maliborski | University of Vienna |
| Jeremy Louis Marzuola | University of North Carolina |
| Lionel Mason | University of Oxford |
| Peter Michor | University of Vienna |
| Pascal Millet | Université Grenoble Alpes |
| Vincent Moncrief | Yale University |
| Gabriele Mondello | Sapienza – Università di Roma |
| Katrina Morgan | Northwestern University Evanston |
| Georgios Moschidis | EPFL, Lausanne |
| Simone Murro | University of Genova |
| Andrea Nützi | ETH Zürich |
| Marius A. Oancea | University of Vienna |
| Maximilian Ofner | University of Vienna |
| Leonid Parnovski | University College London |
| Oliver Petersen | KTH Stockholm |
| Ronald Quirchmayr | University of Groningen |
| Kasia Rejzner | University of York |
| Paola Rioseco | Universidad de Chile |
| Andrzej Rostworowski | Jagiellonian University |
| Ashkan Sadat Kyaee | Sorbonne University |
| Gautam Satishchandran | Princeton University |
| Gabriel Schmid | Università di Genova |
| Birgit Schörkhuber | University of Innsbruck |
| Walter Simon | University of Vienna |
| Roland Steinbauer | University of Vienna |
| Thomas Stucker | ETH Zürich |
| Ethan Sussman | Massachusetts Institute of Technology |
| Zhongkai Tao | University of California, Berkeley |
| Greg Taujanskas | University of Cambridge |
| Rita Teixeira da Costa | University of Cambridge |
| Ryan Unger | Princeton University |
| Liam Urban | University of Vienna |
| András Vasy | Stanford University |
| Amir Vig | University of Michigan |
| Magnus von Terzi | University of Vienna |
| Robert Wald | University of Chicago |
| David Wallauch-Hajdin | University of Vienna |
| Claude Warnick | University of Cambridge |
| Alden Waters | University of Leeds |
| Michał Wrochna | Cergy Paris Université |
| Jared Wunsch | Northwestern University Evanston |
| Raphaela Wutte | Arizona State University |
| Zoe Wyatt | University of Cambridge |
| Ruben Zeitoun | CY Cergy Paris Université |
| Xuwen Zhu | Northeastern University |
| Maciej Zworski | University of California, Berkeley |
Clotilde Fermanian Kammerer (UPEC): Semi-classical approximation for time-dependent systems
June 13, 2023 15:00 — 15:50
June 13, 2023 15:00 — 15:50
Jonathan Glöckle (U Regensburg): Initial data rigidity via Dirac-Witten operators
June 14, 2023 15:00 — 15:50
June 14, 2023 15:00 — 15:50
Ethan Sussman (MIT, Cambridge): Massive waves gravitationally bound to static bodies
June 15, 2023 15:00 — 15:50
June 15, 2023 15:00 — 15:50
Maciej Zworski (UC, Berkeley): Microlocal methods for operators with analytic coefficients I: FBI transforms, inversion formulas and analytic wave front sets
June 19, 2023 13:30 — 14:30
June 19, 2023 13:30 — 14:30
Alexander Strohmaier (U Leeds): Spectral theory of stationary spacetimes I: Normally hyperbolic operators on spacetimes and solution theory
June 20, 2023 10:30 — 11:30
June 20, 2023 10:30 — 11:30
Maciej Zworski (UC, Berkeley): Microlocal methods for operators with analytic coefficients II: Microlocal elliptic regularity
June 20, 2023 14:30 — 15:30
June 20, 2023 14:30 — 15:30
Alexander Strohmaier (U Leeds): Spectral theory of stationary spacetimes II: Fourier integral operators and microlocal theory
June 21, 2023 10:30 — 11:30
June 21, 2023 10:30 — 11:30
Maciej Zworski (UC, Berkeley): Microlocal methods for operators with analytic coefficients III: Kashiwara's watermelon theorem
June 22, 2023 09:00 — 10:00
June 22, 2023 09:00 — 10:00
Alexander Strohmaier (U Leeds): Spectral theory of stationary spacetimes III: Trace formulas
June 22, 2023 13:30 — 14:30
June 22, 2023 13:30 — 14:30
Alexander Strohmaier (U Leeds): Spectral theory of stationary spacetimes IV: Spectral asymptotics
June 23, 2023 09:00 — 10:00
June 23, 2023 09:00 — 10:00
Maciej Zworski (UC, Berkeley): Microlocal methods for operators with analytic coefficients IV: Applications to unique continuation
June 23, 2023 10:30 — 11:30
June 23, 2023 10:30 — 11:30
Maciej Zworski (UC, Berkeley): Classically forbidden regions and analytic hypoellipticity
June 23, 2023 15:00 — 15:50
June 23, 2023 15:00 — 15:50
Oliver Petersen (KTH Stockholm): Wave equations in Kerr-de Sitter spacetimes: the full subextremal range
June 28, 2023 15:00 — 15:50
June 28, 2023 15:00 — 15:50
Gautam Satishchandran (Princeton U): Infrared Finite Scattering Theory in QFT and Quantum Gravity
June 30, 2023 14:00 — 14:50
June 30, 2023 14:00 — 14:50
Alden Waters (U Leeds): The relative trace formula in electromagnetic scattering
July 3, 2023 15:00 — 15:50
July 3, 2023 15:00 — 15:50
Simone Murro (U Genova): Hadamard states for Maxwell fields via complete gauge fixing
July 6, 2023 15:00 — 15:50
July 6, 2023 15:00 — 15:50
Kasia Rejzner (U of York): New proposal for renormalisation group equations on curved spacetimes
July 10, 2023 10:00 — 10:50
July 10, 2023 10:00 — 10:50
Dean Baskin (TAMU, College Station): The Feynman propagator for the wave equation with an inverse square potential
July 10, 2023 15:30 — 16:20
July 10, 2023 15:30 — 16:20
Semyon Dyatlov (MIT, Cambridge): Microlocal analysis of internal waves in 2D aquaria
July 11, 2023 10:20 — 11:10
July 11, 2023 10:20 — 11:10
Jeremy Louis Marzuola (U of North Carolina, Chapel Hill): Spectral minimal partitions, nodal deficiency and the Dirichlet-to-Neumann map
July 11, 2023 11:20 — 12:10
July 11, 2023 11:20 — 12:10
Jonathan Luk (Stanford U): Late time tail of waves on dynamic asymptotically flat spacetimes of odd space dimensions
July 11, 2023 15:30 — 16:20
July 11, 2023 15:30 — 16:20
Christian Bär (U of Potsdam): Survey on Index Theory on Lorentzian Manifolds
July 12, 2023 09:00 — 09:50
July 12, 2023 09:00 — 09:50
Stefan Czimek (U Leipzig): Obstruction-free gluing for the Einstein equations
July 12, 2023 10:20 — 11:10
July 12, 2023 10:20 — 11:10
Christoph Kehle (ETH Zurich): A small divisors instability at the Kerr-AdS Cauchy horizon
July 12, 2023 11:20 — 12:10
July 12, 2023 11:20 — 12:10
Claude Warnick (U of Cambridge): Quasinormal modes of (near) extremal black holes
July 13, 2023 10:20 — 11:10
July 13, 2023 10:20 — 11:10
Claudio Dappiaggi (U Pavia): Fundamental solutions and Hadamard states for a scalar field with arbitrary boundary conditions on an asymptotically AdS spacetime.
July 13, 2023 14:00 — 14:50
July 13, 2023 14:00 — 14:50
Jared Wunsch (Northwestern U Evanston): Wave propagation on rotating cosmic string backgrounds
July 13, 2023 15:30 — 16:20
July 13, 2023 15:30 — 16:20
Colin Guillarmou (U Paris-Saclay): Virasoro semi-groups and conformal blocks
July 14, 2023 11:00 — 11:50
July 14, 2023 11:00 — 11:50
Stefan Hollands (U Leipzig): Semi-classical analysis of strong cosmic censorship
July 14, 2023 14:00 — 14:50
July 14, 2023 14:00 — 14:50
At a glance
- Type:
- Thematic Programme
- When:
- June 5, 2023 — July 28, 2023
- Where:
- ESI Boltzmann Lecture Hall
- Organizer(s):
-
Piotr T. Chruściel (U of Vienna)
Peter Hintz (ETH Zurich)
Alexander Strohmaier (U Leeds)
Steven Morris Zelditch † (Northwestern U Evanston)