Non-regular Spacetime Geometry

Recently, regularity issues have increasingly come into the focus of researchers in Mathematical General Relativity and in Lorentzian geometry as they have turned out to be crucial in solving some of the most persistent open questions in the field. Traditionally most studies have assumed, explicitly or implicitly, smoothness of the metric. However, new insights are needed when the metric is not $C^2$ and, consequently, it appears reasonable to call such geometries non-regular spacetimes.

In Riemannian signature geometers have long studied non-regular manifolds using a variety of methods, such as comparison geometry, metric geometry and others. Many of these techniques have yet to be exported to the Lorentzian setting since, of course, a number of difficulties have to be addressed. At the moment the field is very dynamic as new methods and approaches are being developed and merged together with older techniques and accounts.

This workshop aims at gathering researchers at the forefront of the field to discuss and advance recent related results in areas such as causality theory, cone and Lorentz-Finsler structures, Alexandrov geometry, length spaces, metric geometry, ${C}^0$-extendibility of spacetimes, transport theory and curvature-dimension conditions, as well as non-commutative geometry.

In the first week (March 13 - 17) there will be a conference on the topics of the workshop.

 

March 13, 2023
09:00 — 09:30
Registration & Welcome
10:15 — 10:45
Coffee Break
12:15 — 14:00
Lunch Break
15:30 — 16:00
Coffee Break
16:45 — 17:30
March 14, 2023
09:45 — 10:30
10:30 — 11:00
Coffee Break
11:00 — 11:45
Miguel Ángel Javaloyes Victoria (U Murcia)
Finsler spacetimes: regularity and physical interpretations
11:45 — 12:30
12:30 — 14:00
Lunch Break
15:30 — 16:00
Coffee Break
16:00 — 16:45
March 15, 2023
09:00 — 09:45
10:30 — 11:00
Coffee Break
11:45 — 12:30
Lorenzo Mazzieri (University of Trento)
Some Mass Concepts in General Relativity
12:30 — 14:00
Lunch Break
14:45 — 15:30
15:30 — 16:00
Coffee Break
March 16, 2023
09:45 — 10:30
Patrick Bernard (U Paris-Dauphine)
Uniform temporal functions
10:30 — 11:00
Coffee Break
11:00 — 11:45
12:30 — 14:00
Lunch Break
15:30 — 16:00
Coffee Break
18:30 — 23:00
Conference Dinner
March 17, 2023
09:45 — 10:30
10:30 — 11:00
Coffee Break
11:00 — 11:45
11:45 — 12:30
12:30 — 14:00
Lunch Break
14:45 — 15:30
15:30 — 16:00
Coffee Break
16:00 — 16:45
March 20, 2023
14:45 — 15:30
Albert Fathi (GATECH, Atlanta)
Metric weak KAM theory
March 21, 2023
14:45 — 15:30

Organizers

Name Affiliation
Piotr T. Chruściel University of Vienna
Melanie Graf University of Hamburg
Michael Kunzinger University of Vienna
Ettore Minguzzi University of Florence
Roland Steinbauer University of Vienna

Attendees

Name Affiliation
Brian Allen Lehman College
Charlie Beil University of Graz
Tobias Beran University of Vienna
Patrick Bernard Université Paris-Dauphine
Mathias Braun University of Toronto
Matteo Calisti University of Vienna
Peter Cameron University of Edinburgh
Fabio Cavalletti SISSA
Wan Cong University of Vienna
David Fajman University of Vienna
Albert Fathi Georgia Institute of Technology
Christopher Fewster University of York
Filip Ficek University of Vienna
Felix Finster Universität Regensburg
Jose Luis Flores University of Malaga
Leonardo García-Heveling Radboud University
Nicola Gigli SISSA
James D. E. Grant University of Surrey
Finnian Gray University of Vienna
Stacey Harris Saint Louis University
John Harvey Cardiff University
Jonatan Herrera University of Cordoba
Albert Huber University of Applied Sciences Vienna
Miguel Ángel Javaloyes Victoria University of Murcia
Eleni Kontou University of Amsterdam
Klaus Kröncke KTH Stockholm
Eric Ling University of Copenhagen
Miguel Manzano Universidad de Salamanca
Marc Mars University of Salamanca
Pierre Martinetti Università di Genova & INFN
Lorenzo Mazzieri University of Trento
Robert McCann University of Toronto
Benjamin Meco Uppsala University
Tomasz Miller Copernicus Center for Interdisciplinary Studies, Jagiellonian University (Krakow, Poland)
Carla Mladek University of Vienna
Andrea Mondino University of Oxford
Valter Moretti University of Trento
Olaf Müller Humboldt University
Argam Ohanyan University of Vienna
Shin-ichi Ohta Osaka University
Jiri Podolsky University of Prague
Moritz Reintjes City University of Hong Kong
Chiara Rigoni University of Vienna
Carl Rossdeutscher University of Vienna
Felix Rott University of Vienna
Anna Sakovich Uppsala University
Clemens Sämann University of Oxford
Miguel Sanchez Universidad de Granada
Jan Sbierski University of Edinburgh
Jose M M Senovilla University of the Basque Country Bilbao
Walter Simon University of Vienna
Didier Solis Gamboa Universidad Autónoma de Yucatán
Stefan Suhr Ruhr-Universität Bochum
Sumati Surya Raman Research Institute
Georgios Tsimperis Cardiff University
James A. Vickers University of Southampton
Daniele Volpe University of Trento
Eric Woolgar University of Alberta
Preview of Robert McCann - A nonsmooth approach to Einstein‘s theory of gravity
Robert McCann (U Toronto): A nonsmooth approach to Einstein‘s theory of gravity
March 13, 2023 09:30 — 10:15
Preview of Clemens Sämann - A Lorentzian analog for Hausdorff dimension and measure
Clemens Sämann (U Oxford): A Lorentzian analog for Hausdorff dimension and measure
March 13, 2023 16:45 — 17:30
Preview of Shin-ichi Ohta - Geometry of weighted Finsler spacetimes
Shin-ichi Ohta (U Osaka): Geometry of weighted Finsler spacetimes
March 14, 2023 09:45 — 10:30
Preview of Eleni Kontou - Generalizations of classical relativity theorems
Eleni Kontou (U Amsterdam): Generalizations of classical relativity theorems
March 14, 2023 11:45 — 12:30
Preview of Moritz Reintjes - On the regularity implied by the assumptions of geometry
Moritz Reintjes (City U of Hong Kong): On the regularity implied by the assumptions of geometry
March 14, 2023 16:00 — 16:45
Preview of Nicola Gigli - Differentiating in a non-differentiable environment
Nicola Gigli (SISSA, Trieste): Differentiating in a non-differentiable environment
March 15, 2023 09:00 — 09:45
Preview of Lorenzo Mazzieri - Some Mass Concepts in General Relativity
Lorenzo Mazzieri (University of Trento): Some Mass Concepts in General Relativity
March 15, 2023 11:45 — 12:30
Preview of Brian Allen - Properties of the null distance on a spacetime
Brian Allen (CUNY): Properties of the null distance on a spacetime
March 15, 2023 14:00 — 14:45
Preview of Leonardo García-Heveling - Global hyperbolicity through the eyes of the null distance
Leonardo García-Heveling (Radboud U): Global hyperbolicity through the eyes of the null distance
March 15, 2023 14:45 — 15:30
Preview of Patrick Bernard - Uniform temporal functions
Patrick Bernard (U Paris-Dauphine): Uniform temporal functions
March 16, 2023 09:45 — 10:30
Preview of Tomasz Miller - Causal evolution of measures and continuity equation
Tomasz Miller (Jagiellonian University): Causal evolution of measures and continuity equation
March 16, 2023 11:00 — 11:45
Preview of Christopher Fewster - Nonlocal generalisations of Green hyperbolicity
Christopher Fewster (U of York): Nonlocal generalisations of Green hyperbolicity
March 17, 2023 09:45 — 10:30
Preview of James A. Vickers - Quantum Field Theory on low-regularity spacetimes
James A. Vickers (U Southampton): Quantum Field Theory on low-regularity spacetimes
March 17, 2023 11:00 — 11:45
Preview of Stefan Suhr - Gromov-Hausdorff Theory for Lorentzian Spaces
Stefan Suhr (Ruhr U, Bochum): Gromov-Hausdorff Theory for Lorentzian Spaces
March 17, 2023 11:45 — 12:30
Preview of Jan Sbierski - On the uniqueness problem for spacetime extensions
Jan Sbierski (U Edinburgh): On the uniqueness problem for spacetime extensions
March 17, 2023 14:45 — 15:30
Preview of Argam Ohanyan - Sobolev calculus in synthetic Lorentzian geometry
Argam Ohanyan (U of Vienna): Sobolev calculus in synthetic Lorentzian geometry
March 17, 2023 16:00 — 16:45
Preview of Eric Woolgar - Static near horizon geometries and quasi-Einstein metrics
Eric Woolgar (U Alberta, Edmonton): Static near horizon geometries and quasi-Einstein metrics
March 21, 2023 14:45 — 15:30
At a glance
Type:
Workshop
When:
March 13, 2023 — March 24, 2023
Where:
ESI Boltzmann Lecture Hall
Organizer(s):
Piotr T. Chruściel (U of Vienna)
Melanie Graf (U Hamburg)
Michael Kunzinger (U of Vienna)
Ettore Minguzzi (U Florence)
Roland Steinbauer (U of Vienna)