Einstein Spaces and Special Geometry

July 10 - July 14, 2023

Einstein manifolds have played a central role in Riemannian geometry and mathematical physics over the last 100 years. Known examples of Einstein manifolds can be found within the classes of special geometry (for example Hermitian, algebraically special) or special holonomy metrics (for example hyperkähler, G2). Einstein manifolds appear naturally as possible final states and singularity models for the Ricci flow. In mathematical physics, Riemannian Einstein manifolds appear as gravitational instantons in quantum theories of gravity.

In spite of the classical results in the field, and much recent progress, many important questions about construction, classification, existence and uniqueness of Einstein manifolds remain wide open. For example, there is no known obstruction to the existence of Einstein metrics on compact manifolds of dimension n ≥ 5. A classical open question is whether all compact Ricci-flat manifold have special holonomy. There are also many open problems concerning the geometry of complete Ricci-flat with specific asymptotic geometries. For example, it is not known if all 4-dimensional Ricci-flat ALE manifolds are hyperkähler. Recent work has raised the question of whether there are any non-Hermitian gravitational instantons. Further important open problems concern the stability of Einstein manifolds, as well as concentration and bubbling phenomena at boundaries of moduli spaces of Einstein metrics.

Seminars Scroll to the next upcoming seminar

  • Claude LeBrun: Einstein Metrics, Four-Manifolds, and Conformally Kähler Geometry July 10 09:00 - 10:00

    Claude LeBrun: Einstein Metrics, Four-Manifolds, and Conformally Kähler Geometry

  • Jeff Viaclovsky: Gravitational instantons July 10 10:30 - 11:10

    Jeff Viaclovsky: Gravitational instantons

  • Walter Simon: Gravitational Instantons with S^1 Symmetry July 10 11:20 - 12:00

    Walter Simon: Gravitational Instantons with S^1 Symmetry

  • Break July 10 13:30 - 14:15

    Break

  • Gustav Nilsson: The Teukolsky Equation and Mode Stability of Gravitational Instantons of Type D July 10 14:30 - 14:55

    Gustav Nilsson: The Teukolsky Equation and Mode Stability of Gravitational Instantons of Type D

  • Stephen McCormick: A volume-renormalised mass for asymptotically hyperbolic manifolds July 10 15:05 - 15:45

    Stephen McCormick: A volume-renormalised mass for asymptotically hyperbolic manifolds

  • Gover: Poincaré–Einstein asymptotics via conformal fundamental forms, and the Poincare-Einstein Dirichlet-Neumann map July 10 16:15 - 16:55

    Gover: Poincaré–Einstein asymptotics via conformal fundamental forms, and the Poincare-Einstein Dirichlet-Neumann map

  • Paul Gauduchon: Extremal Kähler Metrics and Gravitational Instantons July 11 09:00 - 10:00

    Paul Gauduchon: Extremal Kähler Metrics and Gravitational Instantons

  • Matt Gursky: The ASD deformation complex and a conjecture of Singer July 11 10:30 - 11:10

    Matt Gursky: The ASD deformation complex and a conjecture of Singer

  • Hanci Chi: Existence and non-existence of Einstein metrics of cohomogeneity one July 11 11:20 - 12:00

    Hanci Chi: Existence and non-existence of Einstein metrics of cohomogeneity one

  • Break July 11 13:30 - 14:15

    Break

  • Paul Schwahn: The Lichnerowicz Laplacian on normal homogeneous spaces July 11 14:30 - 14:55

    Paul Schwahn: The Lichnerowicz Laplacian on normal homogeneous spaces

  • Uwe Semmelmann: The kernel of the Rarita-Schwinger operator on Einstein manifolds July 11 15:05 - 15:45

    Uwe Semmelmann: The kernel of the Rarita-Schwinger operator on Einstein manifolds

  • Bernd Ammann: Parallel spinors on Riemannian and Lorentzian manifolds July 11 16:15 - 16:55

    Bernd Ammann: Parallel spinors on Riemannian and Lorentzian manifolds

  • Maciej Dunajski: Intrinsic rigidity of extremal horizons July 12 09:00 - 09:40

    Maciej Dunajski: Intrinsic rigidity of extremal horizons

  • Alan Pinoy: CR compactification of asymptotically complex hyperbolic manifolds July 12 09:45 - 10:10

    Alan Pinoy: CR compactification of asymptotically complex hyperbolic manifolds

  • Jonathan Glöckle: Initial data sets and index theory July 12 10:40 - 11:05

    Jonathan Glöckle: Initial data sets and index theory

  • Louis Yudowitz: Bubble Tree Convergence of Shrinking Ricci Solitons July 12 11:15 - 11:40

    Louis Yudowitz: Bubble Tree Convergence of Shrinking Ricci Solitons

  • Lars Martin Sektnan: The Optimal Symplectic Connection equation and stability of fibrations July 12 11:50 - 12:30

    Lars Martin Sektnan: The Optimal Symplectic Connection equation and stability of fibrations

  • Olivier Biquard: Einstein manifolds and their desingularizations July 13 09:00 - 10:00

    Olivier Biquard: Einstein manifolds and their desingularizations

  • Tristan Ozuch: Holonomy of limits of Einstein 4-manifolds July 13 10:30 - 11:10

    Tristan Ozuch: Holonomy of limits of Einstein 4-manifolds

  • Hans-Joachim Hein: A gluing construction for complex surfaces with hyperbolic cusps July 13 11:20 - 12:00

    Hans-Joachim Hein: A gluing construction for complex surfaces with hyperbolic cusps

  • Break July 13 13:30 - 14:30

    Break

  • Francesca Oronzio: Some inequalities involving the ADM mass via the potential theory July 13 14:30 - 14:55

    Francesca Oronzio: Some inequalities involving the ADM mass via the potential theory

  • Marc Herzlich: The Gauss-Bonnet-Chern Center of Mass for Asymptotically Flat Manifolds July 13 15:05 - 15:45

    Marc Herzlich: The Gauss-Bonnet-Chern Center of Mass for Asymptotically Flat Manifolds

  • Simon Brendle: Scalar curvature rigidity of convex polytopes July 13 16:15 - 16:55

    Simon Brendle: Scalar curvature rigidity of convex polytopes

  • Paul Tod: The twistor construction of black holes and gravitational instan-tons July 14 09:00 - 10:00

    Paul Tod: The twistor construction of black holes and gravitational instan-tons

  • Lionel Mason: Hyper-Kähler metrics on cluster varieties for families of minimal surfaces July 14 10:30 - 11:10

    Lionel Mason: Hyper-Kähler metrics on cluster varieties for families of minimal surfaces

  • Johannes Nordström: Complete cohomogeneity one solitons for G_2 Laplacian flow July 14 11:20 - 12:00

    Johannes Nordström: Complete cohomogeneity one solitons for G_2 Laplacian flow

Participants

Name University Country Arrival and Departure
Bernd
Ammann
University: Universität Regensburg City: Germany Arrival and Departure: -
Lars
Andersson
University: Beijing Institute of Mathematical Sciences and Applications City: China Arrival and Departure: -
Bernardo
Araneda
University: Max Planck Institute for Gravitational Physics City: Germany Arrival and Departure: -
Hugues
Auvray (Online)
University: U. Paris-Saclay / UQAM City: France Arrival and Departure: -
Olivier
Biquard
University: Sorbonne Université City: France Arrival and Departure: -
Christoph
Böhm
University: University of Münster City: Germany Arrival and Departure: -
Simon
Brendle
University: Columbia University City: United States Arrival and Departure: -
David M. J.
Calderbank
University: University of Bath City: United Kingdom Arrival and Departure: -
Hanci
Chi
University: Xi'an Jiaotong-Liverpool University City: China Arrival and Departure: -
Vicente
Cortés (Online)
University: University of Hamburg City: Germany Arrival and Departure: -
Mattias
Dahl
University: KTH Royal Institute of Technology City: Sweden Arrival and Departure: -
Andrew
Dancer
University: Oxford University City: United Kingdom Arrival and Departure: -
Erwann
Delay
University: Avignon University City: France Arrival and Departure: -
Maciej
Dunajski
University: University of Cambridge City: United Kingdom Arrival and Departure: -
Lorenzo
Foscolo
University: University College London City: United Kingdom Arrival and Departure: -
Laura
Fredrickson (Online)
University: University of Oregon City: United States Arrival and Departure: -
Paul
Gauduchon
University: Ecole Polytechnique City: France Arrival and Departure: -
Jonathan
Glöckle
University: Universität Regensburg City: Germany Arrival and Departure: -
Ashwin Rod
Gover
University: University of Auckland City: New Zealand Arrival and Departure: -
Matt
Gursky
University: University of Notre Dame City: United States Arrival and Departure: -
Mark
Haskins
University: Duke University City: United States Arrival and Departure: -
Hans-Joachim
Hein
University: WWU Münster City: Germany Arrival and Departure: -
Marc
Herzlich
University: University of Montpellier City: France Arrival and Departure: -
Nicos
Kapouleas
University: Brown University City: United States Arrival and Departure: -
Klaus
Kröncke
University: KTH Royal Institute of Technology City: Sweden Arrival and Departure: -
Claude
LeBrun
University: Stony Brook University City: United States Arrival and Departure: -
Lionel
Mason
University: University of Oxford City: United Kingdom Arrival and Departure: -
Rafe
Mazzeo
University: Stanford University City: United States Arrival and Departure: -
Stephen
McCormick
University: Luleå University of Technology City: Sweden Arrival and Departure: -
Gustav
Nilsson
University: Max-Plank-Institut für Gravitationsphysik (Albert-Einstein-Institut) City: Germany Arrival and Departure: -
Johannes
Nordström
University: University of Bath City: United Kingdom Arrival and Departure: -
Francesca
Oronzio
University: Università degli studi di Roma "La Sapienza" City: Italy Arrival and Departure: -
Tristan
Ozuch
University: Massachusetts Institute of Technology City: United States Arrival and Departure: -
Alan
Pinoy
University: KTH Royal Institute of Technology City: Sweden Arrival and Departure: -
BIanca
Santoro
University: University of Münster City: Germany Arrival and Departure: -
Paul
Schwahn
University: University of Stuttgart City: Germany Arrival and Departure: -
Lars Martin
Sektnan
University: University of Gothenburg City: Sweden Arrival and Departure: -
Uwe
Semmelmann
University: Universität Stuttgart City: Germany Arrival and Departure: -
Walter
Simon
University: University of Vienna City: Austria Arrival and Departure: -
Paul
Tod
University: St John's College / Oxford University City: United Kingdom Arrival and Departure: -
Jeff
Viaclovsky
University: University of California, Irvine City: United States Arrival and Departure: -
Bernard
Whiting
University: University of Florida City: United States Arrival and Departure: -
Louis
Yudowitz
University: KTH Royal Institute of Technology City: Sweden Arrival and Departure: -