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
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Claude LeBrun: Einstein Metrics, Four-Manifolds, and Conformally Kähler Geometry July 10 09:00 - 10:00 -
Jeff Viaclovsky: Gravitational instantons July 10 10:30 - 11:10 Jeff Viaclovsky: Gravitational instantons
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Walter Simon: Gravitational Instantons with S^1 Symmetry July 10 11:20 - 12:00 Walter Simon: Gravitational Instantons with S^1 Symmetry
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Break July 10 13:30 - 14:15 Break
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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
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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
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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
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Paul Gauduchon: Extremal Kähler Metrics and Gravitational Instantons July 11 09:00 - 10:00 Paul Gauduchon: Extremal Kähler Metrics and Gravitational Instantons
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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
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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
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Break July 11 13:30 - 14:15 Break
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Paul Schwahn: The Lichnerowicz Laplacian on normal homogeneous spaces July 11 14:30 - 14:55 Paul Schwahn: The Lichnerowicz Laplacian on normal homogeneous spaces
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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
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Bernd Ammann: Parallel spinors on Riemannian and Lorentzian manifolds July 11 16:15 - 16:55 Bernd Ammann: Parallel spinors on Riemannian and Lorentzian manifolds
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Maciej Dunajski: Intrinsic rigidity of extremal horizons July 12 09:00 - 09:40 Maciej Dunajski: Intrinsic rigidity of extremal horizons
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Alan Pinoy: CR compactification of asymptotically complex hyperbolic manifolds July 12 09:45 - 10:10 Alan Pinoy: CR compactification of asymptotically complex hyperbolic manifolds
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Jonathan Glöckle: Initial data sets and index theory July 12 10:40 - 11:05 Jonathan Glöckle: Initial data sets and index theory
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Louis Yudowitz: Bubble Tree Convergence of Shrinking Ricci Solitons July 12 11:15 - 11:40 Louis Yudowitz: Bubble Tree Convergence of Shrinking Ricci Solitons
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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
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Olivier Biquard: Einstein manifolds and their desingularizations July 13 09:00 - 10:00 Olivier Biquard: Einstein manifolds and their desingularizations
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Tristan Ozuch: Holonomy of limits of Einstein 4-manifolds July 13 10:30 - 11:10 Tristan Ozuch: Holonomy of limits of Einstein 4-manifolds
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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
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Break July 13 13:30 - 14:30 Break
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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
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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
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Simon Brendle: Scalar curvature rigidity of convex polytopes July 13 16:15 - 16:55 Simon Brendle: Scalar curvature rigidity of convex polytopes
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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
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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
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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 |
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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: - |