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
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 | University: Universität 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: - |
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: - |
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: - |