New equivariant methods in algebraic and differential geometry
EMG
3 January 2024 to 28 June 2024
Programme theme
This programme is concerned with symmetries of spaces which arise naturally in various algebraic
and geometric contexts. It aims to explore applications of the new machinery of non-reductive
geometric invariant theory (NRGIT) to different areas of geometry and beyond.
Actions of linear algebraic groups are of fundamental importance across algebraic and differential
geometry and also in the applications of geometry to the rest of mathematics. Classical
geometric invariant theory (GIT) was developed by David Mumford in the 1960s to construct
and study quotients of algebraic varieties by linear actions of reductive groups, with the main application
to the construction of moduli spaces in algebraic geometry. Since then, GIT has been
linked to symplectic geometry via the theory of Hamiltonian group actions and moment maps, and
infinite-dimensional analogues of GIT have provided motivation for crucial advances in differential
geometry, in particular in gauge theory and other areas motivated by mathematical physics,
and more recently K-stability. Important links also arise via toric and tropical geometry to convex
geometry and combinatorics; here the flow of ideas has gone in both directions over the decades.
Recently, GIT has been extended to cover a large class of linear actions by algebraic groups
which are not necessarily reductive. This new ‘non-reductive’ version of GIT is providing applications
in different areas of geometry (such as singularity theory) and potential applications in others
(such as K-stability), as well as new connections with symplectic and hyperkähler geometry.
Many other potential applications exist and remain to be more thoroughly explored. The aim
of this programme is to bring together a broad spectrum of researchers in diverse areas of algebraic
and differential geometry to collaborate on possible new applications mainly focused around the
following themes, which will be the topics of the workshops: applied algebraic geometry, global
singularity theory, complex geometry and hyperbolicity, symplectic and hyperkähler implosion,
K-stability, moduli stacks and enumerative geometry.
In particular, the programme will focus on:
(i) the interactions of GIT with applied and computational algebraic geometry (including toric
geometry, algebraic statistics and geometric group theory);
(ii) the existence of holomorphic curves contained in projective algebraic varieties (‘hyperbolicity’),
which is a fundamental problem in complex geometry;
(iii) the study of singularities of maps between complex manifolds, which is central to global
singularity theory and enumerative geometry;
(iv) the geometry and topology of Hilbert schemes of points on surfaces and higher dimensional
manifolds, which play a crucial role in enumerative geometry;
(v) the construction of moduli spaces of polarised projective schemes and related constructions
in K-stability, and the description of their geometry and topology;
(vi) the relationship between concepts of stability and wall-crossing in different settings such as
geometric invariant theory, Bridgeland stability, K-stability and moduli stacks.
Organized in partnership with the Clay Mathematics Institute
Workshops
Equivariant methods in geometry
8 January 2024 to 12 January 2024
Applied and computational algebraic geometry
22 January 2024 to 26 January 2024
Singularity theory and hyperbolicity
18 March 2024 to 22 March 2024
K-stability and moment maps
13 May 2024 to 17 May 2024
Moduli stacks and enumerative geometry
17 June 2024 to 21 June 2024
Seminars
| Tuesday 16th January 2024 | |||
|---|---|---|---|
| 10:00 to 16:00 | Room 2 | ||
| Wednesday 17th January 2024 | |||
|---|---|---|---|
| 10:00 to 16:00 | Room 2 | ||
| Thursday 18th January 2024 | |||
|---|---|---|---|
| 10:00 to 16:00 | Room 2 | ||
Organisers
- Gergely Berczi Aarhus Universitet
- Damian Brotbek Université de Lorraine
- Ruadhaí Dervan University of Glasgow
- Victoria Hoskins Radboud Universiteit Nijmegen
- Frances Kirwan University of Oxford
- Vidit Nanda University of Oxford
Participants
- Hamid Abban University of Nottingham
- Jarod Alper University of Washington
- Carlos Amendola Technische Universität Berlin
- Hulya Arguz University of Georgia
- Gergely Berczi Aarhus Universitet
- Pierrick Bousseau University of Georgia
- Leticia Brambila-Paz Centro de Investigación en Matemáticas
- Michel Brion Université Joseph Fourier Grenoble
- Dominic Bunnett Technische Universität Berlin
- Benoit Cadorel Université de Lorraine
- Frederic Campana Université de Lorraine
- Ivan Cheltsov University of Edinburgh
- George Cooper University of Oxford
- Andrew Dancer University of Oxford
- Ved Datar Indian Institute of Science
- Elena Denisova University of Edinburgh
- Anand Deopurkar Australian National University
- Kristin DeVleming University of Massachusetts
- Mahmoud Elimam SISSA
- Barbara Fantechi SISSA
- Gavril Farkas Humboldt-Universität zu Berlin
- László Fehér Eotvos Lorand University
- Marc Fersztand University of Oxford
- Gabriel Frey University of Glasgow
- Lie Fu University of Strasbourg
- Kento Fujita Osaka University
- Natalia Garcia Fritz Pontificia Universidad Católica de Chile
- Lothar Goettsche Abdus Salam International Centre for Theoretical Physics
- Eloise Hamilton University of Cambridge
- Masafumi Hattori Kyoto University
- Jochen Heinloth Universität Duisburg-Essen
- Martin Helmer North Carolina State University
- Evelyne Hubert INRIA Sophia Antipolis
- Andrés Ibáñez Núñez University of Oxford
- Eiji Inoue RIKEN
- Joshua Jackson University of Sheffield
- Joachim Jelisiejew University of Warsaw
- Anne-Sophie Kaloghiros Brunel University
- Inder Kaur Loughborough University
- Sohaib Khalid SISSA
- Young-Hoon Kiem Korea Institute for Advanced Study (KIAS)
- Eveline Legendre Université Claude Bernard Lyon 1
- Alina Marian Abdus Salam International Centre for Theoretical Physics; Northeastern University
- Johan Martens University of Edinburgh
- Jesus Martinez Garcia University of Essex
- Laurentiu Maxim University of Wisconsin-Madison
- Anton Mellit Universität Wien
- Joël Merker Université Paris-Saclay
- Felix Minddal Aarhus Universitet
- Ludvig Modin Universität Duisburg-Essen
- Samouil Molcho ETH Zürich
- Tommi Muller University of Oxford
- Vidit Nanda University of Oxford
- Yusra Naqvi University College London
- Junjiro Noguchi University of Tokyo
- András Némethi Renyi Institute for Mathematics, Hungarian Academy of Sciences; Eotvos Lorand University
- Georg Oberdieck KTH - Royal Institute of Technology
- Dragos Oprea University of California, San Diego
- Annamaria Ortu SISSA
- Piotr Oszer Uniwersytet Warszawski
- Theodoros Stylianos Papazachariou Isaac Newton Institute
- Jihun Park POSTECH; Institute for Basic Science
- Simon Pepin lehalleur Universiteit van Amsterdam
- Ragni Piene Universitetet i Oslo
- Vamsi Pingali Indian Institute of Science
- Aaron Pixton University of Michigan
- Lu Qi Princeton University
- Dhruv Ranganathan University of Cambridge
- Rémi Reboulet Chalmers University of Technology
- Richard Rimanyi University of North Carolina
- Ilaria Rossinelli EPFL - Ecole Polytechnique Fédérale de Lausanne
- Erwan Rousseau Université de Bretagne Occidentale
- Carlo Scarpa UQAM - Université du Québec à Montréal
- Henry Schenck Auburn University
- Johannes Schmitt ETH Zürich
- Jörg Schürmann Universität Münster
- Anna Seigal Harvard University
- Lars Martin Sektnan Göteborgs Universitet
- Junliang Shen Yale University
- Clayton Shonkwiler Colorado State University
- Frank Sottile Texas A&M University
- Samuel Stark
- Jacopo Stoppa SISSA
- Balázs Szendröi University of Vienna
- Andras Szenes None / Other
- Hendrik Süß Friedrich-Schiller-Universität Jena
- Lisanne Taams Radboud Universiteit Nijmegen
- Michael Thaddeus Columbia University
- Richard Thomas Imperial College London
- Olga Trapeznikova University of Geneva
- Antonio Trusiani Université Paul Sabatier Toulouse III
- Xiaowei Wang Rutgers, The State University of New Jersey
- Rachel Webb University of California, Berkeley
- Andrzej Weber University of Warsaw
- Jakub Wiaterek University of Oxford
- Yueqiao Wu Institute for Advanced Study, Princeton
- Dimitri Wyss EPFL - Ecole Polytechnique Fédérale de Lausanne
- Mingchen Xia Institut de Mathématiques de Jussieu
- Chenyang Xu Princeton University
- Aline Zanardini EPFL - Ecole Polytechnique Fédérale de Lausanne
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