Scientific Organisers
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Ivan Cheltsov, University of Edinburgh
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Daniel Loughran, University of Bath
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Antoine Pinardin (Lead organiser), University of Edinburgh
About:
Classifying varieties up to birational equivalence is one of the driving forces for modern research in algebraic geometry. Some of the greatest results in 20th and 21st Century algebraic geometry lie in birational geometry, with both Mori and Birkar awarded the Fields medal for their work in this area. Birational geometry has seen some very healthy and surprising interactions with number theory over the last decade.
Firstly, many of the existing techniques and results in birational geometry only work over the field of complex numbers, due to the use of transcendental methods. There has been a push to make these methods algebraic and make them work over algebraically closed fields of positive characteristic, or even non-algebraically closed fields. Number theory has also fed into birational geometry, with the realisation that rational curves should behave like rational points, i.e. solutions to Diophantine equations.
Recent developments suggest that there is much to be gained at the interface between number theory and birational geometry, and this workshop was one of the first attempts in the form of an international meeting to explore these interactions.
Programme
| MONDAY 28 OCTOBER 2024 | ||
| Registration and Refreshments | ||
| Welcome and Housekeeping | ||
| Nicholas Shepherd-Barron, King’s College London | Recognizing flag varieties and Coxeter systems | |
| Break | ||
| Hamid Abban, University of Nottingham | A pointless approach to K-stability | |
| Refreshments | ||
| Alexei Skorobogatov, Imperial College London | Spectral sequences for semiabelian varieties over non-closed fields | |
| Lunch | ||
| Evgeny Shinder, University of Sheffield | Shafarevich–Tate twists of Lagrangian fibrations | |
| Break | ||
| Julia Schneider, University of Sheffield | Birational maps of Severi-Brauer surfaces, with applications to Cremona groups of higher rank | |
| Refreshments | ||
| Tim Santens, University of Cambridge | The birational geometry of BG | |
| Break | ||
| Andrea Fanelli, University of Bordeaux | The Cremona group over imperfect fields | |
| Welcome Reception, hosted at ICMS | ||
| TUESDAY 29 OCTOBER 2024 | ||
| Lena Ji, University of Illinois Urbana-Champaign | Rationality problems for linear spaces on pencils of quadrics | |
| Break | ||
| Frédéric Mangolte, University of Aix-Marseille | Real Fano threefolds which are graphs of cubo-cubic transformations | |
| Refreshments | ||
| Gebhard Martin, University of Bonn | Isolated quotient singularities in positive characteristic | |
| Lunch | ||
| Livia Campo, University of Vienna | K-stablity of Fano threefold hypersurfaces of index 1 | |
| Break | ||
| Jakob Glas, Institute of Science and Technology Austria (ISTA) | Terminality of moduli spaces of curves on hypersurfaces via the circle method | |
| Refreshments | ||
| Zhijia Zhang, New York University | Equivariant geometry of Pfaffian cubic threefolds | |
| Break | ||
| Damián Gvirtz-Chen, University of Glasgow | Non-thin rational points for doubly elliptic K3 surfaces | |
| WEDNESDAY 30 OCTOBER 2024 | ||
| Nikolaos Tziolas, University of Cyprus | ||
| Break | ||
| Hiromu Tanaka, University of Tokyo | Classification of smooth Fano threefolds in positive characteristic | |
| Refreshments | ||
| Egor Yasinsky, Université de Bordeaux | Birational involutions of the real projective plane | |
| Break | ||
| Susanna Zimmermann, Institut de mathematiques d'Orsay | Maximal algebraic groups of birational maps | |
| Lunch and free afternoon | ||
| THURSDAY 31 OCTOBER 2024 | ||
| Jean-Louis Colliot-Thélène, University of Paris-Saclay | On the rationality problem for quadric surface bundles over the real projective line. This is a joint work with Alena Pirutka | |
| Break | ||
| Sho Tanimoto, Nagoya University | The spaces of rational curves on del Pezzo surfaces via conic bundles | |
| Refreshments | ||
| Ulrich Derenthal, Leibniz Universität Hannover | Rational and integral points of bounded height on quintic del Pezzo surfaces | |
| Lunch | ||
| Brian Lehmann, Boston College | Restriction theorems for curves | |
| Break | ||
| Yuri Tschinkel, New York University | Equivariant birational geometry | |
| Refreshments | ||
| Aline Zanardini, EPFL | A glimpse into the birational geometry of quasihomogeneous cAn singularities | |
| Break | ||
| Runxuan Gao, Nagoya University | Zariski dense exceptional sets in Manin’s conjecture: dimension 2 | |
| Conference dinner (exact time TBA) | ||
| FRIDAY 1 NOVEMBER 2024 | ||
| Bianca Viray, University of Washington | On rationality of conic bundles threefolds over nonclosed fields | |
| Refreshments | ||
| Gregory Sankaran, University of Bath | Rationality and arithmetic of the moduli of abelian varieties. This is a joint work with Daniel Loughran | |
| Refreshments | ||
| Marta Benozzo, University of Paris-Saclay | On the canonical bundle formula in positive characteristic | |
| Lunch and end of workshop |