Organiser(s):
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Anne-Sophie Kaloghiros, Brunel University London
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Carolina Araujo, Instituto de Matemática Pura e Aplicada (IMPA)
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Fabrizio Catanese, Bayreuth University & KIAS Seoul
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Ivan Cheltsov, University of Edinburgh
About:
Notions of K-stability attracted interest as purely algebro-geometric characterisations of the existence of Kähler-Einstein metrics on Fano manifolds. Since then, exciting developments in the field have shown that shows that K-stability is also the right framework to understand the moduli theory of Fano varieties - or in layman’s terms, how Fano varieties behave in families. Yet, our understanding of K-stability is still very partial!
Birational geometry gives us tools to further this understanding and to construct geometrically meaningful degenerations of Fano manifolds. This interplay between birational geometry, moduli theory and K-stability was at the heart of the workshop.
Resources
Programme:
| Monday 21 November | ||
| Registration and Refreshments | ||
| Welcome and Housekeeping | ||
| Jihun Park, IBS-CGP / POSTECH | Factoriality of sextic double solids, revisited | |
| Livia Campo, Korea Institute for Advanced Study | Flags on Fano 3-fold hypersurfaces | |
| Refreshments | ||
| Maksym Fedorchuk, Boston College | Towards standard models of Fano hypersurface fibrations over one-dimensional bases | |
| Lunch | ||
| Yuchen Liu, Northwestern University | K-moduli of cyclic covers and wall crossing | |
| Refreshments | ||
| Adrien Dubouloz, CNRS - UNiversité de Bourgogne | Additive groups, Rees algebras and test configurations | |
| Jesus Martinez-Garcia, University of Essex | Some observations on the dimension of Fano K-moduli | |
| Welcome Reception, hosted at ICMS | ||
| Tuesday 22 November | ||
| Tiago Duarte-Guerreiro, University of Essex | On the birational geometry of Fano 3-fold complete intersections | |
| Ciro Ciliberto, Università di Roma Tor Vergata | Elliptic curves, ACM and Ulrich bundles on prime Fano threefolds | |
| Refreshments | ||
| Nivedita Viswanathan, Loughborough University | K-stability of smooth Fano 3-folds of certain families | |
| Lunch | ||
| Piotr Pokora, Pedagogical University of Cracow | Maximizing curves | |
| Refreshments | ||
| Gavin Brown, University of Warwick | Simple 3-fold flops | |
| Public Talk, by Carolina Araujo | Algebraic Geometry - history, challenges and applications | |
| Wednesday 23 November | ||
| Thibaut Delcroix, Univ. Montpellier | Effective conditions of existence of extremal Kähler metrics | |
| Hamid Abban, University of Nottingham | On K-moduli of quartic threefolds | |
| Refreshments | ||
| Ana-Maria Castravet, Paris Saclay, University of Versailles | Exceptional collections on moduli spaces of stable rational curves | |
| Lunch | ||
| Andrea Petracci, University of Bologna | Toric degenerations, mutations and applications to K-moduli | |
| Refreshments | ||
| Egor Yasinsky, École Polytechnique | Birational maps of Severi-Brauer surfaces and quotients of higher Cremona groups | |
| Kento Fujita, Osaka University | The Calabi problem for Fano threefolds | |
| Reception / Light Supper, hosted at ICMS | ||
| Thursday 24 November | ||
| Cristiano Spotti, Aarhus University | Towards a stability notion for LCK manifolds | |
| Paolo Cascini, Imperial College | MMP for algebraically integrable foliations | |
| Refreshments | ||
| Francesco Zucconi, Università degli studi di Udine | On integral points of some Fano threefolds and their Hilbert schemes of lines and conics | |
| Lunch | ||
| Ruadhai Dervan, University of Glasgow | Stability and Kähler-Einstein metrics in big classes | |
| Refreshments | ||
| Inder Kaur, Loughborough University | Hodge conjecture for singular varieties | |
| Alessio Corti, Imperial College London | Toric degenerations of Fano manifolds | |
| Workshop Dinner, hosted at Blonde Restaurant | ||
| Friday 25 November | ||
| Takashi Kishimoto, Saitama University | Equivariant completions of vector groups into Fano varieties | |
| Liana Heuberger, University of Bath | Towards classifying Q-Fano threefolds |