Constructions and Obstructions in Birational Geometry

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Constructions and Obstructions in Birational Geometry

 05 - 09 Nov 2018
 ICMS, Bayes Centre, 47 Potterrow Edinburgh

Scientific Organisers:

  • Arend Bayer, University of Edinburgh

  • Ivan Cheltsov, University of Edinburgh

  • Liana Heuberger, University of Angers

  • Evgeny Shinder, University of Sheffield

The main aims of the workshop included reviewing the most important recent developments in birational geometry, relating to the explicit methods and toric varieties and degenerations on the constructions side, and Chow groups, derived categories and the Grothendieck ring of varieties on the obstructions side, and subsequently initiating the discussion between experts, leading to further progress in the two neighboring fields (constructions and obstructions). The workshop was dedicated to William Edge (born 8 November 1904) who pioneered research in algebraic geometry in the UK and worked at the University of Edinburgh for most of his career

The schedule was devised to allow the audience to access experts in both fields, as it is rare for a mathematician to be interested in a singular approach to their research. The workshop brought together leading experts in the field with younger researchers. The organisers had a strong commitment to considering the gender balance of their speakers and ten of the 21 speakers were women.

Claire Voisin, Collège de France gave the Clay Mathematical Institute lecture Decomposition of the diagonal and nilpotence. A recording of Claire Voisin’s lecture can be viewed here.

The abstracts of all the talks can be read here.

The organisers final workshop report can be downloaded here. In their report the organisers noted ten papers that had come out of the workshop at the time of writing. They also commented on the vibrant atmosphere of the workshop and that "the blackboards next to the lecture hall were constantly occupied with intense mathematical discussions."

A short film about ICMS was made during the workshop and can be viewed here. The film features Lian Heuberger and Arend Bayer.


  • Susanna Zimmermann, Université d'Angers - Quotients of Cremona Groups

  • Enrica Floris, Université de Poitiers - On the B-Semiampleness Conjecture

  • Hamid Ahmadinezhad, Loughborough University - Models of 3-fold Mori Fibre Spaces

  • Cinzia Casagrande, Università di Torino - Fano 4-folds With Rational Fibrations

  • Piotr Pokora, Polish Academy of Sciences - On the Bounded Negativity Conjecture

  • Alexander Kuznetsov, Steklov Mathematical Institute - Semiorthogonal Decompositions of Singular Surfaces

  • Claire Voisin, Collège de France - Decomposition of the Diagonal and Nilpotence

  • Alessio Corti, Imperial College London - Volume-Preserving Birational Maps of PP3

  • John Ottem, University of Oslo - The Integral Hodge Conjecture for Curve Classes

  • Marta Pieropan, École Polytechnique Fédérale de Lausanne - On Rationally Connected Varieties Over C_1 Fields of Characteristic 0

  • Rita Pardini, Universita' di Pisa - Higher Dimensional Clifford-Severi Equalities

  • Gavin Brown, University of Warwick - Flops and Contraction Algebras

  • Anne-Sophie Kaloghiros, Brunel University - Maximal Intersection Calabi-Yau Pairs

  • Jean-Louis Colliot-Thelene, CNRS et Université Paris-Sud - A Few Results on Cubic Surfaces and Hypersurfaces

  • Ekaterina Amerik, Université de Paris-Sud - Contraction Loci on Hyperkaehler Manifolds in Families

  • Nicolas Addington, University of Oregon - Exoflops

  • Elisa Postinghel, Loughborough University - Mutations of Newton-Okounkov Polytopes and Classification of Fano Manifolds

  • Francesco Zucconi, Universitá degli Studi di Udine - Rationality of Special Sub-Loci in the Moduli Space of Spin Curves

  • Sergey Gorchinskiy, Steklov Mathematical Institute - Categorical Measures for Varieties with Finite Group Actions

  • Diane Maclagan, University of Warwick - Tree Compactifications of the Moduli Space of Genus Zero Curves

  • Lev Borisov, Rutgers University - Explicit Equations of Ball Quotients


The organisers acknowledge the generous support of the Clay Mathematical Institute who contributed to the costs of Claire Voisin and four early career researchers. In addition the organisers acknowledge the financial support from Arend Bayer’s ERC grant.