Derived categories and Chow groups of hyperkaehler and Calabi-Yau varieties: September 19-23, 2016.

Organized by: Daniel Huybrechts, Ljudmila Kamenova, Emanuele Macri, Eyal Markman

Attendee ListDownload Talk Schedule Download Poster

The Chow group of an algebraic variety encodes information about its algebraic cycles up to rational equivalence. The study of Chow groups is intimately related to the study of the derived categories of coherent sheaves, as illustrated, for example, by recent results on rational points on derived equivalent K3 surfaces. The workshop will bring together researchers in the fields of derived categories of hyperkälhler and Calabi-Yau varieties and researchers in the theory of algebraic cycles on such varieties. Both fields experienced intensive activity recently and witnessed exciting new results. Facilitating the interaction between the two groups would likely yield further progress.

K3 surfaces and their higher-dimensional generalizations provided by compact hyperkälhler manifolds are a perfect testing ground for central conjectures in algebraic geometry, like the Hodge conjecture, the Tate conjecture, Grothendieck’s standard conjectures, Bloch-Beilinson conjectures, etc.. Significant new insight has been obtained in recent years, but many new and old questions remain open. These developments put hyperkälhler manifolds at a central place in the interaction between complex geometry, arithmetic algebraic geometry, and the theory of motives.

Derived categories on algebraic varieties have been of fundamental importance in many branches of Mathematics in the past years mostly due to the notion of equivalence between them. Equivalences both give rise to “hidden symmetries” among varieties (e.g., the McKay Correspondence) and provide interesting information on the variety itself. Among the topics to be addressed are: Bridgeland stability conditions and birational geometry, existence of stability conditions on threefolds, Bridgeland’s Conjecture on the structure of the group of autoequivalences of the derived categories of K3 surfaces, Kawamata’s Conjecture on derived equivalences between K-equivalent varieties, interesting examples of equivalences, and derived categories of GIT quotients.

Talk Schedule


Time Title Presenter Location
9:30am On Beauville’s conjectural weak splitting property Ulrike Riess SCGP 102
10:30am Coffee Break N/A SCGP Cafe
11:00am Decomposition of the small diagonal for families of K3 surfaces Yin Qizheng SCGP 102
12:00pm Lunch N/A SCGP Cafe
2:15pm Motivic Hyper-Kähler resolution conjecture Lie Fu SCGP 102
3:30pm Tea Time N/A SCGP Lobby
4:00pm Some new rational cubic 4-folds Nick Addington SCGP 102


Time Title Presenter Location
9:30am Torsion points of sections of Lagrangian fibrations Claire Voisin SCGP 102
10:30am Coffee Break N/A SCGP Cafe
11:00am Cubic fourfolds and O’Grady 10 Hyperkahler manifolds Radu Laza SCGP 102
12:00pm Lunch N/A SCGP Cafe
2:15pm Covering families of lagrangian subvarieties of hyperkaehler varieties Kieran O’Grady SCGP 102
3:30pm Tea Time N/A SCGP Lobby
4:00pm Perverse coherent sheaves on hyperkahler manifolds and
Weil conjectures
Misha Verbitsky SCGP 102


Time Title Presenter Location
9:30am Stability conditions and Fourier-Mukai theory Dulip Piyaratne SCGP 102
10:30am Coffee Break N/A SCGP Lobby
11:00am Derived equivalences between moduli spaces of coherent sheaves on a K3 surface Daniel Halpern-Leistner SCGP 102
12:00pm Lunch N/A SCGP Cafe
2:15pm The birational geometry of moduli spaces of sheaves on surfaces Izzet Coskun SCGP 102
3:30pm Tea Time N/A SCGP Lobby
4:00pm Algebraic Geometry: More applications of stability conditions Arend Bayer SCGP 102
5:15pm Every Rational Hodge Isometry Between Two K3
Surfaces is Algebraic
Nikolay Buskin SCGP 102


Time Title Presenter Location
9:30am Rationality problems Yuri Tschinkel SCGP 102
10:30am Coffee Break N/A SCGP Cafe
11:00am Moduli spaces of stable sheaves on Enriques surfaces Kota Yoshioka SCGP 102
12:00pm Lunch N/A SCGP Cafe
2:15pm Zero-cycles and constant cycle subvarieties in some hyper-Kähler varieties Hsueh-Yung Lin SCGP 102
3:30pm Tea Time N/A SCGP Lobby
4:00pm Math Colloquium: K3 surfaces and lattices Daniel Huybrechts SCGP 102


Time Title Presenter Location
9:30am Cubic fourfolds, K3 surfaces, and derived equivalences Brendan Hassett SCGP 102
10:30am Coffee Break N/A SCGP Cafe
11:00am Categories and filtrations Ludmil Katzarkov SCGP 102
12:00 pm Lunch N/A SCGP Cafe
1:15pm Birational geometry of moduli spaces of sheaves on the projective plane via wall crossing Xiaolei Zhao SCGP 102
2:30pm Geometry of O’Grady’s 6 dimensional example Giulia Sacca SCGP 102
3:30 pm Tea Time N/A SCGP Lobby

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