

1985  1992  Studies of Mathematics, HU Berlin and Max Planck Institute, Bonn  1992  PhD, HU Berlin  1993  1994  Postdoc, Max Planck Institute, Bonn  1994  1995  Postdoc, Institute for Advanced Study, Princeton, NJ, USA  1995  1996  Postdoc, Max Planck Institute, Bonn  1996  1997  Assistant Professor (C1), UniversityGH Essen  1997  1998  MarieCurie Fellow, ENS Paris, France  1998  Habilitation, UniversityGH Essen  1998  2002  Professor (C3), University of Cologne  2002  2005  Professor, Paris Diderot University (Paris 7), France  Since 2005  Professor (C4/W3), University of Bonn 


My main focus is on K3 surfaces and higher dimensional analogues which can be studied in terms of algebraic invariants like Hodge structures and derived categories. K3 surfaces and related moduli spaces are particularly interesting test cases for some of the central conjectures in algebraic geometry (e.g. Tate, Hodge, BlochBeilinson). I have studied Chow groups of K3 surfaces from a geometric and a categorical perspective. In particular, I have introduced the notion of constant cycle curves and studied the action of symplectic automorphisms on Chow groups, providing further evidence for one of Bloch's elusive conjectures. Finite group of symplectic derived autoequivalences have been classified completely in terms of the Conway group, one of the exotic sporadic simple groups. For Kuznetsov's K3 category associated with any cubic fourfold I have extended work of Addington and Thomas to the twisted case and described the group of autoequivalences in the generic case. This has subsequently led to a new proof of the global Torelli theorem for cubic fourfolds (with Rennemo).
It has been conjecture that rationality of cubic fourfolds is determined by the structure of the associated K3 category. Further investigations of the structure of Kuznetsov's category should shed more light on the role of derived techniques on rationality questions in broader generality. The bearing of derived techniques on our understanding of cycles on K3 surfaces and cubics hypersurfaces needs to be clarified. Cohomological methods relating classical invariants like the Jacobian ring of a hypersurface with categorical invariants similar to Hochschild cohomology may lead to global Torelli theorems for cubics of higher dimensions. The role of mirror symmetry needs to be explored. Further foundational questions concerning the motivic nature of K3 surfaces shall be addressed.


DFG Collaborative Research Center SFB/TR 45 “Periods, moduli spaces and arithmetic of algebraic varieties”
Local coordinator, since 2006


Research Area C Homological mirror symmetry relates symplectic and algebraic geometry as an equivalence of categories (Fukaya category of Lagrangians resp. derived category of coherent sheaves). Fundamental aspects of both sides can thus be seen also from the mirror perspective which has led to new insight. In [1], we have proved the mirror analogue of a theorem of Donaldson on the action of the diffeomorphism group of a K3 surface. The conjectured braid group like description of the group of autoequivalences of the derived category of CalabiYau varieties of dimension two is an example and one of the main open problems in the area.  Former Research Area E Spaces of stability conditions on abelian and triangulated categories form a new kind of moduli spaces with an intriguing wall and chamber structure reflecting the change of moduli spaces of stable objects. The main open questions in the are concern the global geometry of the space of stability conditions and the change of numerical and motivic invariants of the associated moduli spaces of stable objects. The case of the derived category of coherent sheaves on a K3 surface is of particular interest as moduli spaces of sheaves and complexes yield higher dimensional varieties with special geometries. A surprising relation to conjectures on the structure of Chow groups has been discovered in [2].  Research Area DE



[ 1] Daniel Huybrechts, Emanuele Macrì, Paolo Stellari
Derived equivalences of K3 surfaces and orientation Duke Math. J. , 149: (3): 461507 2009 ISSN: 00127094 DOI: 10.1215/001270942009043[ 2] Daniel Huybrechts
Chow groups of K3 surfaces and spherical objects J. Eur. Math. Soc. (JEMS) , 12: (6): 15331551 2010 ISSN: 14359855 DOI: 10.4171/JEMS/240[ 3] D. Huybrechts
Curves and cycles on K3 surfaces With an appendix by C. Voisin Algebr. Geom. , 1: (1): 69106 2014 ISSN: 22142584 DOI: 10.14231/AG2014005[ 4] Daniel Huybrechts, Richard P. Thomas
Deformationobstruction theory for complexes via Atiyah and KodairaSpencer classes Math. Ann. , 346: (3): 545569 2010 ISSN: 00255831 DOI: 10.1007/s0020800903976[ 5] Daniel Huybrechts, Manfred Lehn
The geometry of moduli spaces of sheaves Cambridge Mathematical Library : xviii+325 Publisher: Cambridge University Press, Cambridge 2010 ISBN: 9780521134200 DOI: 10.1017/CBO9780511711985[ 6] D. Huybrechts
FourierMukai transforms in algebraic geometry Oxford Mathematical Monographs : viii+307 Publisher: The Clarendon Press, Oxford University Press, Oxford 2006 ISBN: 9780199296866; 0199296863 DOI: 10.1093/acprof:oso/9780199296866.001.0001[ 7] Daniel Huybrechts, Richard Thomas
\Bbb Pobjects and autoequivalences of derived categories Math. Res. Lett. , 13: (1): 8798 2006 ISSN: 10732780 DOI: 10.4310/MRL.2006.v13.n1.a7[ 8] Daniel Huybrechts
Compact hyperKähler manifolds: basic results Invent. Math. , 135: (1): 63113 1999 ISSN: 00209910 DOI: 10.1007/s002220050280[ 9] Daniel Huybrechts, Emanuele Macrì, Paolo Stellari
Stability conditions for generic K3 categories Compos. Math. , 144: (1): 134162 2008 ISSN: 0010437X DOI: 10.1112/S0010437X07003065[ 10] Daniel Huybrechts
Lectures on K3 surfaces Cambridge Studies in Advanced Mathematics, 158 : 496 Publisher: Cambridge University Press, Cambridge 2016 ISBN: 9781107153042



• Bulletin et Mémoires de la SMF (2005  2013)
• Kyoto Journal of Mathematics (since 2010)
• Crelle Journal (since 2012)
• Inventiones mathematicae (since 2014)


2008  AlgebroGeometric Derived Categories and Applications, Institute for Advanced Study, Princeton, NJ, USA  2009  Classical Algebraic geometry today, Mathematical Sciences Research Institute (MSRI), Berkeley, CA, USA  2010  ICM, Hyderabad, India  2011  Moduli spaces and moduli stacks, Columbia University, New York, USA  2011  Spring lectures in algebraic geometry, Ann Arbor, MI, USA  2015  Perspectives on Complex Algebraic Geometry, Columbia University, New York, USA  2015  Schrödinger Lecture, ESI, Vienna, Austria  2016  Homological Mirror Symmetry, Methods and Structures, IAS, Princeton, NJ, USA  2016  Generalised Geometry and Noncommutative Algebra, Clay Mathematics Institute, Oxford, England, UK 


2008  University of Heidelberg 


Vladimir Lazic (2015), now Professor in Universität des Saarlandes


Marc NieperWißkirchen (2002): “Characteristic Classes and RozanskyWitten Invariants of Compact Hyperkähler Manifolds”,
now Professor, University of Augsburg
Sven Meinhardt (2008): “Stability conditions on derived categories”,
now Research Assistant, University of Sheffield, England, UK
Michael Kemeny (2015): “Stable maps and singular curves on K3 surfaces”,
now Szegö Assistant Professor, Stanford University, CA, USA
Stefan Schreieder (2015): “Construction problems in algebraic geometry and the Schottky problem”,
now Postdoc, University of Bonn
Ulrike Riess (2016): “On irreducible symplectic varieties: Chow rings and base loci of certain line bundles”


 Master theses: 17, currently 2
 Diplom theses: 12
 PhD theses: 12, currently 1


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