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| 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), University-GH Essen | | 1997 - 1998 | Marie-Curie Fellow, ENS Paris, France | | 1998 | Habilitation, University-GH 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 |
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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, Bloch-Beilinson). 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 auto-equivalences 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 auto-equivalences 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.
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DFG Collaborative Research Center SFB/TR 45 “Periods, moduli spaces and arithmetic of algebraic varieties”
Local coordinator, since 2006
Oberwolfach Workshops on “Algebraic Geometry”
Organizer, 2015, 2017
Conference “Panorama of Mathematics” (Bonn),
Organizer, 2015
DFG Cluster of Excellence “Hausdorff Center for Mathematics”
Principal investigator
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[ 1] D. Huybrechts
Curves and cycles on K3 surfaces
With an appendix by C. Voisin
Algebr. Geom. , 1: (1): 69--106
2014
DOI: 10.14231/AG-2014-005[ 2] Daniel Huybrechts
Chow groups of K3 surfaces and spherical objects
J. Eur. Math. Soc. (JEMS) , 12: (6): 1533--1551
2010
DOI: 10.4171/JEMS/240[ 3] Daniel Huybrechts, Richard P. Thomas
Deformation-obstruction theory for complexes via Atiyah and Kodaira-Spencer classes
Math. Ann. , 346: (3): 545--569
2010
DOI: 10.1007/s00208-009-0397-6[ 4] Daniel Huybrechts, Emanuele Macr\`\i, Paolo Stellari
Derived equivalences of K3 surfaces and orientation
Duke Math. J. , 149: (3): 461--507
2009
DOI: 10.1215/00127094-2009-043[ 5] Daniel Huybrechts, Manfred Lehn
The geometry of moduli spaces of sheaves
Cambridge Mathematical Library : xviii+325
Publisher: Cambridge University Press, Cambridge
2010
ISBN: 978-0-521-13420-0
DOI: 10.1017/CBO9780511711985[ 6] D. Huybrechts
Fourier-Mukai transforms in algebraic geometry
Oxford Mathematical Monographs : viii+307
Publisher: The Clarendon Press, Oxford University Press, Oxford
2006
ISBN: 978-0-19-929686-6; 0-19-929686-3
DOI: 10.1093/acprof:oso/9780199296866.001.0001[ 7] Daniel Huybrechts, Richard Thomas
\Bbb P-objects and autoequivalences of derived categories
Math. Res. Lett. , 13: (1): 87--98
2006
DOI: 10.4310/MRL.2006.v13.n1.a7[ 8] Daniel Huybrechts
Compact hyper-Kähler manifolds: basic results
Invent. Math. , 135: (1): 63--113
1999
DOI: 10.1007/s002220050280[ 9] Daniel Huybrechts, Emanuele Macr\`\i, Paolo Stellari
Stability conditions for generic K3 categories
Compos. Math. , 144: (1): 134--162
2008
DOI: 10.1112/S0010437X07003065[ 10] Daniel Huybrechts
Lectures on K3 surfaces
of Cambridge Studies in Advanced Mathematics : xi+485
Publisher: Cambridge University Press, Cambridge
2016
ISBN: 978-1-107-15304-2
DOI: 10.1017/CBO9781316594193 |
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• Bulletin et Mémoires de la SMF (2005 - 2013)
• Kyoto Journal of Mathematics (since 2010)
• Crelle Journal (since 2012)
• Inventiones mathematicae (since 2014)
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| 2017 | Member of the Academia Europaea | | 2020 - 2026 | ERC Synergy Grant |
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| 2008 | Algebro-Geometric 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 | International Congress of Mathematicians, 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 | | 2020 | DMV Annual Meeting, Plenary Talk |
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Vladimir Lazic (2015), now Professor, Saarland University
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Marc Nieper-Wißkirchen (2002): “Characteristic Classes and Rozansky-Witten 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 Assistant Professor, University of Wisconsin–Madison, Madison, Wisconsin, United States
Stefan Schreieder (2015): “Construction problems in algebraic geometry and the Schottky problem”,
now Professor, Hannover
Ulrike Riess (2016): “On irreducible symplectic varieties: Chow rings and base loci of certain line bundles”, now Junior Fellow ITS ETH Zurich
Emma Brakkee (2019): “Moduli spaces of K3 surfaces and cubic fourfolds”, now Postdoc in Amsterdam
David Ploog (2005): “Groups of autoequivalences of derived categories of smooth projective varieties”, now professor in Stavanger
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- Master theses: 27, currently 2
- Diplom theses: 12
- PhD theses: 14, currently 4
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