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| 1985--1992 | Studies of mathematics, HU Berlin, MPI Bonn | | 1992 | PhD, HU Berlin | | 1993--1994 | Postdoc, Max Planck Institute Bonn | | 1994--1995 | Postdoc, Institute for Advanced Study Princeton | | 1995--1996 | Postdoc, Max Planck Institute Bonn | | 1996--1997 | Assistant (C1), University-GH Essen | | 1998 | Habilitation, University-GH Essen | | 1997--1998 | Marie-Curie fellow, ENS Paris | | 1998--2002 | Professor (C3), Cologne University | | 2002--2005 | Professor, University Denis Diderot, Paris 7 | | 2005-- | Professor (C4/W3), Bonn |
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Algebraic geometry aims at classifying geometries that can be described in terms of polynomials. I am interested in special geometries with a rich algebraic, analytic and arithmetic structure. 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 (eg. Tate, Hodge, Bloch-Beilinson).
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[ 1] Daniel Huybrechts, Emanuele Macri, Paolo Stellari
Derived equivalences of K3 surfaces and orientation
Duke Math. J. , 149: (3): 461--507
2009
ISSN: 0012-7094
DOI: 10.1215/00127094-2009-043[ 2] Daniel Huybrechts
Chow groups of K3 surfaces and spherical objects
J. Eur. Math. Soc. (JEMS) , 12: (6): 1533--1551
2010
ISSN: 1435-9855
DOI: 10.4171/JEMS/240[ 3] Daniel Huybrechts, Emanuele Macri, Paolo Stellari
Formal deformations and their categorical general fibre
Comment. Math. Helv. , 86: (1): 41--71
2011
ISSN: 0010-2571[ 4] 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[ 5] Daniel Huybrechts, Richard P. Thomas
Deformation-obstruction theory for complexes via Atiyah and Kodaira-Spencer classes
Math. Ann. , 346: (3): 545--569
2010
ISSN: 0025-5831
DOI: 10.1007/s00208-009-0397-6[ 6] Daniel Huybrechts, Emanuele Macri, Paolo Stellari
Stability conditions for generic K3 categories
Compos. Math. , 144: (1): 134--162
2008
ISSN: 0010-437X
DOI: 10.1112/S0010437X07003065[ 7] Daniel Huybrechts
Derived and abelian equivalence of K3 surfaces
J. Algebraic Geom. , 17: (2): 375--400
2008
ISSN: 1056-3911[ 8] Daniel Huybrechts, Paolo Stellari
Proof of C\u ald\u araru's conjecture. Appendix: ``Moduli spaces of twisted sheaves on a projective variety" [in Moduli spaces and arithmetic geometry, 1--30, Math. Soc. Japan, Tokyo, 2006] by K. Yoshioka
Moduli spaces and arithmetic geometry
of Adv. Stud. Pure Math. : 31--42
Publisher: Math. Soc. Japan, Tokyo
2006[ 9] 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[ 10] Daniel Huybrechts
Compact hyper-Kähler manifolds: basic results
Invent. Math. , 135: (1): 63--113
1999
ISSN: 0020-9910
DOI: 10.1007/s002220050280 |
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| 2010 | ICM, Hyderabad | | 2009 | Classical Algebraic geometry today, MSRI Berkeley | | 2008 | Algebro-Geometric Derived Categories and Applications, IAS Princeton | | 2011 | Moduli spaces and moduli stacks, Columbia NYC | | 2011 | Spring lectures in algebraic geometry, Ann Arbor Michigan |
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Bulletin et Mémoires de la SMF, (2005--); Kyoto Journal of Mathematics, (2010--)
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Local coordinator of the Collaborative Research Center SFB/TR 45, (2006--)
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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 Calabi-Yau varieties of dimension two is an example and one of the main open problems in the area. | 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]. |
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M. Nieper-Wisskirchen 2002, now Professor (W3) Augsburg; D. Ploog 2005, now Postdoc Hannover; S. Meinhardt 2008, now Assistant Bonn; P. Sosna 2010, now DFG Postdoc, Milano, H. Hartmann (2011), now Postdoc Oxford.
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- Bachelor theses: 1, currently 1
- Master theses currently: 3
- Diplom theses: 12, currently 2
- PhD theses: 10, currently 1
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