Daniel Huybrechts - Hausdorff Center for Mathematics

Daniel Huybrechts
Date of birth: 09 Nov 1966
Academic career
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
Offers
2008 Heidelberg
Invited Lectures
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
Research Projects and Activities
Local coordinator of the Collaborative Research Center SFB/TR 45, (2006–)
Research profile
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).
Editorships
Bulletin et Mémoires de la SMF, (2005–); Kyoto Journal of Mathematics, (2010–)
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 [HMS09] 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.
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 [Huy10].
Research Area DE
Supervised theses
Bachelor theses: 1, currently 1
Master theses currently: 3
Diplom theses: 12, currently 2
PhD theses: 10, currently 1
Selected PhD students
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.
Selected publications
[HL10] HUYBRECHTS, Daniel ; LEHN, Manfred: The geometry of moduli spaces of sheaves. Second. Cambridge :
Cambridge University Press, 2010 (Cambridge Mathematical Library). – xviii+325 S. – ISBN 978–0–521–
13420–0
[HMS08] HUYBRECHTS, Daniel ; MACRI, Emanuele ; STELLARI, Paolo: Stability conditions for generic K3 categories.
In: Compos. Math. 144 (2008), Nr. 1, S. 134–162. – ISSN 0010–437X
[HMS09] HUYBRECHTS, Daniel ; MACRI, Emanuele ; STELLARI, Paolo: Derived equivalences of K3 surfaces and
orientation. In: Duke Math. J. 149 (2009), Nr. 3, S. 461–507. – ISSN 0012–7094
[HMS11] HUYBRECHTS, Daniel ; MACRI, Emanuele ; STELLARI, Paolo: Formal deformations and their categorical
general fibre. In: Comment. Math. Helv. 86 (2011), Nr. 1, S. 41–71. – ISSN 0010–2571
[HS06] HUYBRECHTS, Daniel ; STELLARI, Paolo: Proof of Căldăraru’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. In: Moduli spaces and arithmetic geometry Bd. 45. Tokyo : Math.
Soc. Japan, 2006, S. 31–42
[HT10] HUYBRECHTS, Daniel ; THOMAS, Richard P.: Deformation-obstruction theory for complexes via Atiyah and
Kodaira-Spencer classes. In: Math. Ann. 346 (2010), Nr. 3, S. 545–569. – ISSN 0025–5831
[Huy99] HUYBRECHTS, Daniel: Compact hyper-Kähler manifolds: basic results. In: Invent. Math. 135 (1999), Nr. 1,
S. 63–113. – ISSN 0020–9910
[Huy06] HUYBRECHTS, D.: Fourier-Mukai transforms in algebraic geometry. Oxford : The Clarendon Press Oxford
University Press, 2006 (Oxford Mathematical Monographs). – viii+307 S. – ISBN 978–0–19–929686–6;
0–19–929686–3
[Huy08] HUYBRECHTS, Daniel: Derived and abelian equivalence of K3 surfaces. In: J. Algebraic Geom. 17 (2008),
Nr. 2, S. 375–400. – ISSN 1056–3911
[Huy10] HUYBRECHTS, Daniel: Chow groups of K3 surfaces and spherical objects. In: J. Eur. Math. Soc. (JEMS)
12 (2010), Nr. 6, S. 1533–1551. – ISSN 1435–9855