Profile
Profile

Prof. Dr. Gerd Faltings

E-mail: faltings(at)mpim-bonn.mpg.de
Phone: +49 228 402 229
Homepage: http://www.mpim-bonn.mpg.de/node/102
Location: Max-Planck-Institute for Mathematics
Institute: Max-Planck-Institute for Mathematics
Research Areas: Former Research Area E (Leader)
Research Area DE
Former Research Area D
Former Research Area F
Birthdate: 28.Jul 1954
Mathscinet-Number: 65080

Academic Career

1978

PhD, University of Münster

1978 - 1979

Visitor, Harvard University, Cambridge, MA, USA

1979 - 1982

Assistant Professor, University of Münster

1981

Habilitation, University of Münster

1982 - 1984

Professor, University of Wuppertal

1985 - 1994

Professor, Princeton University, NJ, USA

Since 1994

Scientific Member, Max Planck Institute for Mathematics, Bonn

Since 1995

Director, Max Planck Institute for Mathematics, Bonn

Research Profile

Diophantine equations

Arakelov theory

Abelian varieties

Moduli spaces of vectorbundles

p-adic Hodge theory

Research Projects and Activities

I do research on whatever I find interesting.

Contribution to Research Areas

Former Research Area D
I have found a crystalline version of nonabelian p-adic Hodge theory for ‘small’ representations. Motivic cohomology and Diophantine equations: Kim has introduced a new method into Diophantine approximation. The paper [1] constructs a motivic logarithm for arbitrary curves. An open question is the construction of such an object in algebraic K-theory, as well as a good definition of torsors over it.
Former Research Area E
Using the Hitchin fibration, the dimension of global sections for line-bundles of central charge one on moduli spaces of G-bundles has been computed in [2]. In [3], I determined the image of the Rapoport-Zink period map in the case of GL(n), confirming conjectures of Hartl and Rapoport-Zink.
Research Area DE
I extended the definition of the category MF to the semistable case. As an application I could construct semistable models for certain Shimura-varieties defined by Spin-groups with level-structure, see [4]. I also obtained estimates for the norms of Weierstrass-sections on curves.

Selected Publications

[1] Gerd Faltings
Mathematics around Kim's new proof of Siegel's theorem
Diophantine geometry
of CRM Series : 173--188
Publisher: Ed. Norm., Pisa
2007
[2] Gerd Faltings
Theta functions on moduli spaces of G-bundles
J. Algebraic Geom. , 18: (2): 309--369
2009
ISSN: 1056-3911
DOI: 10.1090/S1056-3911-08-00499-2
[3] Gerd Faltings
Coverings of p-adic period domains
J. Reine Angew. Math. , 643: : 111--139
2010
ISSN: 0075-4102
DOI: 10.1515/CRELLE.2010.046
[4] G. Faltings
The category {\CalMF} in the semistable case
Izv. Ross. Akad. Nauk Ser. Mat. , 80: (5): 41--60
2016
ISSN: 1607-0046
DOI: 10.4213/im8490
[5] Gerd Faltings
Algebraic loop groups and moduli spaces of bundles
J. Eur. Math. Soc. (JEMS) , 5: (1): 41--68
2003
ISSN: 1435-9855
DOI: 10.1007/s10097-002-0045-x
[6] Gerd Faltings
Almost étale extensions
Cohomologies p-adiques et applications arithmétiques, II
Astérisque (279): 185--270
2002
ISSN: 0303-1179
[7] Gerd Faltings
A relation between two moduli spaces studied by V. G. Drinfeld
Algebraic number theory and algebraic geometry
of Contemp. Math. : 115--129
Publisher: Amer. Math. Soc., Providence, RI
2002
DOI: 10.1090/conm/300/05145
[8] Gerd Faltings
A proof for the Verlinde formula
J. Algebraic Geom.
, 3: (2): 347--374
1994
ISSN: 1056-3911
[9] Gerd Faltings
Stable G-bundles and projective connections
J. Algebraic Geom. , 2: (3): 507--568
1993
ISSN: 1056-3911
[10] Gerd Faltings
Diophantine approximation on abelian varieties
Ann. of Math. (2) , 133: (3): 549--576
1991
ISSN: 0003-486X
DOI: 10.2307/2944319
[11] Gerd Faltings, Ching-Li Chai
Degeneration of abelian varieties
With an appendix by David Mumford
of Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)] : xii+316
Publisher: Springer-Verlag, Berlin
1990
ISBN: 3-540-52015-5
DOI: 10.1007/978-3-662-02632-8
[12] Gerd Faltings
Calculus on arithmetic surfaces
Ann. of Math. (2) , 119: (2): 387--424
1984
ISSN: 0003-486X
DOI: 10.2307/2007043

Publication List

Editorships

• Compositio Mathematica (Associate Editor)
• Journal of Algebraic Geometry (Editorial Board Member)

Awards

1984

Dannie Heinemann Preis

1986

Fields Medal

1988

Guggenheim Fellowship

1996

Leibniz Prize

2008

Karl Georg Christian von Staudt Prize

2009

Bundesverdienstkreuz I. Klasse (Officer's Cross of the Order of Merit of the Federal Republic of Germany)

2010

Gumin-Preis

2014

King Faisal International Prize

2015

Shaw Prize

2017

Cantor medal of the German Mathematical Society (Deutsche Mathematiker-Vereinigung, DMV)

Selected Invited Lectures

1986

ICM, Plenary Address, Berkeley, CA, USA

1994

ICM, Invited Talk, Zürich, Switzerland

Selected PhD students

Michael Larsen (1988): “Unitary Groups and L-Adic Representations”,
now Professor, Indiana University, IN, USA

Wieslawa Niziol (1991): “On A Cohomological Functor Associated To Crystalline Representations”,
now Directrice de recherche, CNRS, UMPA, École Normale Supérieure de Lyon, France

Shinichi Mochizuki (1992): “The Geometry of the Compactification of the Hurwitz Scheme”,
now Professor, Kyoto University, Japan

Tyler Jarvis (1994): “Compactification Of The Moduli Space Of Generalized Spin Curves”,
now Professor, Brigham Young University, UT, USA

Christian Liedtke (2004): “On Fundamental Groups of Galois Closures of Generic Projections”,
now Professor, TU Munich

Majid Hadian (2010): “Motivic Fundamental Groups and Integral Points”,
now Scott-Russell-Johnson Research Assistant Professor, California Institute of Technology, Pasadena, CA, USA

Supervised Theses

  • PhD theses: 1, currently 1
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