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 arieties
• 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

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
[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] Gerd Faltings
Néron models and formal groups
Milan J. Math. , 76: : 93--123
2008
ISSN: 1424-9286
DOI: 10.1007/s00032-008-0086-z
[5] Gerd Faltings
Thetafunktionen auf Modulräumen von Vektorbündeln
Jahresber. Deutsch. Math.-Verein. , 110: (1): 3--17
2008
ISSN: 0012-0456
[6] Gerd Faltings
A p-adic Simpson correspondence
Adv. Math. , 198: (2): 847--862
2005
ISSN: 0001-8708
DOI: 10.1016/j.aim.2005.05.026
[7] 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
[8] 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
[9] Gerd Faltings
p-adic Hodge theory
J. Amer. Math. Soc. , 1: (1): 255--299
1988
ISSN: 0894-0347
DOI: 10.2307/1990970
[10] G. Faltings
Endlichkeitssätze für abelsche Varietäten über Zahlkörpern
Invent. Math. , 73: (3): 349--366
1983
ISSN: 0020-9910
DOI: 10.1007/BF01388432

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 (Order of Merit of the Federal Republic of Germany)

2010

Gumin-Preis

2014

King Faisal International Prize

2015

Shaw Prize

Selected Invited Lectures

1986

ICM Plenary Address

1994

ICM Invited Talk

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 (Caltech), Pasadena, CA, USA
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