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
Date of birth: 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.

DFG Cluster of Excellence “Hausdorff Center for Mathematics”,
Principal Investigator and member of the Board of Directors

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
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
DOI: 10.1515/CRELLE.2010.046
[4] G. Faltings
The category ℳℱ in the semistable case
Izv. Ross. Akad. Nauk Ser. Mat. , 80: (5): 41--60
2016
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
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
[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
[9] Gerd Faltings
Stable G-bundles and projective connections
J. Algebraic Geom. , 2: (3): 507--568
1993
[10] Gerd Faltings
Diophantine approximation on abelian varieties
Ann. of Math. (2) , 133: (3): 549--576
1991
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
DOI: 10.2307/2007043

Publication List

Editorships

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

Awards

1984

Dannie Heinemann Prize

1986

Fields Medal

1988

Guggenheim Fellowship

1991

Member of the Göttingen Academy of Sciences and Humanities

1992

Member of the German National Academy of Sciences Leopoldina

1996

Leibniz Prize

1999

Member of the Berlin-Brandenburg Academy of Sciences and Humanities

1999

Member of the North Rhine-Westphalian Academy of Sciences, Humanities and the Arts

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

Heinz Gumin Prize for Mathematics

2012

Honorary Doctorate, University of Münster

2014

King Faisal International Prize

2014

Member of the Academia Europaea

2015

Shaw Prize

2016

Foreign Associate of the Royal Society

2017

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

Selected Invited Lectures

1986

International Congress of Mathematicians, plenary address, Berkeley, CA, USA

1994

International Congress of Mathematicians, invited talk, Zürich, Switzerland

2014

Heidelberg Laureate Forum

2015

Harald Bohr Lecture, Copenhagen, Denmark

2015

Chinese Academy of Sciences, Peking, China

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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