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| 1976 | These d'Etat, University of Paris-Sud, France | | 1976 - 1980 | Assistant Professor, HU Berlin | | 1982 - 1986 | Professor (C3), University of Heidelberg | | 1986 - 1989 | Professor (C3), University of Bonn | | 1989 - 1996 | Professor (C4), University of Wuppertal | | 1996 - 2003 | Professor (C4), University of Cologne | | 2003 - 2012 | Professor (C4), University of Bonn | | 2012 - 2017 | Professor (W3), University of Bonn | | Since 2017 | Retired | | Since 2017 | Visiting Professor University of Maryland |
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My aim is to use algebraic geometry to establish higher reciprocity laws, which serve as a bridge between the field of arithmetic and the theory of automorphic forms. I am interested in the theory of Shimura varieties and their local variants, in particular Rapoport-Zink spaces. I am particularly fascinated by the possibility of constructing through them interesting Galois representations, of algebraic cycles on them and of deformations. My current research focusses on the following topics. I am interested in constructing arithmetic models of Shimura varieties through the correct formulation of a moduli problem whose solution gives such a model. For Shimura varieties attached to unitary groups this naturally leads to the problem of defining a crystalline discriminant of polarized  -divisible groups. So far, I have succeeded in this in the case of even height (joint work with S. Kudla). I am also interested in understanding the structure of natural stratifications of the reduction modulo of integral models of Shimura varieties (the Newton stratification, the Ekedahl-Oort stratification, the Kottwitz-Rapoport stratification). In joint work with X. He, I have given an axiomatic framework for studying these questions. I am also interested in the Arithmetic Fundamental Lemma conjecture of W. Zhang. This conjecture predicts the intersection number of two arithmetic cycles of half-dimension on a Rapoport-Zink space. In joint work with U. Terstiege and W. Zhang I solved this conjecture in the minuscule case. Recently, in joint work with B. Smithling and W. Zhang, I extended the conjecture to ramified cases and solved it in a number of cases of small dimension.
In my future research I want to understand better the dependence of Rapoport-Zink spaces on the underlying group theory. My recent theorem with T. Zink on the Drinfeld moduli problem of -divisible groups deals in a special case related to  with the effect of changing the relevant cocharacter by a central cocharacter. In future work with S. Kudla and T. Zink, I want to treat the analogous problem for the group  and apply this to the -adic uniformization of certain Shimura curves. I want to understand the influence of exceptional isomorphisms between orthogonal groups and unitary groups on their associated Rapoport-Zink spaces (which exist, due to recent work of B. Howard/G. Pappas and of W. Kim). Another topic I want to explore is the relation between the conjectures of S. Kudla and myself on arithmetic divisors on Rapoport-Zink spaces and the conjectures of W. Zhang on arithmetic cycles of half-dimension. I want to understand the impact of Scholze's ideas and methods on the study of integral models of Shimura varieties. I also want to return to the theory of  -modules which I started with G. Pappas and make progress after the recent contributions of M. Emerton/T. Gee.
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[ 1] Michael Rapoport, Ulrich Terstiege, Wei Zhang
On the arithmetic fundamental lemma in the minuscule case
Compos. Math. , 149: (10): 1631--1666
2013
DOI: 10.1112/S0010437X13007239[ 2] Stephen Kudla, Michael Rapoport
Special cycles on unitary Shimura varieties I. Unramified local theory
Invent. Math. , 184: (3): 629--682
2011
DOI: 10.1007/s00222-010-0298-z[ 4] G. Pappas, M. Rapoport
Twisted loop groups and their affine flag varieties
With an appendix by T. Haines and Rapoport
Adv. Math. , 219: (1): 118--198
2008
DOI: 10.1016/j.aim.2008.04.006[ 5] Stephen S. Kudla, Michael Rapoport, Tonghai Yang
Modular forms and special cycles on Shimura curves
of Annals of Mathematics Studies : x+373
Publisher: Princeton University Press, Princeton, NJ
2006
ISBN: 978-0-691-12551-0; 0-691-12551-1
DOI: 10.1515/9781400837168[ 6] M. Rapoport, Th. Zink
Period spaces for p-divisible groups
of Annals of Mathematics Studies : xxii+324
Publisher: Princeton University Press, Princeton, NJ
1996
ISBN: 0-691-02782-X; 0-691-02781-1
DOI: 10.1515/9781400882601[ 7] G. Laumon, M. Rapoport, U. Stuhler
{D}-elliptic sheaves and the Langlands correspondence
Invent. Math. , 113: (2): 217--338
1993
DOI: 10.1007/BF01244308 |
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• Duke Math. J. (Associate Editor, 1995 - 2000)
• Ergebnisse der Mathematik, Springer Verlag (Editor, 1998 - 2003)
• International Mathematics Research Notices (Editor, 2003 - 2019)
• Algebra and Number Theory (Editor, since 2015)
• Epiga (Editor, 2016 - 2019)
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| 1991 | Akademiestipendium of the VW-foundation | | 1992 | Leibniz Prize | | 2000 | Prix Gay-Lussac/Humboldt of the French Ministry of Education | | 2003 | Member of the Leopoldina (German National Academy of Sciences) | | 2011 | Heinz Hopf Prize | | 2012 | Teaching prize of the University of Bonn | | 2013 | Staudt Prize | | 2013 | Member of the Academia Europaea |
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| 1993 | Distinguished Ordway visitor in Mathematics, University of Minnesota, Minneapolis, MN, USA | | 1994 | Invited speaker, International Congress of Mathematicians, Zürich, Switzerland | | 1995 | Invited plenary speaker at Annual Conference of DMV, Ulm | | 2001 | Distinguished Ordway visitor in Mathematics, University of Minnesota, Minneapolis, MN, USA | | 2011 | Heinz Hopf Lectures, ETH Zürich, Switzerland |
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Torsten Wedhorn (2005)
Ulrich Görtz (2006)
Sascha Orlik (2007)
Eva Viehmann (2011)
Eugen Hellmann (2016)
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Torsten Wedhorn (1998): “Ordinariness in Good Reductions of Schimura Varieties of PEL-Type”,
now Professor, TU Darmstadt
Sascha Orlik (1999): “Kohomologie von Periodenbereichen”,
now Professor, University of Wuppertal
Ulrich Görtz (2000): “On the flatness of certain Shimura varieties of PEL-Type”,
now Professor, University of Duisburg-Essen
Eva Viehmann (2005): “On affine Deligne-Lusztig varieties for  ”,
now Professor, TU Munich
Ulrich Terstiege (2009): “Intersections of Arithmetic Hirzebruch-Zagier Cycles”,
now Scientific Staff, RWTH Aachen
Eugen Hellmann (2011): “On arithmetic families of filtered f-modules and crystalline representations”,
now Professor, University of Münster
Peter Scholze (2012): “Perfectoid Spaces”,
now Professor (Hausdorff Chair), University of Bonn
Timo Richarz (2014): “On geometric Satake equivalences”,
now Scientific Staff, University of Duisburg-Essen
Daniel Kirch (2015): “Construction of a Rapoport-Zink space for split  in the ramified 2-adic case”,
now DFG-fellow, University of Paris VI, France
Andreas Mihatsch (2016): “Relative RZ-spaces and the Arithmetic Fundamental Lemma”
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- Master theses: 3
- Diplom theses: 19
- PhD theses: 14
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