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| 2010 | Master, University of Bonn | | 2012 | Dr. rer. nat., University of Bonn | | Since 2012 | Hausdorff Chair (W3), University of Bonn | | Since 2018 | Director, Max Planck Institute for Mathematics, Bonn |
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My research is at the intersection of number theory and algebraic geometry, and deals with the basic questions and structures that underly our modern understanding of diophantine equations. This concerns on the one hand the Langlands program, which connects objects from arithmetic geometry, such as elliptic curves over number fields, with analytic or topological objects, such as modular forms or the cohomology of hyperbolic manifolds. On the other hand, this concerns the cohomological invariants attached to arithmetic varieties themselves, which forms the subject of Hodge theory, or more particularly p-adic Hodge theory.
My own contributions to these questions include the construction of Galois representations associated for example with torsion classes on hyperbolic 3-manifolds, and the development of a geometric framework underlying much of p-adic Hodge theory, in the form of perfectoid spaces. In the future, I plan to pursue these questions. In particular, building on perfectoid spaces, I want to transport some machinery from the geometric Langlands program to the case of p-adic fields, and I hope to use this to obtain new results on the local Langlands conjecture for general groups over p-adic fields. On the other hand, in work with Bhatt and Morrow, we found new cohomological invariants of arithmetic varieties, which lead to a surprising q-deformation of de Rham cohomology, which I plan to study further.
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[ 1] Bhargav Bhatt, Peter Scholze
Projectivity of the Witt vector affine Grassmannian
Invent. Math. , 209: (2): 329--423
2017
DOI: 10.1007/s00222-016-0710-4[ 2] Peter Scholze
On torsion in the cohomology of locally symmetric varieties
Ann. of Math. (2) , 182: (3): 945--1066
2015
DOI: 10.4007/annals.2015.182.3.3[ 3] Bhargav Bhatt, Peter Scholze
The pro-étale topology for schemes
Astérisque (369): 99--201
2015
ISBN: 978-2-85629-805-3[ 4] Peter Scholze, Jared Weinstein
Moduli of p-divisible groups
Camb. J. Math. , 1: (2): 145--237
2013
DOI: 10.4310/CJM.2013.v1.n2.a1[ 5] Peter Scholze
p-adic Hodge theory for rigid-analytic varieties
Forum Math. Pi , 1: : e1, 77
2013
DOI: 10.1017/fmp.2013.1[ 6] Peter Scholze
The local Langlands correspondence for GLn over p-adic fields
Invent. Math. , 192: (3): 663--715
2013
DOI: 10.1007/s00222-012-0420-5[ 7] Peter Scholze, Sug Woo Shin
On the cohomology of compact unitary group Shimura varieties at ramified split places
J. Amer. Math. Soc. , 26: (1): 261--294
2013
DOI: 10.1090/S0894-0347-2012-00752-8[ 9] Ana Caraiani, Peter Scholze
On the generic part of the cohomology of compact unitary Shimura varieties
Ann. of Math. (2) , 186: (3): 649--766
2017
DOI: 10.4007/annals.2017.186.3.1 |
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• Journal of the AMS
• Compositio Math
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| 2011 | Clay Research Fellow | | 2012 | Prix Peccot | | 2013 | SASTRA Ramanujan Prize | | 2014 | Clay Research Award | | 2015 | Frank Nelson Cole Prize in Algebra from the American Mathematical Society | | 2015 | Ostrowski Prize | | 2016 | Prix Fermat | | 2016 | Leibniz Prize | | 2016 | EMS Prize | | 2016 | Academy Prize of the Berlin-Brandenburg Academy of Sciences and Humanities | | 2017 | Ordinary Member of the Academy of Science and Literature, Mainz | | 2017 | Ordinary Member of the Berlin-Brandenburg Academy of Sciences and Humanities | | 2017 | Member of the Leopoldina (German National Academy of Sciences) | | 2018 | Fields Medal | | 2019 | \"Große Verdienstkreuz“ (Great Cross of Merit) |
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| 2012 | Clay Research Conference, University of Oxford, England, UK | | 2012 | Current Developments in Mathematics, Harvard University, Cambridge, MA, USA | | 2014 | International Congress of Mathematicians, Seoul, South Korea | | 2014 | Takagi Lectures, Tokyo, Japan | | 2015 | Clay Research Conference, Oxford, UK | | 2015 | Current Developments in Mathematics, Harvard University, Cambridge, MA, USA | | 2016 | Plenary talk, European Congress of Mathematics, Berlin | | 2018 | Plenary speaker, International Congress of Mathematicians, Rio de Janeiro, Brasil |
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