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Analytic geometry

NUMBER THEORY

February 3, 2021      3:00 pm
Speaker: Peter Scholze - University of Bonn

We will outline a definition of analytic spaces that relates to complex- or rigid-analytic varieties in the same way that schemes relate to algebraic varieties over a field. Joint with...
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Arithmetic dynamics of random polynomials

NUMBER THEORY

January 27, 2021      3:00 pm
Speaker: Niki Myrto Mavraki - Harvard University

We begin with an introduction to arithmetic dynamics and heights attached to rational maps. We then introduce a dynamical version of Lang's conjecture concerning the minimal canonical height of non-torsion...
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Hermite interpolation and counting number fields

NUMBER THEORY

December 9, 2020      3:00 pm
Speaker: Jean-Marc Couveignes - University of Bordeaux

There are several ways to specify a number field. One can provide the minimal polynomial of a primitive element, the multiplication table of a $\bf Q$-basis, the traces of a...
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Eichler-Shimura relations for Hodge type Shimura varieties

NUMBER THEORY

November 18, 2020      3:00 pm
Speaker: Si Ying Lee - Harvard University

The well-known classical Eichler-Shimura relation for modular curves asserts that the Hecke operator $T_p$ is equal, as an algebraic correspondence over the special fiber, to the sum of Frobenius and...
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Frobenius and the Hodge numbers of the generic fiber

NUMBER THEORY

November 11, 2020      3:00 pm
Speaker: Zijian Yao - CNRS/Harvard

For a smooth proper (formal) scheme X defined over a valuation ring of mixed characteristic, the crystalline cohomology H of its special fiber has the structure of an F-crystal, to...
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A geometric approach to the Cohen-Lenstra heuristics

NUMBER THEORY

November 4, 2020      3:00 pm
Speaker: Aaron Landesman - Stanford University

For any positive integer $n$, we explain why the total number of order $n$ elements in class groups of quadratic fields of discriminant having absolute value at most $X$ is...
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Supersingular representations of p-adic reductive groups

NUMBER THEORY

October 28, 2020      3:00 pm
Speaker: Karol Koziol - University of Michigan

The local Langlands conjectures predict that (packets of) irreducible complex representations of p-adic reductive groups (such as GL_n(Q_p), GSp_2n(Q_p), etc.) should be parametrized by certain representations of the Weil-Deligne group. ...
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