### Elliptic surfaces, bifurcations, and equidistribution

NUMBER THEORY

February 10, 2021 3:00 pm*Harvard University*

Zoom: https://harvard.zoom.us/j/99334398740 Password: The order of the permutation group on 9 elements.

Read more

NUMBER THEORY

February 10, 2021 3:00 pmSpeaker: Laura DeMarco - *Harvard University*

Zoom: https://harvard.zoom.us/j/99334398740 Password: The order of the permutation group on 9 elements.

Read more

NUMBER THEORY

February 3, 2021 3:00 pmSpeaker: 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...

Read more

NUMBER THEORY

January 27, 2021 3:00 pmSpeaker: 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...

Read more

NUMBER THEORY

December 9, 2020 3:00 pmSpeaker: 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...

Read more

NUMBER THEORY

December 2, 2020 3:00 pmSpeaker: Arul Shankar - *University of Toronto*

The Cohen--Lenstra--Martinet conjectures have been verified in only two cases. Davenport--Heilbronn compute the average size of the 3-torsion subgroups in the class group of quadratic fields and Bhargava computes the...

Read more

NUMBER THEORY

November 18, 2020 3:00 pmSpeaker: 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...

Read more

NUMBER THEORY

November 11, 2020 3:00 pmSpeaker: 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...

Read more

NUMBER THEORY

November 4, 2020 3:00 pmSpeaker: 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...

Read more

NUMBER THEORY

October 28, 2020 3:00 pmSpeaker: 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. ...

Read more

NUMBER THEORY

October 21, 2020 3:00 pmSpeaker: Elena Mantovan - *Caltech*

In this talk, we will discuss a geometric construction of p-adic analogues of Maass--Shimura differential operators on automorphic forms on Shimura varieties of PEL type A or C (that is,...

Read more