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Arithmetic Geometry and Number Theory Group
Università degli Studi di Milano

This is the webpage of the Arithmetic Algebraic Geometry and Number Theory Group at Università degli Studi di Milano, Dipartimento di Matematica "Federigo Enriques".

The arithmetic geometry group at the University of Milan covers a broad range of topics including

  • \(p\)-adic Hodge theory;

  • algebraic cycles and \(L\)-functions;

  • arithmetic of modular and automorphic forms;

  • motivic homotopy theory;

  • logarithmic and rigid analytic geometry;

  • analytic and algorithmic aspects of number theory.

Members WS 2023/2024


Wataru Kai, Tohoku University

Joseph Leclere, Ecole Normale Supérieure de Paris

ALGANT Seminars

Hereafter are listed the upcoming talks of the ALGANT Seminar. These events are mainly aimed at (ALGANT) Master students and Ph.D. ones however, everyone is welcome to join.

Jan Vonk, Leiden University, 28/11/2023 (h12:00, Sala di Rappresentanza)

Title: Primes of the form \(x^2 + 27 y^2\)

Abstract: In this talk, we will discuss some classical problems of Fermat, Euler, and Gauss related to explicit class field theory in a hands-on way, and give an overview of the current state of knowledge, as well as open problems.

Arithmetic Geometry Seminar / Seminario di Geometria Aritmetica

Upcoming talks

Past talks

Hereafter are listed the upcoming and past talks of our Arithmetic Geometry Seminar.

Upcoming talks

Jan Vonk, Leiden University, 27/11/2023 (h14:00, Sala di Rappresentanza)

Title: \(p\)-adic height pairings of geodesics

Abstract: We will discuss recent progress on a tentative theory of differences of singular moduli for real quadratic fields, and in particular how it leads to the construction of a mysterious p-adic height pairing of real quadratic geodesics on modular curves.

Jie Lin, Universität Duisburg-Essen, 04/12/2023 (h14:15, Remote streaming in Sala di Rappresentanza)

Title: Period Relations for Arithmetic Automorphic Periods on Unitary Groups

Abstract: Given an automorphic representation of a unitary group, one can define an arithmetic automorphic period as the Petersson inner product of a deRham rational form. Here the deRham rational structure comes from the cohomology of Shimura varieties. When the form is holomorphic, the period can be related to special values of \(L\)-functions and is better understood. In this talk, we formulate a conjecture on relations among general arithmetic periods of representations in the same \(L\)-packet and explain a conditional proof.

Veronika Ertl, Institute of Mathematics Polish Academy of Sciences, 11/12/2023 (h14:00, Sala di Rappresentanza)

Title: Conjectures on \(L\)-functions for varieties over function fields and their relatisation

Abstract: (Joint work with T. Keller (Groningen) and Y. Qin (Regensburg)) We consider versions for smooth varieties \(X\) over finitely generated fields \(K\) in positive characteristic \(p\) of several conjectures that can be traced back to Tate, and study their interdependence. In particular, let \(A/K\) be an abelian variety. Assuming resolutions of singularities in positive characteristic, I will explain how to relate the BSD-rank conjecture for \(A\) to the finiteness of the \(p\)-primary part of the Tate-Shafarevich group of \(A\) using rigid cohomology. Furthermore, I will discuss what is needed for a generalisation.

Lennart Gehrmann, Universität Bielefeld, 22/01/2024 (h14:00, Aula Dottorato)

Title: TBA

Abstract: TBA

Daniel Kriz, Insitut de Mathématiques de Jussieu in Paris, 29/01/2024 (h14:00, Aula Dottorato)

Title: TBA

Abstract: TBA

(TBC) Antonio Cauchi, Concordia University, February 2024

Title: TBA

Abstract: TBA

(TBC) Michele Fornea, Centre de Recerca Matemàtica in Barcelona, February 2024

Title: TBA

Abstract: TBA