ARITHTMETIC GEOMETRY AND NUMBER THEORY
DEPARTMENT OF MATHEMATICS ⟡ UNIVERSITY OF MILAN
THE GROUP
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
- K-theory
- logarithmic and rigid analytic geometry
- analytic and algorithmic aspects of number theory
Faculty members
- Fabrizio Andreatta
- Federico Binda
- Luca Barbieri-Viale
- Carlo Mazza
- Giuseppe Molteni
- Amnon Neeman
- Marco Adamo Seveso
- Rodolfo Venerucci
- Alberto Vezzani
- Paul Arne Østvær
Post-docs and PhD students
- Raphaël Ruimy
- Kaixing Cao
- Xiaomin Chu
- Ruichuan Zhang
SEMINARS
We host a regular seminar, focusing in arithmetic geometry, number theory and motivic homotopy theory
15 November 2024 – 11.30-18.00 Aula 3
Giada Grossi (LAGA – Sorbonne Paris Nord)
Ben Heuer (Frankfurt)
Guido Kings (Regensburg)
Pol Van Hoften (VU Amsterdam)
Arithmetica Transalpina
More information on this page.
24 October 2024 – 11.00 Aula 10
Jarod Alper (Washington)
Colloquium: Seminari Enriques – Algebra e Geometria
Evolution of Moduli
In the rich landscape of algebraic varieties, moduli spaces stand out as some of the most enchanting varieties, capturing the imagination of algebraic geometers with their profound elegance and deep connections to other branches of mathematics. Moduli, the plural of modulus, is a term coined by Riemann to describe a space whose points afford an alternative description as certain classes of geometric objects. We will trace the origins of moduli spaces through the discoveries of Riemann, Hilbert, Grothendieck, Mumford, and Deligne, as a means to explain many of the fundamental concepts and results. We will then survey how the foundations of moduli theory have further evolved over the last 50 years.
PIZZA SEMINARS
“Pizza seminars”, funded by the ALGANT Consortium, offer a laid-back atmosphere in which students and young researchers can interact with the speaker and with each other…eating pizza!
14 November 2024 – 12.30 Aula Dottorato
Giada Grossi (LAGA – Sorbonne Paris Nord)
Iwasawa theory: from class groups to elliptic curves
Elliptic curves are a central object of study in Number Theory and describing the rational points on such curves is the subject of the Birch and Swinnerton-Dyer conjecture, one of the Clay Millenium Prize problems. One of the strategies that has been proven to be successful to tackle certain aspects of the conjecture is Iwasawa theory, which can be described as the study of both algebraic and analytic invariants of motives on p-adic towers. This theory has its roots in the work of Iwasawa in the 70s aiming to describe the class groups of cyclotomic fields, a central object in algebraic number theory. In this talk I will gently touch upon some of these topics, giving an overview of this area of research.