Welcome to the web page of the Seminar Series of the Number Theory Group at the University of Pisa and Scuola Normale Superiore.
Upcoming Seminars
List of all Seminars
2025
On the Tamagawa number conjecture for motives of modular forms – Matteo Longo (Università di Padova)
mercoledì 4 giu 2025 2:00 PM — 3:00 PM Aula Riunioni (Department of Mathematics) Seminars, Number Theory Seminar
I would like to present a work in collaboration with Stefano Vigni and Maria Rosaria Pati, in which we study the Tamagawa number conjecture, formulated by Bloch-Kato, in the case of motives attache...
On the torsion and rational points of some families of curves – Evelina Viada (Georg-August-Universität Göttingen)
giovedì 22 mag 2025 1:00 PM — 2:00 PM Aula Seminari (Department of Mathematics) Seminars, Number Theory Seminar
I will present an overview of some explicit methods in the context of the Manin-Mumford and Mordell Conjecture. I will give several new specific examples (obtained with R. Pengo) of curves whos...
Isogeny decompositions and the Tate--Shafarevich group modulo squares – Alexandros Konstantinou (University of Cyprus)
mercoledì 2 apr 2025 2:15 PM — 3:15 PM Aula Riunioni (Department of Mathematics) Seminars, Number Theory Seminar
We present a method for decomposing abelian varieties up to isogeny using group actions. As an application, we show that given a square-free natural number n, there exists an abelian variety with f...
2024
Bogomolov property for some Galois representations – Lea Terracini (Università di Torino)
giovedì 7 nov 2024 4:30 PM — 5:30 PM Aula Seminari (Department of Mathematics) Seminars, Number Theory Seminar
In 2013 P. Habegger proved the Bogomolov property for the field generated over by the torsion points of a rational elliptic curve. We explore the possibility of applying the same strat...
The Grunwald Problem for solvable groups – Julian Demeio (University of Bath)
mercoledì 4 set 2024 2:00 PM — 3:00 PM Aula Magna (Department of Mathematics) Seminars, Number Theory Seminar
Let be a number field. The Grunwald problem for a finite group (scheme) G/K asks what is the closure of the image of . For a general , there is a B...
Some applications of the profinite completion – Ignazio Longhi (Università di Torino)
martedì 21 mag 2024 2:30 PM — 3:30 PM Aula Seminari (Department of Mathematics) Seminars, Number Theory Seminar
Many estimates for the "size" of a subset of the natural numbers (a "size" usually expressed by some notion of density) come from "local" conditions, like reduction modulo prime powers. The idea c...
On perfect powers that are sums of cubes of a nine term arithmetic progression – Nirvana Coppola (Université de Strasbourg)
martedì 9 apr 2024 2:00 PM — 3:00 PM Aula Seminari (Department of Mathematics) Seminars, Number Theory Seminar
Solving Diophantine equations has always been one of the most fascinating problems in number theory, since even if it can be easily formulated, it almost always requires advanced techniques. In thi...
High vanishing of twisted L-functions – Matthew Bisatt (Università di Pisa)
giovedì 14 mar 2024 8:00 AM — 9:00 AM Aula Magna (Department of Mathematics) Seminars, Number Theory Seminar
The Birch—Swinnerton-Dyer conjecture famously connects the rank of an elliptic curve to the vanishing of its L-function, and one can generalise this conjecture to include Artin twists. I will illus...
Heights of CM jacobians of curves with good reduction everywhere – Samuel Le Fourn (Université Grenoble Alpes)
martedì 5 mar 2024 3:00 PM — 4:00 PM Aula Seminari (Department of Mathematics) Seminars, Number Theory Seminar
The problem of singular moduli (j-invariants of CM elliptic curves) admits several generalisations to higher dimension, for example the following one. For a real quadratic field F and K/F a CM exte...
The modular support problem – Francesco Campagna (Université Clermont Auvergne)
martedì 27 feb 2024 3:00 PM — 4:00 PM Aula Seminari (Department of Mathematics) Seminars, Number Theory Seminar
In 1988, during a conference in Banff, Erdős posed the following question: if two positive integers a and b have the property that for all natural numbers n the set of primes dividing a^n-1 is equa...
2023
Triviality of the Hecke action on ordinary Drinfeld cuspforms of level $\Gamma_1(t^n)$ – Shin Hattori (Tokyo City University)
venerdì 15 dic 2023 11:00 AM — 12:00 PM Aula Seminari (Department of Mathematics) Seminars, Number Theory Seminar
Let be a rational prime, a -power integer and a non-constant irreducible polynomial in . The notion of Drinfeld modular form is an analogue over $\mathbb{F}_q(t)...
Galois representations attached to elliptic curves and Serre’s uniformity question – Lorenzo Furio (Università di Pisa)
martedì 27 giu 2023 11:00 AM — 12:00 PM Aula Seminari (Department of Mathematics) Seminars, Number Theory Seminar
The study of Galois representations attached to elliptic curves is a very fruitful branch of number theory, leading to the solution of very difficult problems, such as Fermat’s Last Theorem. Given ...
2022
Some remarks on the component group of the Sato-Tate group – Victoria Cantoral Farfán (Georg-August-Universität Göttingen)
giovedì 1 dic 2022 11:00 AM — 12:00 PM Aula Magna (Department of Mathematics) Seminars, Number Theory Seminar
The famous Sato-Tate conjecture for elliptic curves defined over a number field (without complex multiplication) predicts the equidistribution of Frobenius traces with respect to the Haar measure o...
The degree of Kummer extensions of number fields – Flavio Perissinotto (University of Luxembourg)
venerdì 25 nov 2022 9:00 AM — 10:00 AM Aula Seminari (Department of Mathematics) Seminars, Number Theory Seminar
Under the Generalized Riemann Hypothesis, densities of prime ideals of a number field for which a given subgroup of has a certain cardinality modulo those primes can be computed,...
2021
Explicit integral Galois module structure of weakly ramified extensions of local fields – Henri Johnston (University of Exeter)
giovedì 22 apr 2021 2:00 PM — 4:00 PM Online Seminars, Number Theory Seminar
Let be a finite Galois extension of complete local fields with finite residue fields and let . Let and be the first and second ramification groups. Thus $L...
2020
2019
Divisibility questions in commutative algebraic groups – Laura Paladino (Università di Pisa)
martedì 7 mag 2019 3:00 PM — 4:00 PM Aula Seminari (Department of Mathematics) Seminars, Number Theory Seminar
Venue
Sala Seminari (Dip. Matematica).