STNB2020(34th edition)
Dates
Monday 3 to Friday 7 February, 2020
Location
Room: B7. Math.Faculty, University of Barcelona, Gran Via de les Corts Catalanes 585, Barcelona, Catalonia. (${\scriptsize\text{with partial support of IMUB}}$)
Organising committee
Francesc Bars Cortina, Bernat Plans Berenguer and Artur Travesa
Themes
Galois Representations and Diophantine Equations
Co-ordinators: Luis Dieulefait and Nuno Freitas
- Introduction to the modular method
Nicolas Billerey - On the Asymptotic Fermat Conjecture
Samir Siksek - Fermat's Last Theorem and Wendt's Resultant
Alain Kraus - The Darmon program for the Generalized Fermat equation
Luis Dieulefait - A multi-Frey approach to Fermat equations of signature~$(7,7,p)$ combining Frey varieties of different dimensions.
Nuno Freitas - A modular approach to Fermat equations of signature $(p,p,5)$ using Frey hyperelliptic curves
Imin Chen
Valuations
Co-ordinators: Enric Nart
Talks and communications
Co-ordinators: Bernat Plans Berenguer
- Hecke eigenvalue fields and Maeda's conjecture
Samuele Anni - Periods of modular functions and diophantine approximation
Paloma Bengoechea - Potentially diagonalizable representations. A conjecture.
Iván Blanco Chacón - Wild Galois representations of hyperelliptic curves
Nirvana Coppola - Abelian varieties with everywhere good reduction over certain real quadratic fields
Lassina Dembélé - The Serre filtration on mod p Hilbert modular forms of level p
Fred Diamond - The level of pairs of polynomials
Alberto Fernandez Boix - Criptografia basada en isogènies
Enric Florit - Restrictions on endomorphism algebras of Jacobians
Pip Goodman - Tate module tensor decompositions and Sato-Tate conjecture for varieties potentially of $\mathrm{GL}_2$-type
Xavier Guitart - Automating the modular method for Frey Q-curves
Joey van Langen - Delinge-Lusztig curves are diophantine stable
Joan-C. Lario - Images of residual Galois representations of elliptic curves without CM
Pedro Lemos - Anticyclotomic p-adic L-functions and Darmon points
Santiago Molina Blanco - Torsion of Q-curves over quadratic fields
Filip Najman - Kummer theory for number fields via entanglement groups
Antonella Perucca - Exceptional zeros, p-adic L-functions and Euler systems
Óscar Rivero Salgado - On the order of the reductions of algebraic numbers
Pietro Sgobba - Reduction type of genus-3 curves in special strata of their moduli space
Anna Somoza - On local constancy phenomena for reductions of 2-dimensional crystalline representations
Emiliano Torti - Kummer Theory for Elliptic Curves
Sebastiano Tronto - p-adic families of d-th Shintani liftings
Carlos de Vera Piquero
Calendar
Monday 3
10.30 - 11.30:
Introduction to the modular method (Nicolas Billerey)
12.00 - 13.10:
Ordered abelian groups. (Alberto Fernández)
15.00 - 15.50:
Abelian varieties with everywhere good reduction over certain real quadratic fields (Lassina Dembélé)
16.00 - 16.20:
Kummer theory for number fields via entanglement groups (Antonella Perucca)
16.40 - 17.30:
Images of residual Galois representations of elliptic curves without CM (Pedro Lemos)
17.40 - 18.00:
Torsion of Q-curves over quadratic fields (Filip Najman)
Tuesday 4
09.30 - 10.20:
Exceptional zeros, p-adic L-functions and Euler systems (Óscar Rivero Salgado)
10.30 - 11.30:
On the Asymptotic Fermat Conjecture (Samir Siksek)
12.00 - 13.00:
Fermat's Last Theorem and Wendt's Resultant (Alain Kraus)
15.00 - 15.50:
Anticyclotomic p-adic L-functions and Darmon points (Santiago Molina Blanco)
16.00 - 16.30:
Tate module tensor decompositions and Sato-Tate conjecture for varieties potentially of $\mathrm{GL}_2$-type (Xavier Guitart)
16.40 - 17.30:
Delinge-Lusztig curves are diophantine stable (Joan-C. Lario)
Wednesday 5
09.30 - 10.20:
p-adic families of d-th Shintani liftings (Carlos de Vera Piquero)
10.30 - 11.30:
The Darmon program for the Generalized Fermat equation (Luis Dieulefait)
12.00 - 13.10:
The Serre filtration on mod p Hilbert modular forms of level p (Fred Diamond)
15.00 - 15.50:
Periods of modular functions and diophantine approximation (Paloma Bengoechea)
16.00 - 16.20:
Hecke eigenvalue fields and Maeda's conjecture (Samuele Anni)
16.40 - 17.30:
Automating the modular method for Frey Q-curves (Joey van Langen)
17.40 - 18.00:
Criptografia basada en isogènies (Enric Florit)
18.10 - 18.30:
Reduction type of genus-3 curves in special strata of their moduli space (Anna Somoza)
Thursday 6
09.30 - 10.20:
The level of pairs of polynomials (Alberto Fernandez Boix)
10.30 - 11.30:
A multi-Frey approach to Fermat equations of signature~$(7,7,p)$ combining Frey varieties of different dimensions. (Nuno Freitas)
12.00 - 13.10:
Small extensions of ordered groups (Enric Nart)
15.00 - 15.50:
Restrictions on endomorphism algebras of Jacobians (Pip Goodman)
16.00 - 16.20:
On local constancy phenomena for reductions of 2-dimensional crystalline representations (Emiliano Torti)
16.40 - 17.30:
Wild Galois representations of hyperelliptic curves (Nirvana Coppola)
17.40 - 18.00:
Kummer Theory for Elliptic Curves (Sebastiano Tronto)
18.10 - 18.30:
On the order of the reductions of algebraic numbers (Pietro Sgobba)
Friday 7
09.30 - 10.20:
Potentially diagonalizable representations. A conjecture. (Iván Blanco Chacón)
10.30 - 11.30:
A modular approach to Fermat equations of signature $(p,p,5)$ using Frey hyperelliptic curves (Imin Chen)
12.00 - 13.10:
Equivalence classes of valuations on a polynomial ring (Jordi Guàrdia)
