STNB2026 (39th edition)
Dates
Monday 26 to Friday 30 January, 2026
Location
Mathematics Faculty, University of Barcelona, 585 Gran Via de les Corts Catalanes 08007 Barcelona, Catalonia ******************************************************************************* Attention: If you want to present a communication, please register and contact with the organizing committee, before January 12, 2026, at stnbarcelona@gmail.com Paritially supported by IMUB (Institut de Matemàtica UB)
Organising committee
Francesc Bars Cortina, Luis Dieulefait, Bernat Plans Berenguer and Artur Travesa
Themes
Hopf-Galois theory and applications to number theory
Co-ordinators: Daniel Gil Muñoz and Cornelius Greither
Four lectures on $p$-adic Hodge-Tate theory and applications.
Co-ordinators: Josu Pérez Zarraonandia
- Overview and Motivation.
Josu Pérez Zarraonandia - Hodge-Tate Representations
Matilde Vieira Lino da Costa - Three Period Rings for the Elven-kings
Filip Gawron - Classification of $p$-adic Representations of Elliptic Curves
Jose Castro-Moreno
Invited talks and communications
Co-ordinators: Bernat Plans Berenguer
- Modular Entanglement
Samuele Anni - Paraules
Francesc Bars Cortina - Exploring extensions of Dirichlet and Green-Tao theorems on arithmetic progressions over polynomial and formal power series rings
Alberto Fernandez Boix - Corbes el·líptiques associades a varietats abelianes 3-dimensionals amb multiplicació imaginària
Francesc Fité Naya - Recognizing fake elliptic curves
Enric Florit - Hasse principle and twists of the modular curve X(p)
Nuno Freitas - Primes ramified in coefficient fields of modular forms
Filip Gawron - Squares in arithmetic progression over number fields
Enrique González-Jiménez - Elliptic curves attached to abelian threefolds with imaginary multiplication
Pip Goodman - Explicit base-change lifts of modular forms
Antti Haavikko - Fermat curves over number fields and the Hasse principle
Alain Kraus - Extension of root-based attacks against fully-split PLWE instances via isomorphisms
Rodrigo Martín Sánchez-Ledesma - Revisiting the Fermat equation of exponents (3,3,p)
Diana Mocanu - Explicit lower bounds on the conductors of elliptic curves and abelian varieties over number fields
Pierre Tchamitchian - Additively indecomposable quadratic forms over totally real number fields
Magdaléna Tinková - Divertiment aritmètic per a relax
Artur Travesa - Todo entero se puede escribir como suma de un cuadrado y un libre de cuadrados.
Jorge Urroz - Correspondence theorems for infinite Hopf–Galois extensions
Gabor Wiese
Calendar
Monday 26
10.00 - 10.50:
Exploring extensions of Dirichlet and Green-Tao theorems on arithmetic progressions over polynomial and formal power series rings (Alberto Fernandez Boix)
11.10 - 12.00:
Hasse principle and twists of the modular curve X(p) (Nuno Freitas)
12.10 - 12.30:
Revisiting the Fermat equation of exponents (3,3,p) (Diana Mocanu)
12.40 - 13.00:
Recognizing fake elliptic curves (Enric Florit)
15.00 - 15.50:
Correspondence theorems for infinite Hopf–Galois extensions (Gabor Wiese)
16.10 - 16.30:
Todo entero se puede escribir como suma de un cuadrado y un libre de cuadrados. (Jorge Urroz)
16.40 - 17.00:
Primes ramified in coefficient fields of modular forms (Filip Gawron)
17.05 - 17.25:
Explicit base-change lifts of modular forms (Antti Haavikko)
17.30 - 17.50:
Additively indecomposable quadratic forms over totally real number fields (Magdaléna Tinková)
17.55 - 18.45:
Modular Entanglement (Samuele Anni)
Tuesday 27
10.00 - 11.30:
Overview and Motivation. (Josu Pérez Zarraonandia)
11.45 - 13.15:
Hodge-Tate Representations (Matilde Vieira Lino da Costa)
Wednesday 28
10.00 - 11.30:
Hopf algebras and their actions on modules (Daniel Gil Muñoz)
11.45 - 13.15:
Three Period Rings for the Elven-kings (Filip Gawron)
15.00 - 15.50:
Fermat curves over number fields and the Hasse principle (Alain Kraus)
16.10 - 16.35:
Explicit lower bounds on the conductors of elliptic curves and abelian varieties over number fields (Pierre Tchamitchian)
16.40 - 17.00:
Extension of root-based attacks against fully-split PLWE instances via isomorphisms (Rodrigo Martín Sánchez-Ledesma)
17.05 - 17.25:
Elliptic curves attached to abelian threefolds with imaginary multiplication (Pip Goodman)
17.30 - 18.20:
Corbes el·líptiques associades a varietats abelianes 3-dimensionals amb multiplicació imaginària (Francesc Fité Naya)
Thursday 29
10.00 - 11.30:
Hopf-Galois extensions and Hopf-Galois objects (Cornelius Greither)
11.45 - 13.15:
Classification of $p$-adic Representations of Elliptic Curves ( Jose Castro-Moreno)
15.00 - 15.50:
Squares in arithmetic progression over number fields (Enrique González-Jiménez)
16.10 - 16.30:
Paraules (Francesc Bars Cortina)
Friday 30
09.45 - 11.15:
Hopf-Galois structures on separable extensions (Cornelius Greither)
11.30 - 13.00:
Hopf-Galois extensions in number theory (Daniel Gil Muñoz)
13.15 - 13.45:
Divertiment aritmètic per a relax (Artur Travesa)
