Number Theory

Dates
from January 23, 2017 to March 5
Duration
5 weeks
Venue
UB, UPC, and CRM.
Scienti c Committee:
Organizing Committee:
List of BGSmath Research Groups involved with the proposal:
  • Seminari de Teoria de Nombres de Barcelona (STNB)
With the support of the Ministerio de Economía y Competitividad, under the María de Maeztu grant (MDM-2014-0445), the European Research Council (ERC) under the European Union’s Horizon 2020 Research and Innovation Programme (grant agreement No 682152), CRM, IMUB, UB, UPC.

Registration

The deadline for registration was January 27th, 2017.

Planning

Week 1:

The STNB is an annual meeting that puts together the whole Number Theory community in Barcelona. This year the STNB celebrates its 31st edition and it is organized by Francesc Bars (UAB), Xevi Guitart (UB), Bernat Plans (UPC), and Artur Travesa (UB). It will include research talks by the participants, and a 10 lectures instructional study group on “Hida families and p-adic methods in elliptic curves“ coordinated by Francesc Fité and Santi Molina. This is the program for the 10 lectures course.

From Monday 23 to Friday 27, January 2017.

Week 2:

Week 3:

Week 4:

From Monday February 13 to Friday February 17.

Week 5:

 

Link to the Graduate Couses p-adic methods for Galois representations and modular forms

Presentation

The STNB has experience in organizing international scienti c events. In 1995, the STNB organized in Barcelona the 19èmes Journées Arithmétiques, a forum for presentation and discussion of recent number-theoretical developments with a long tradition and recognized as the main international meeting devoted to number theory.

In July 2001, the STNB organized an Advanced Course at the CRM on Modular forms and p-adic Hodge theory, co- financed by the program High Level Scienti c Conferences of the European Commission.

In July 2002, the STNB organized a large conference on Modular Curves and Abelian Varieties, which took place at the CRM. Papers with the contents of some talks at the conference were published in the volume 224 of Progress in Mathematics, Birkhauser-Verlag (2004).

In 2009-2010, the STNB organized the Research Program in Arithmetic Geometry, at the CRM, which included several advanced courses, conferences, and workshops and it enjoyed the participation of many of the most well-known number theorists in the fi eld.

In the recent years, the fi eld of Arithmetic Geometry has seen signi cant and exciting advances towards the complete or partial solution of some outstanding open conjectures, such as the Sato-Tate conjecture for Hilbert modular forms, some cases of the Weight Monodromy Conjecture, or the Iwasawa main conjecture for GL2.

Among the recent discoveries and new techniques that have emerged lately, special mention deserve the new cases of the Birch and Swinnerton-Dyer conjecture and new modularity theorems of automorphic representations, because of the active and crucial role played by some STNB and BGSMath members. These topics where explored in the 2009-2010 Research Program at the CRM and parts of these projects started during that period, taking advantage of the fruitful mathematical
atmosphere it provided.

It seems thus the right time for the STNB to organize a six-week intensive program on number theory. It will contribute to maintain the level of exceptional research that is being done in Barcelona in the fi eld. In addition, it will be a great opportunity to train a new generation of graduate students and to introduce them to this active, exciting, and fruitful area of research.