Welcome to International Conference on Class Groups of Number Fields and Related Topics-2018

This is the second edition of the conference `International conference on class groups of number fields and related topics' to be held at Harish-Chandra Research Institute, Allahabad, India, covering the various topics related to the class groups of number fields. The previous conference was well supported and successful. The feedback received from senior Mathematicians as well as junior participants was very encouraging and motivated us for this edition.

This conference will have a Key-note talk, plenary talks, invited talks and a few young scholars talks on current research on the theme topics. Along with the themes explored in the last edition (Diophantine equations, class groups, units, computational aspects, connection to elliptic curves etc.) we also wish to include non-divisibility of class numbers as prominent focus of the 2018 edition. In the non-divisibility side there are very few known results. The approaches to the non-divisibility of class numbers so far are all encompassed under `coefficients of half integral weight modular forms'. We wish to explore the new ideas needed to open this field. The idea of annihilators of class groups reveal some interesting facts about class groups, providing various relations in the class groups. This is an effective way to study problems related to class groups (e.g. resolution of Catalan's conjecture due to Preda Mihailescu). The study of Cohen-Lenstra heuristics is intimately connected to Diophantine equations. Both the divisibility problem and non-divisibility problems have deep connections with super Fermat equation. The conference aims to bring this connection at forefront with the help of the eminent. We also intend to touch upon the quantitative works on the divisibility problems and non-divisibility problems. Among other concepts to be explored during the conference we have ABC conjecture for number fields and some consequences of ABC conjecture, relative class numbers, computational aspect of class groups and  geometric techniques to study class groups. We hope to cultivate an active group of researcher in the area which is in making since 2017 edition.

The main purpose of this thematic
conference is to bring various experts working in different aspects of the main theme of the conference. This will provide young researchers an unique opportunity to learn the techniques in the subject and also scope to collaborate with the experts.

       Topics of interest include:
  • Ideal class groups of number fields: algebraic, analytic as well as computational aspects.
  • Relative class numbers of number fields.
  • Annihilators of class groups.
  • Class field Theory.
  • Diophantine equations.
  • Elliptic curves.
  • Iwasawa Theory.

News & Updates

Dates of Conference:               October 08--11, 2018

Place: Harish-Chandra Research Institute, Allahabad, India

Last date of receiving application: July 31, 2018

Appearance of selected participants list: August, 02, 2018