Wednesday, October 16, 2019 - 10:00am to Saturday, October 19, 2019 - 6:00pm

This is the third program in the series "International conference on class groups of number fields and related topics". The previous programs were well supported and  appreciated. The feedback received from senior Mathematicians as well as junior participants was very encouraging and motivated us for this edition.

The conference will have a Key-note talk, plenary talks, invited talks and a few young scholars talks. Along with the themes explored in the last two editions (Diophantine equations, class groups, units, computational aspects, connection to elliptic curves, non-divisibility of class numbers etc.) we also wish to include the connections among class groups, Picard groups and Selmer groups as a prominent focus of the 2019 edition. We wish to explore the new ideas needed to open this field. 

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 Mathematicians. We also intend to touch upon the quantitative works on the divisibility problems and non-divisibility problems. 

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). We hope to touch some aspects of this theory during the conference. Among other concepts to be explored during the conference are relative class numbers, computational aspect of class groups and  geometric techniques to study class groups. 

The main purpose of this thematic conference is to bring various experts working on different aspects of the Class Groups at one place. This will provide young researchers an unique opportunity to learn the techniques in the subject and also scope to collaborate with the experts. We hope to cultivate an active group of researcher in the area which is in making from 2017 and 2018 editions.

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.
  • Picard groups.
  • Selmer groups.
  • Diophantine equations.
  • Elliptic curves. 
  • Iwasawa Theory.
Harish-Chandra Research Institute
Harish-Chandra Research Institute
Chhatnag Road, Jhunsi
Allahabad Uttar Pradesh 211019