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This is the third program of the series "International conference on class groups of number fields and related topics (ICCGNFRT)". The previous programs were well supported and  appreciated. The previous two programs did help in creating groups working on class groups and related topics, and encouraged healthy interaction among many researchers. More details can be obtained at ICCGNFRT-2017 and ICCGNFRT-2018.

The main focus of ICCGNFRT 2019 will be on class number of number fields, Diophantine equations and interplay between them.  Apart from qualitative results on class numbers, quantitative results on class numbers, the computational aspect of class groups and some geometric techniques to study class groups will be explored. The other concepts to be explored during the conference include relative class number, Picard groups and Selmer groups. In previous programs, various class number problems in special families of number fields were discussed, and this time some recent researches on class number of fields of Richaud- Degert type will be presented.

This shall be the last program in the series ICCGNFRT at Harish-Chandra Research Institute, Prayag Raj. Our emphasis will be to outline a good roadmap for future researches in the area. For this  purpose there will be a couple of keynote talks and 4-5 plenary talks during the conference. We hope to bring various experts working on different aspects of the Class Groups at one place. The conference will provide young researchers an unique opportunity to learn the techniques in the subject and also give them a 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.

• Picard groups.

• Selmer groups.

• Diophantine equations.

• Elliptic curves. 

• Iwasawa Theory.