## Number Theory Seminar

### Wednesday, July 18th, 2018

**Time:** 2:30-3:20p.m. **Place:** Jeffery Hall 422

**Speaker:** Kalyan Chakraborty (Harish-Chandra Research Institute, Allahabad, India)

**Title:** ON CLASS NUMBER OF CERTAIN QUADRATIC FIELDS.

**Abstract:** Class number of a number field and in particular that of a quadratic number field, is one of the fundamental and mysterious objects in algebraic number theory and related topics. I will discuss some results concerning the divisibility of the class numbers of certain families of real (respectively, imaginary) quadratic fields in both qualitative and quantitative aspects. I will also look at the 3-rank of the ideal class groups of certain imaginary quadratic fields. The talk will be based on some recent works done along with my collaborators.