讲座题目1：Class numbers of quadratic fields
报告人：Professor Kalyan Chakraborty
Class number of a number field is one of the fundamental and mysterious objects in algebraic number theory. In this talk, I will discuss the class numbers of some quadratic fields. More precisely, 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 is based on some works done jointly with A Hoque, Y Kishi and P P Pandey.
Dr. Chakraborty earned his Ph. D. in Mathematics in 1998 from Harish-Chandra Research Instiute, Allahabad, India under the supervision of Prof. B Ramakrishnan. In 1997, he joined The Institute of Mathematical Sciences,Chennai,Indiaas a post-doctoral fellow. After that he joined Queen’s University, Canada as a post-doctoral fellow. Dr. Chakraborty came back toIndiain 2001, and joined Harish-Chandra Research Insitute as an assistant professor. Currently, he is a professor at Harish-Chandra Research Insitute,Allahabad,India. He visited University of Paris VI, Paris, University of Paris VII, Paris, Tokyo Metropolitan University, Japan, Kinki University, Japan, Kyoto Sangyo University, Japan, Waseda University, Japan, Universitá Roma Tre, Italy, the University of Hong Kong, Hong Kong, Northwest University, China, Shandong University, China, Shangluo University, China, Mahidol University, Thailand, Mandalaya University, Myanmar, Eötvös Loránd University, Budapest, and many more.
The broad area of research of Dr. Chakraborty lies in Algebraic Number Theory as well as in Analytic Number Theory. In particular, his research areas include: ideal class groups of algebraic numbers fields; Diophantine equations; automorphic forms; arithmetic functions; elliptic curves, cryptography and special functions. He has published more than 50 research articles in reputed journals. He has also published 2 books in number theory. He has produced 5 Ph. D. students under his guidance. He is also serving as an editorial member of some reputed journals.
讲座题目2：Pell-type equations and class groups of cyclotomic fields
报告人：Doctor Azizul Hoque
In this talk, I will discuss the solvability of some Pell-type equations. Then I will apply these results to find some families of cyclotomic fields whose class groups are non-trivial. Finally, I will produce a family of cyclotomic fields whose class groups has an element of order 3. The talk is based on some recent works done jointly with K Chakraborty.
Dr. Hoque earned his M.Sc. degree in Mathematics from Gauhati University, Guwahati, India, in 2008 and then he did his M. Tech. degree from Tezpur University, Tezpur India in 2011. After that he joined Regional Institute of Science and Technology, Meghalaya, India in 2011 as an Assistant Professor. He joined Ph.D. programme in 2012 at Gauhati University , Guwahati , India under the supervision of Prof. Helen K. Saikia and finished his Ph. D. in 2015. He also worked at Gauhati University Institute of Scinece and Technology, Guwahati, India during the period October, 2012–February, 2016 as an assistant professor. He has joined Harish-Chandra Research Institute, Allahabad , India on March, 2016. He visited the University of Hong Kong, Hong Kong, Northwest University, China, Shangluo University, China, Mahidol University, Thailand, Mandalaya University, Myanmar etc.
The broad research area of Dr. Hoque lies in Algebraic Number Theory as well as in Analytic Number Theory. In particular, his research areas include: ideal class groups of algebraic numbers fields; Diophantine equations; arithmetic functions; elliptic curves and zeta functions. The title of his Ph. D. thesis is “A study on the class numbers of quadratic and cyclotomic fields”. He has published more than 20 research articles in well-known journals.