September 8 (Joint with Algebra Seminar, at 2:50 -4:00 pm, Zoom link:
https://binghamton.zoom.us/j/95069915454 )
Speaker: Fikreab Solomon Admasu
Title: Composition laws from Gauss to Bhargava
Abstract: One of the fundamental objects of interest in number theory is the composition law of binary quadratic forms. In this talk, we will start with a review of the original complicated formulation due to Gauss and then discuss subsequent simplifications by Dirichlet, et al. Another approach involves identifying equivalence classes of binary quadratic forms with ideal classes in a quadratic ring and using the natural group structure of the ideal class group to formulate the composition law of binary quadratic forms. After about 200 years, M. Bhargava gave a new perspective on Gauss' composition law using so-called 2x2x2 cubes of integers and derived more composition laws. We will discuss the main theorems in 'Higher Composition Laws I' by Bhargava and mention the applications if time permits.