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Course: Integral Binary Quadratic Forms [January 06th - 10th, 2025]

Which numbers can be written as sums of two squares -- as x^(2) + y^(2), for integers x, y?  Which numbers can be written as x^(2) + 2y^(2)?  Such questions have been studied for centuries, with notable contributions by Fermat, Lagrange, Euler, Gauss, and Dirichlet.  The study of binary quadratic forms is one of the most beautiful areas of Number Theory. Some years ago, one cumbersome construction in the theory was substantially simplified by Manjul Bhargava.

Instructor: Chandan Singh Dalawat, Central University of Rajasthan

Background required: We will give an overview of the theory that is accessible to a wide audience.  No prior knowledge of Number Theory, beyond the rudimentary properties of integers, will be assumed. MSc students, PhD scholars and young faculty members are eligible to apply. 

Deadline for application: December 25, 2024.  

The list of selected candidates will be available on the website by 27th December 2024.