Seminar Event Detail

Student Arithmetic

Date:  Wednesday, September 20, 2017
Location:  3866 East Hall (3:00 PM to 4:00 PM)

Title:  Quadratic Forms

Abstract:   This is a quick lecture about the classical theory of positive definite quadratic forms, in a style convenient for modern people. I will start from the basics, including the reduction theory, the correspondence between quadratic forms and ideals of orders of imaginary quadratic fields, and the composition of forms. Next, I will address a key question from ancient: what numbers (especially primes) are represented by a quadratic form? Some remarkable results include genus theory, classification of representable primes by congruence, and Hasse local-global principle, all of which are closely related to class field theory. Time permitting, I will sketch a class field theoretic approach to one of these.

Reference: David Cox, Primes of the form x^2+ny^2


Speaker:  Yifeng Huang
Institution:  UM

Event Organizer:     


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