Quadratic Forms and Gauss Composition -
One of the simplest problems in mathematics is to find all the solutions of a given equation. If we are searching for integer solutions, then this is a much deeper problem than just finding all complex solutions. A very important and classical problem in number theory is the question of which integers are represented by a given polynomial. For example, what integers are represented by x^2 + y^2, as x and y run through all the integers? We will focus on quadratic equations, those of degree two. There is a long and rich history and at the same time many unsolved problems about representation by quadratic equations. We will explain some classical and contemporary ways to study which integers are represented by binary quadratic forms.
Thursday, November 12, 2020 at 4:45pm to 5:30pmVirtual Event
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