curso por Ramin Takloo-Bighash (Universidade de Princeton, EUA)
Abstract:
A quadratic form is a polynomial which is of degree two. Quadratic forms
have been of interest since essentially the beginning of time. The first
known example of a quadratic form studied by mankind is what is known as the
Pythagorean equation discovered in the context of geometry: given a right
angle triangle of sides a, b, c, we know that
a2 = b2 + c2 if a is the
biggest side. There is historical evidence suggesting that ancient Egyptians
used triangles with sides 3, 4, 5 to construct right angle triangles; they
used these triangles as a practical tool in architecture, and we all know
what they were capable of building!
Topics:
Let's complicate things: Continued Fractions;
How to count the number of cows of a certain Greek god:
Pell's Equation;
To square or not to square: Quadratic forms in general;
Not all quadratic forms are born equal:
Equivalence and Gauss' theory of genera;
World through the eyes of a quadratic form:
Representability by quadratic forms;
and finally
