On Quadratic Forms Representing Integers.

I will talk about the counting problem in which we count the number of integer solutions $\mathbf{x} = (x_1, \dots, x_n) \in \mathbb{Z}^n$ to the Diophantine equation F(\mathbf{x}) = m, where F is a fixed non-singular quadratic form in n \geq 4 variables with integer coefficients, and m \neq 0.