Distribution of values of quadratic forms

Study of values of integral quadratic forms is a classical area in number theory, dating back to Fermat, Euler, Gauss and Lagrange. Quantitative questions on distribution of values of quadratic forms arise naturally in many different contexts, including, for instance, the distribution of primes in arithmetic progressions. In this talk, we are going to discuss some classical and modern results on distribution of values of quadratic forms in long and short intervals, connections of this area with $L$-functions, character sums and modular forms.