Group Theory

Let $p$ be a prime. The main subject of my talks is the estimation of exponential sums over an arbitrary subgroup $G$ of the multiplicative group ${\mathbb Z}^*_p$: $$S(a, G) = \sum_{x\in G} \exp(2\pi iax/p), a \in \mathbb Z_p.$$ These sums have numerous applications in additive problems modulo $p$, pseudo-random generators, coding theory, theory of algebraic curves and other problems.