Prof. Yong Hu，Southern University of Science and Technology

Let $k$ be a field of characteristic 0 and let $C$ be the a smooth affine curve over $k$. We will first discuss applications of strong approximation to the theory of integral quadratic forms over $C$. Then we will focus on strong approximation for semisimple simply connected groups over the function field $k(C)$. In a number of interesting cases (e.g. $k=\mathbb{C}((t))$), only type A requires further study. We show that if the cohomological dimension of $k$ is at most 2, all groups of inner type A or isotropic outer type A over the function field $k(C)$ satisfy strong approximation. This is based on a joint work in progress with Yisheng Tian.