My current research has two main branches. The first concerns with the theory of algebraic groups and particularly its manifestations in topics such as quadratic and hermitian forms and central simple algebras (often with involution). The questions which I study usually concern with torsors of algebraic groups over a general base ring or scheme. The second branch of my research concerns wit high dimensional expanders. It includes the use of algebraic and number-theoretic techniques for constructing them, as well as applications to coding theory and computational complexity.