Abstract:Let $X$ be a compact connected smooth manifold with boundary. The paper deals with contact $1$-forms $\beta$ on $X$, whose Reeb vector fields $v_\b$ admit Lyapunov functions $f$. We prove that any odd-dimensional $X$ admits such a contact form.We tackle the question: how to recover $X$ and $\beta$ from the appropriate data along the boundary $\partial X$? We describe such boundary dat...
IntroductionHodge conjecture is one of the millennium conjectures for which the evidences are not so much: It is proved for surfaces (Lefschetz (1,1) theorem) and surface type varieties (like cubic fourfolds), and we do not know even it is true for all Fermat varieties (despite some partial result by T. Shioda and his coauthors). The main goal of the course is introduce computational methods fo...