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Title: Topological circle bundle structure on complex smooth projective varieties Speaker: Feng Hao Abstract: It is well known that complex smooth projective varieties of general type do not admit nontrivial global holomorphic tangent vector fields. Moreover, one of Yau’s conjecture says that a canonically polarized complex projective manifold does not even admit a nontrivial differentiable global tangent vector field, in particular, it does not admit a nontrivial differentiable $S^1$-action. Motivated by the above results, I will give a talk on topological $S^1$-actions on complex projective manifolds, and show that a canonically polarized complex projective manifold does not admit free topological $S^1$-actions if its Albanese variety is simple. Title: On the Iitaka volumes of log canonical surfaces Speaker: Wenfei Liu Abstract: For projective log canonical pairs with nonnegative Kodaira dimension, the Iitaka volume measures the asymptotic growth of the pluricanoical systems. In the general type case, it is just the usual notion of volume, and plays a key role in the classification theory. In this talk, I will introduce some results related to boundedness of the Iitaka volumes of log canonical pairs with intermediate Kodaira dimension. For log canonical surfaces with Iitaka dimension 1, we develop a recipe to explicitly describe the set of Iitaka volumes. The talk is based on joint work in progress with Guodu Chen and Jingjun Han. Title: The geography of slopes of fibrations Speaker: Xiao-Lei Liu Abstract: The slopes of fibrations of genus $g \geq 2$ have sharp lower (resp., upper) bound, namely $\lambda_m(g)$ (resp., $\lambda_M(g)$). In this talk, we will first show that for each $g\geq2$ and each rational number $r\in [\lambda_m(g), \lambda_M(g)]$, there exists a fibration of genus $g$ with slope $r$. As Kodaira fibrations have non-trivial vertical fundamental groups and their slopes are all 12, we will also show that 12 is indeed the sharp upper bound for the slopes of fibrations with trivial vertical fundamental groups. Precisely, for each $g \ge 3$ we will prove the existence of fibrations of genus $g$ with trivial vertical fundamental groups whose slopes can be arbitrarily close to 12. This is a joint work with professors Jun Lu and Xin Lu. Title: Multiplier S-sheaf and application Speaker: Junchao Shentu Abstract: We introduce a kind of coherent sheaf that combine Saito's S-sheaf and the multiplier ideal sheaf. These sheaves provide a right candidate to establish the Nadel vanishing theorem in coefficients in a pure Hodge module. An application on a Kawamata's conjecture is provided. This is a joint work with Chen Zhao. |