报告人：徐万元，上海师范大学

题目: On a conjecture of Schnell 

摘要: In this talk, I shall talk about the following conjecture of C. Schnell: Let $f: X \to Y$  be a fibration with $\kappa(F)\geq 0$. Suppose that the divisor class $mK_X-f^*H$ is pseudo-effective for some $m\geq 1$, then $mK_X-f^*H$ is effective for $m$ sufficiently large and divisible. Schnell proved this conjecture by himself with the assumption that $K_Y$ is pseudo-effective. We prove this conjecture in the surface case. This is joint work with Jun Lu.

报告人：孙浩，上海师范大学

题目: Bridgeland stability conditions on fibred threefolds

摘要: The existence of stability conditions on threefolds is often considered the biggest open problem in the theory of Bridgeland stability conditions. In 2014, Bayer, Macri and Toda introduced a conjectural construction of Bridgeland stability conditions for any projective threefold. Here the problem was reduced to proving a Bogomolov-Gieseker type inequality for the third Chern character of tilt-stable objects. It has been shown to hold for Fano 3-folds, abelian 3-folds, quintic threefolds, etc. In this talk, we will give a conjectural construction of stability conditions on the derived category of fibred threefolds. The construction also depends on a conjectural Bogomolov-Gieseker type inequality for certain stable complexes. We will show the conjectural Bogomolov-Gieseker type inequalities for ruled threefolds.

时间：10月20日（周五）14:00-16:30

地点：科大东区5教5205

联系人：张磊 zhlei18@ustc.edu.cn