Xin LU

Lecture 1:
Title:  The slope of a fibred surface.
Abstract:  For a fibred surface it is known that the slope inequality proved by Xiao (and by Cornalba-Harris in the semi-sta
ble case) is strict.
 It the arises a natural question to investigate the influence of some properties of the fibration on the behaviour of the s
lope.
In this talk I will talk about some recent joint work with Zuo on this problem.

Lecture 2:
Title:  Geometry of an irregular surface of general type
Abstract:  Let S be a minimal surface of general type and of maximal Albanese dimension.
The Severi inequality implies that $K_S^2\geq 4\chi(\omega_S)$.
With the help of our new slope inequalities for non-hyperelliptic fibrations, we discovered the existence of an involution
on such a surface with $K_S^2 < 9/2\chi(\omega_S)$. As a consequence, we obtained a characterization of the surfaces on the
Severi line.
This is a joint work with Zuo.