报告题目：On smooth complex surfaces of general type with minimal holomorphic Euler characteristic
The talks focus on complex smooth surfaces of general type with minimal holomorphic Euler characteristic (namely $\chi=1$). A complete classification of such surfaces is still missing.
The first talk is introductory. I will introduce inequalities in the theory of fibrations on surfaces and Beauville's result which shows surfaces with $\chi=1$ have invariants $p_g=q\leq 4$. Then I report the complete classification on surfaces with $p_g=q=3$, due to Catanese-Ciliberto-Mendes Lopes, Pirola and Hacon-Pardini. Finally, I will talk about the surfaces with $p_g=q\leq 2$, mostly concerning those with geometric genus zero.
In the second talk, I will talk about several families of smooth surfaces of general type with invariants $p_g=0$ and $K^2=7$. One of which is recently constructed by Y. Shin and myself. Then I will discuss their bicanonical maps, automorphism groups, moduli spaces and Bloch conjecture for these surfaces.
报告人简介：陈伊凡，现任北京航空航天大学数学科学学院副教授。主要从事一般型复代数曲面和三维代数簇的分类及复曲面模空间的研究，已在Math. Z, Math. Res. Lett., Advances in Mathematics等国际数学期刊上发表多篇论文。