LISMATH
Lisbon Mathematics PhD

The LisMath Seminar

The purpose of the LisMath seminar is to provide an initiation into research as well as to make students train their oral skills.  Each LisMath student will be asked to give a talk, based on research papers, chosen from a list covering a variety of research topics. The seminar should be comprehensible to everyone. The student will be asked to make an effort to explain why he/she finds the topic interesting, and how it fits into the broader research picture. The LisMath seminar will thus help broadening the students training.
 
The LisMath seminar takes place on a weekly basis in the Spring semester. Attendance is mandatory for LisMath students. Venue: Wednesday 17h-18h, alternating between FCUL (seminar room 6.2.33 of the Department of Mathematics) and IST (seminar room P9 of the Department of Mathematics) except for 26/6/2018 and 15/7/2019, LisMath Seminar Day, when all sessions will be held at the former location.

– Europe/Lisbon — Online

Vicente Lorenzo García, LisMath, Instituto Superior Técnico, Universidade de Lisboa.
Group actions on surfaces of general type and moduli spaces.

The main numerical invariants of a complex projective algebraic surface $X$ are the self-intersection of its canonical class $K^2_X$ and its holomorphic Euler characteristic $\chi(\mathcal{O}_X)$. If we assume $X$ to be minimal and of general type then $K^2_X\geq 2\chi(\mathcal{O}_X)-6$ by Noether's inequality.

Minimal algebraic surfaces of general type $X$ such that $K^2_X=2\chi(\mathcal{O}_X)-6$ or $K^2_X=2\chi(\mathcal{O}_X)-5$ are called Horikawa surfaces and they admit a canonical $\mathbb{Z}_2$-action. In this talk we will discuss other possible group actions on Horikawa surfaces. In particular, $\mathbb{Z}_2^2$-actions and $\mathbb{Z}_3$-actions on Horikawa surfaces will be studied.

In the case of $\mathbb{Z}_2^2$-actions we will not settle for Horikawa surfaces and results regarding the geography of minimal surfaces of general type admitting a $\mathbb{Z}_2^2$-action will be discussed. They will yield some consequences on the moduli spaces of stable surfaces $\overline{\mathfrak{M}}_{K^2,\chi}$.