Institute of Mathematical Sciences
Time：4:00pm-5:00pm, July 13, Friday
Location：Room 302, Library
Speaker: Mario Garcia-Fernandez
Mario Garcia-Fernandez is an Assistant Professor at the Universidad Autónoma de Madrid. Previously, he had postdoctoral appointments at the ICMAT in Madrid (Marie Curie Fellow, Nigel Hitchin Lab Fellow), at the École Polytechnique Fédéral de Lausanne (Switzerland) and at the Centre for Quantum Geometry of Moduli Spaces (Denmark). He obtained his PhD in 2009 at the Universidad Autónoma de Madrid.
Mario Garcia-Fernandez works in the areas of differential geometry and algebraic geometry. His research has strong links with geometric analysis and theoretical physics, in particular with string theory, and is devoted to the study of special metrics and connections in complex geometry and their relation to stability conditions in algebraic geometry, moduli spaces, special holonomy with torsion, and mirror symmetry.
Title: Canonical metrics in complex non-Kähler geometry.
Abstract:In the 1950s Calabi asked the question of whether a compact complex manifold admits a preferred Kähler metric, distinguished by natural conditions on the volume or the Ricci tensor. Following recent important advances in Kähler geometry, such as the solution of the Kähler-Einstein problem by Donaldson, Chen and Sun, there is a renewed interest in extending Calabi's Programme to the case of compact complex manifolds which do not admit a Kähler metric. In this talk I will discuss a concrete proposal for a theory of canonical metrics in complex non-Kähler geometry, inspired by string theory and based on holomorphic Courant algebroids. If time allows, I will also comment on a potential extensión of mirror symmetry for these new geometries.
题目：在复杂的非Kähler几何中规范的度量
摘要：在20世纪50年代，Calabi提出了一个问题：一个紧凑的复杂的流形是否承认了一个更受欢迎的科勒度量，它是根据体积或里奇张量的自然条件来区分的。继最近在科勒的几何学上取得了重要的进展，例如唐纳森、陈和孙的khler-einstein问题的解决方案之后，人们又重新燃起了对卡比拉的计划的兴趣，那就是将卡比拉的方案扩展到不承认khler度量的紧凑复杂的流形。在这次讲座中，我将讨论一个具体的方法，即在复杂的非khler几何中，由弦理论和基于全纯的Courant代数的理论来提出一个规范矩阵的理论。如果时间允许，我还将对这些新几何图形的镜像对称的潜在扩展进行注释。