报告题目：Lie Groupoids and Related Structures
报 告 人：Matias del Hoyo
所在单位：Universidade Federal Fluminense
报告时间：2025年2月18,19,20日 10:00-11:00
报告地点：吉林大学数学楼第五研讨室
报告摘要: Talk 1: Lie Groupoids
Abstract: Lie groupoids generalize Lie groups and can be seen as structures on manifolds that encode both internal and external symmetries. Over the last few decades, their theory has significantly evolved, driven by connections to Poisson geometry, non-commutative geometry, and mathematical physics. In this talk, I will provide an overview of Lie groupoids, including basic definitions, key examples, and constructions. I will also discuss the Linearization Theorem and some of its applications, with a particular focus on the theory of Riemannian metrics.
Talk 2: Lie Algebroids and Differentiable Stacks
Abstract: The infinitesimal geometry of a Lie groupoid is captured by its Lie algebroid, a structure that generalizes regular foliations and Lie algebra bundles. Not every abstract Lie algebroid can be integrated, and topological obstructions can be explicitly computed. The transverse geometry of a Lie groupoid is represented by its orbit stack, a structure generalizing manifolds and orbifolds. Two groupoids yield the same stack if and only if they are Morita equivalent, and many invariants and constructions are Morita invariant. I will review these constructions, highlight key results, and discuss my contributions to the field.
Talk 3: Higher Lie Groupoids
Abstract: Higher Lie groupoids arise from the simplicial approach to higher category theory. Notable examples include the global counterparts of Courant algebroids in Poisson Geometry. Just as Lie groupoids relate to Lie algebroids and stacks, higher Lie groupoids connect with differential graded manifolds and higher stacks. However, these theories are still in their early stages, with foundational questions remaining unanswered. In this talk, I will introduce the theory of higher Lie groupoids, present my recent work in the area, and discuss some open problems.
报告人简介： Prof. Matias del Hoyo has been a faculty member at the Universidade Federal Fluminense (Niterói, Brazil) since 2016. He earned his Ph.D. in Mathematics from the Universidad de Buenos Aires (Argentina) in 2010 and conducted postdoctoral research at Instituto Superior Técnico (Lisbon, Portugal) and Utrecht University (Netherlands) from 2011 to 2013. He also served as a Visiting Professor at IMPA (Rio de Janeiro, Brazil) from 2014 to 2016 and at the Center de Recerca Matemàtica (Barcelona, Spain) in 2019. His research focuses on Lie groupoids, Lie algebroids, and differentiable stacks, with applications in Poisson Geometry.
