报告题目/Title： An Introduction to Key Cohomology Theories in Differential Geometry
Time: 20:00-21:00, Aug 25-27, 2025
报 告 人/Speaker： Rosa Marchesini
Affiliation： Georg-August-Universität Göttingen
Zoom Id: 904 645 6677，Password: 2025
会议链接：
//zoom.us/j/9046456677?pwd=Y2ZoRUhrdWUvR0w0YmVydGY1TVNwQT09&omn=89697485456
Abstract: Talk 1: An Introduction to Lie Theory.
Lie theory is an active and fruitful area of study in differential geometry, and it is widely used in mathematical physics. After providing an overview of smooth manifolds and vector bundles, we will explain the correspondence between Lie groups and Lie algebras.
Talk 2: An Introduction to de Rham and Chevalley-Eilenberg Cohomology.
Cohomology theories are useful tools for studying some geometric and topological properties of objects in a given category. De Rham cohomology provides information about manifolds, and Chevalley-Eilenberg plays a central role in studying Lie algebras. After defining differential forms of vector spaces and vector bundles, we will introduce de Rham and Chevalley-Eilenberg cohomologies. We will explain some of their properties. We will focus particularly on the homotopy invariance of de Rham cohomology.
Talk 3: An Invitation to Lie Algebroid Cohomology.
Lie groups and Lie algebras are not general enough to describe some physical phenomena. Relaxing their definitions allows for more flexibility. Therefore, we move on to the field of higher Lie theory, in which Lie groupoids and Lie algebroids play a central role in research. Our focus is on Lie algebroid cohomology, also because it allows us to address several types of cohomology theories simultaneously. These include de Rham and Chevalley-Eilenberg cohomology, as well as foliated, Poisson, and equivariant de Rham cohomologies. After introducing Lie algebroids and their cohomology, we will discuss recent research on homotopy for Lie algebroids. These results are a joint work with M. Jotz.
Bio：Rosa Marchesini has completed her bachelor's degree in Mathematics at the University of Turin in Italy. She then studied in the Algant Double Master's Degree Excellence Program at the universities of Milan, Italy, and Bordeaux, France. She is currently a Ph.D. student at the University of Göttingen in Germany. Her advisor is Madeleine Jotz. Starting in October, She will be a postdoc at the University of Würzburg in Germany.
