The Reading Groupoid is a weekly collective study session dedicated to the systematic exploration of Lie groupoids, Lie algebroids, and their profound connections to modern differential geometry and mathematical physics.
Our journey begins with a comprehensive study of Kirill C. H. Mackenzie's book General Theory of Lie Groupoids and Lie Algebroids, which provides the foundational framework for understanding these remarkable geometric structures. We shall proceed methodically through the theory, examining the intricate relationships between groupoids and algebroids, their cohomological properties, and the rich interplay between local and global perspectives.
A particular focus will be placed on the groundbreaking integrability theorem of Fernandes and Crainic, which resolves the fundamental question of when a Lie algebroid can be integrated to a Lie groupoid. This result represents one of the most significant advances in the field and opens pathways to numerous applications across mathematics and theoretical physics.
Each weekly session features a detailed presentation by a rotating speaker, encouraging an environment of shared expertise and collaborative learning. The format encourages active participation, with ample opportunity for discussion, questions, and the exploration of connections to participants' own research interests.
The format will be hybrid, with the possibility to attend in person either in Madrid (at ICMAT), in Warsaw (at IMPAN), or online. If you wish to attend online, please contact us.