25 Feb 2025. Talk by Jaime Pedregal at the University of Castilla La Mancha.
Abstract: The concept of connection in differential geometry is a way to coherently answer questions such as “What is a constant vector field on a manifold?” or “What is the acceleration of a curve on a manifold?” The holonomy group is one of our best tools for studying the geometric content of a connection. The first part of the talk will focus on a friendly introduction to the concepts of connection and holonomy group, with numerous examples. The second part, initially unrelated to the first, will offer an introduction to generalized geometry, starting with its linear aspect and then moving on to its strictly geometric aspect. In the final section, we will briefly and superficially outline how our research seeks to combine these two concepts to provide new answers in the theory of holonomy using techniques from generalized geometry.