This introductory talk will cover basic definitions and examples of representation and character theory. It will be accessible to a general math audience.
Introduction to Representation Theory
Sep. 08, 2015 1pm (Math350)
Pearce Washabaugh Manifolds of maps
Sep. 08, 2015 2pm (MATH 350)
Lie Theory
Nat Thiem (CU)
X
Set partition statistics have been recently studied as a family be Diaconis et al, where they study their algebraic and probabilistic properties. On the other hand, these statistics come about naturally in the representation theory of finite unipotent groups. Viewed in this context, it is natural to consider a wider family of unipotent groups whose representation theory is governed by the integer lattice points inside a family of polytopes (called transportation polytopes). This talk develops these ideas, and raises some questions about the geometry of set partition statistics suggested by this connection.
The Linearization Theorem for Lie groupoids provides an organizing framework for classic results on the geometry of fibrations, actions and foliations. It was conjectured by A. Weinstein and solved by N. Zung using analytical methods. In a joint work with R. Fernandes, building on previous works by M. Pflaum et al, we abord the linearization problem from a new perspective, developing a notion of metrics on Lie groupoids, obtaining a simpler proof and a stronger result. I will discuss the linearization problem for groupoids, our solution by metrics, and if time permits, future lines of research.
Lie groupoids, linearization and metrics Sponsored by the Meyer Fund
Introduction to Representation Theory