Title: Toric Topology
Speaker: Tadeusz Januszkiewicz (Mathematical Institute, Polish Academy of Sciences)
Abstract: Toric topology is the study of actions of a torus $T^n$ on a manifold $M^{2n}$, satisfying two simplifying assumptions
1. The action is locally standard, i.e. locally it looks like the action of $T^n$ on ${\Bbb C}^n$
2. The quotient map $\pi: M\to M/T$ admits a section. Motivating examples come from algebraic and symplectic geometry (toric varieties), from manifolds related to the Toda flow, and form certain complex manifolds which are intersections of special real quadrics.
The general study of such actions, beyond algebro-geometric or symplectic one was initiated in 1992 paper of Mike Davis and myself. The present state of much of the theory is descried in a book of M.V. Buchstaber and T. Panov. In the talk I will describe main results of the theory, together with some applications. I will also discuss limitations of methods used at present, and an approach to overcome some of them..
Biosketch: Tadeusz Januszkiewicz got his PhD from Wroclaw University; currently he works at the Mathematical Institute of Polish Academy of Sciences and teaches part time at Wroclaw.
During 2003-2010 he was a member of OSU Mathematics Department.
He was an invited speaker (section Geometry) at ICM 2010 Hyderabad. He is a corresponding member of Polish Academy of Sciences, and received several prizes incliding Stefan Banach prize of Polish Mathematicsl Society (2009) and the the Prize of the Prime Minister of Poland (2012).
Colloquium URL: https://web.math.osu.edu/colloquium/
