Organizers: David Allen, Aradhana Kumari, Margaret H. Dean, and Marcos Zyman.
Unless otherwise noted, the colloquium meets at 2:30 PM on certain Wednesdays in FH 604 . Cookies are offered during every talk. All talks should be accessible to a general mathematical audience. Everyone is welcome. This page is constantly updated as information on speakers becomes available.
10/23: Mikael Vejdemo-Johansson (College of Staten Island, CUNY)
Topological Data Analysis - applying homology in medicine, robotics, sensor networks, and graphics
11/6: Oleg Muzician (BMCC, CUNY)
Dynamics of regularly ramified rational maps
12/4: James Mathew (Memorial Sloan Kettering Cancer Center)
Wasserstein and Fisher-Rao via de Rham and Poincaré duality, with applications to medical data analysis
I will explain the homogeneous space point of view on the optimal mass transport problem and the Wasserstein and Fisher-Rao metrics on the space of probability densities. The proof of the optimality condition amounts to Poincaré duality. A gauge-theoretic version is also explored, with the curvature form obstructing a straightforward generalization of the optimality proof. After discussing computational issues, applications to medical image analysis and gene regulatory networks will be given.