## Summer 2018 Graduate Student Seminar

Meeting Tuesdays at 10:30am in room WXLR A202.

 Date Speaker Title & Abstract (click the title to expand) 05/22 Joe Wells Hybrid Lattices in PU(2,1) In the 1980's Gromov and Piatetsky-Shapiro came up with a technique called "hybridization" to produce hyperbolic lattices (and in particular, nonarithmetic lattices). It has been asked whether there is an analogous technique for complex hyperbolic lattices. In this talk I'll present some recent results relating to this question and the construction of complex hyperbolic hybrids in the Picard modular groups. This is joint work with Julien Paupert. 05/29 06/05 06/12 06/19 Lauren Crider A coordinate system for the Grassmann Manifold We're going to chat about the Grassmann Manifold $G_{K,N}$​​ of all $K$​​-dimensional subspaces in $\mathbb{C}^N​$​. A friendly back-pocket example of the Grassmann manifold is $G_{1,N}$​​, which is nothing but the very familiar and very well loved projective space on $\mathbb{C}^N$. With a tiny bit of background in statistical signal processing, we'll discover why we might care about the Grassmann manifold in practice, and why it may be beneficial to regard $G_{K,N}$ as rank-$K$ (orthogonal) projection operators on $\mathbb{C}^N$. We'll use the correspondence between points on $G_{K,N}$ and rank-$K$ projection operators to to develop a local coordinate system on $G_{K,N}$, so we can we can exploit probability measures on the manifold itself. 06/26 Joe Sadow [Title TBD] [Abstract TBD] 07/02 Scott [Title TBD] [Abstract TBD] 07/09 David Polletta [Title TBD] [Abstract TBD] 07/16 Mary Cook [Title TBD] [Abstract TBD] 07/23 [Title TBD] [Abstract TBD] 07/30 Sarah El Jamous* [Title TBD] [Abstract TBD]

*unconfirmed