(October 8) Daniel Allcock: Hyperplane arrangements in complex hyperbolic space. - Imagine removing an arrangement of hyperplanes in complex hyperbolic space. Then mod out by a discrete group with finite-volume quotient. In the case that the hyperplanes are either orthogonal or disjoint, the fundamental group of the quotient can never be a lattice in any Lie group with finitely many components. The central part of the proof is some pretty and elementary hyperbolic geometry.

(May 6) Perinkulam Krishnaprasad: Momentum Maps, Constrained Dynamics, and Control. - Abstract:

The equations of classical mechanics in the presence of nonholonomic constraints and symmetries admit conservation laws in the spirit of Noether's theorem, but in a form different from the familiar setting of holonomically constrained systems. These momentum equations suggest a notion of momentum map that may be of broader interest. Here we show how to use momentum equations to understand and control the dynamics of some low-dimensional constrained examples. This is joint work with Bloch. Marsden, Murray and Tsakiris.

(May 13) Rebecca Goldin: Schubert calculus on Bott-Samelson manifolds - In this talk, I will define Schubert calculus and discuss its manifestation as a geometric question (the number of points in an appropriate triple intersection), an algebraic question (the product structure in the cohomology ring of a flag variety), and, time permitting, as a combinatorial question (involving divided difference operators). Then I will show how Schubert calculus can be done on a tower of projective bundles (a Bott-Samelson manifold), gaining computability but losing complex structure. As usual, computations are more easily done in equivariant, rather than ordinary, cohomology.