Tuesday April 21:

15:40 - 16:30: Ser Peow Tan
17:00 - 17:50: Martin Bridgeman
20:00: Conference Dinner at the Persian Grill

Wednesday April 22:

10:30 - 11:20: Feng Luo
11:50 - 12:40: Greg McShane

Titles/Abstracts:

Ser Peow Tan (NUS): Polynomial automorphisms of C^n preserving the Markoff-Hurwitz polynomial

We will talk about the action of the group of polynomial automorphisms of C^n which preserve the Markoff-Hurwitz polynomial. Our main results include the determination of the group, the description of a non-empty open subset of C^n on which the group acts properly discontinuously (domain of discontinuity), and identities for the orbit of points in the domain of discontinuity which generalize the original McShane identity in this setting.
This is joint work with Hengnan Hu and Ying Zhang.

Martin Bridgeman (Boston College): Moments of the boundary hitting function for geodesic flow

We consider the distribution of the time for the geodesic flow to hit the boundary of a hyperbolic manifold with geodesic boundary and derive a formula for the moments of the associated random variable in terms of the orthospectrum. We show that the the first two moments correspond to two cases of known identities. We further obtain an explicit formula in terms of the trilogarithm functions for the average time for the geodesic flow to hit the boundary in the surface case, using the third moment. This is joint work with S. P. Tan.

Feng Luo (Rutgers University): Discrete uniformization theorem for polyhedral surfaces

The classical uniformization theorem states that every Riemann surface carries a complete constant curvature Riemannian metric in its conformal class. However, it is difficult to implement the uniformization theorem for polyhedral surfaces. We introduce a notion of discrete conformality for polyhedral surfaces and prove a discrete version of the uniformization theorem. This is a joint work with David Gu, Jian Sun and Tianqi Wu.

Greg McShane (Grenoble): Perspectives on identities

I will discuss the relationship between different identities for fuchsian groups with boundary. In particular, I will give a proof that the identities of Caligari and Bridgeman-Kahn are the same.