To be held Saturday June 2 at DePaul University

Also sponsored by the University of Chicago.

Howard Masur masur@math.uchicago.edu

Slightly-higher Teichmuller theory

Abstract: Given a Fuchsian representation g of a surface group G, an affine deformation is a representation of G into the affine transformations of R^3 whose linear part is g. The translational part of the representation is a cocycle u that can be interpreted as a tangent vector to Teichmuller space at the point defined by g. Goldman-Labourie-Margulis studied conditions for such a representation (g,u) to be proper (and hence produce an affine 3-manifold homotopy-equivalent to the surface): Properness is equivalent to the condition that the derivative along u of all length functions of currents in the surface have the same sign (this generalizes a necessary condition originally due to Margulis). Note that this requires the Fuchsian group to be of infinite covolume. With Goldman and Margulis we study the cone of proper deformations and its boundary. We show that the condition on currents reduces to a condition just on laminations, and that the boundary of the cone is divided into facets associated to the vanishing of derivatives of length functions of laminations. Much of this description is related at least in spirit to Thurston's description of stretch maps and the Lipschitz metric. In the case of the one-holed torus we give a complete description.

11:00-12:00 Ken Bromberg (Utah)

2:00- 3:00 Martin Bridgeman (Boston College)

Title: Hitting Measures on Hyperbolic Manifolds

Abstract: We consider the pushforward of volume measure on the unit tangent bundle of a hyperbolic manifold by natural hitting functions. We show that this gives rise to summation identities in terms of length spectra of the manifold as well as summation formulae for geometric averages. In particular we show that the average time for a vector to hit the boundary for a surface with geodesic boundary is a summation of a Trilogarithm function evaluated on the orthospectrum of the surface.

3:30-4:30 Chris Leininger (UIUC)

Title: Short geodesics in moduli space.

Abstract: I'll discuss joint work with Margalit, building on previous work with Farb and Margalit, on the number and location of the short geodesics in moduli space.

The address is 2322 N. Kenmore. Here is a link to a map. map

Days Inn 644 West Diversey (888) 576-3297

Best Western 3434 N. Broadway (888) 860-3400

Willows Hotel 555 W. Surf (800) 787-3108

Majestic Hotel 528 W. Brompton (800) 727-5180

Chicago Getwaway 616 W. Arlington (773) 929-5380

Note: participants will need to make their own hotel arrangements.