Geometric structures on manifolds (Canaryfest)
A conference in honor of 50th birthday of Dick Canary.
To be held Saturday June 2 at DePaul University
Also sponsored by the University of Chicago.
Organizers
Benson Farb farb@math.uchicago.edu
Howard Masur masur@math.uchicago.edu
Schedule
9:30-10:30 Yair Minsky (Yale)
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.
Location
All talks will be in Room 100 of the Levan Center at Depaul University.
The address is 2322 N. Kenmore. Here is a link to a map.
map
Local Hotels (all within walking distance of DePaul)
Belden Stratford 2300 N. Lincoln Park (800) 276-7415
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.