All talks are held on Friday in 381-T, starting at 2:15 pm, unless otherwise noted.
Friday, October 5, 2012
Speaker: Yitwah Cheung (SFU)
Title: Generalized Gauss measures and Levy's constant
Friday, October 12, 2012
No Seminar
Friday, October 19, 2012
Speaker: Ronen Mukamel (Stanford)
Title:Trace fields and Veech groups without parabolics
Friday, October 26, 2012
No Seminar
Friday, November 2, 2012
Speaker: No Seminar
Friday, November 9, 2012
Speaker:Rafe Mazzeo
Friday, November 16, 2012
Speaker: Jayadev Athreya
Title: Gap Distributions and Homogeneous Dynamics
Abstract: The Farey sequence F(Q) is the collection of fractions between [0,1] whose denominator (when written in lowest terms) is at most Q. As Q grows, these points become uniformly distributed in the interval, so in some sense, look `random'. However, when you look at the gaps between them, they do not behave like those for uniformly distributed random variables, but instead follow an unusual law known as Hall's Distribution. We will explain a proof of this result that uses horocycle flow on the space of lattices SL(2,R)/SL(2, Z), and, time permitting discuss how this picture can be generalized to understanding gaps between directions of saddle connections on Veech surfaces. This talk will include elements from joint work with Y. Cheung, joint work with J. Chaika, and joint work with J. Chaika and S. Lelievre.
Friday, November 23, 2012
No Seminar
Friday, November 30, 2012
Speaker Alex Wright
Title: SL(2,R) orbit closures of translation surfaces.
Friday, Jan. 18, 2013
Speaker Kenji Kozai
Title: Singular hyperbolic structures from Sol.
Friday, Jan. 25, 2013
Speaker Martin Bridgeman
Title: The Pressure metric for convex Anosov representations
Abstract Using the thermodynamics formalism, we introduce a notion of intersection for convex Anosov representations. We also produce a Out-invariant Riemannian metric on the smooth points of the deformation space of convex, irreducible representations of a word hyperbolic group G into SL(m,R) whose Zariski closure contains a generic element. In particular, we produce a mapping class group invariant Riemannian metric on Hitchin components which restricts to the Weil–Petersson metric on the Fuchsian locus.
Friday, Feb. 1, 2013
Speaker Ara Basmajian
Title: Lengths of closed geodesics and their intersection numbers on a hyperbolic surface
Abstract We'll discuss in various contexts the relationship between the lengths of closed geodesics and their number of intersections on a hyperbolic surface.
Friday, Feb. 8, 2013
Speaker Zhiren Wang
Title Global rigidity of abelian Anosov actions on tori
Abstract As part of a more general conjecture, the following statement was expected to hold: if a smooth $\mathbb Z^r$-action $\alpha$ on a torus contains one Anosov element and has no rank-1 factor, then it must be smoothly conjugate to its linearization $\alpha_0$, which is an action by toral automorphisms. Fisher, Kalinin and Spatzier showed this holds under the assumption that $\alpha$ has at least one Anosov element in every Weyl chamber of the linearization action. We will verify that this assumption is redundant, hence fully establish the statement above. This is a joint work with Federico Rodriguez Hertz.
Friday, Feb. 15, 2013
Speaker Amie Wilkinson
Title: Absolute continuity, exponents, and rigidity.
Abstract The geodesics in a compact surface of negative curvature display stability properties originating in the chaotic, hyperbolic nature of the geodesic flow on the associated unit tangent bundle. Considered as a foliation of this bundle, this collection of geodesics persists in a strong way when one perturbs of the Riemannian metric, or the geodesic flow generated by this metric, or even the time-one map of this flow: for any perturbed system there is a corresponding "shadow foliation" with one-dimensional smooth leaves that is homeomorphic to the original geodesic foliation. A counterpart to this foliation stability is a curious rigidity phenomenon that arises when one studies the disintegration of volume along the leaves of this perturbed shadow foliation. I will describe this phenomenon and its underlying causes. This is work with Artur Avila and Marcelo Viana.
Friday, Feb. 22, 2013
Speaker No Seminar
Friday, March 1, 2013
Speaker John Pardon
Title: Obstruction bundles and counting holomorphic disks in Heegaard Floer homology
Abstract: I will discuss an approach to count the holomorphic disks which give the boundary operator in Heegaard Floer homology. However, no previous knowledge of Heegaard Floer homology is necessary to understand the talk. I'll discuss how to rephrase the problem of counting holomorphic disks in a certain high dimensional symplectic manifold as a lower dimensional enumerative problem. To approach this problem, we consider a Hurwitz space of ramified covers of a "domain" on a Riemann surface $\Sigma_g$ and ask to count the covers $S\to\Sigma_g$ where $S$ admits a holomorphic map to the unit disk. It turns out that in some cases, this number is equal to a certain relative Euler class of an "obstruction bundle" over the Hurwitz space, whereas in others, there are parts of the boundary that we don't yet understand how to deal with.
Friday, January 13th, 2012
Speaker: Ronen Mukamel (Stanford)
Title: Lattice Veech groups in SL(2,O_D), Part I
Friday, January 20th, 2012
Speaker: Ronen Mukamel (Stanford)
Title: Lattice Veech groups in SL(2,O_D), Part II
Friday, January 27th, 2012
Speaker: Kenji Kozai (Stanford)
Title: Ideal triangulations of pseudo-Anosov mapping tori
Friday, February 3rd, 2012
Speaker: Yitwah Cheung (San Francisco State)
Title: Bounded geodesics are winning (with Jon Chaika and Howard Masur)
Friday, February 10th, 2012
Speaker: Dimitri Zvonkine (Stanford)
Title: The psi-classes on the space of stable maps, I
Friday, February 17th, 2012
Speaker: Dimitri Zvonkine (Stanford)
Title: The psi-classes on the space of stable maps, II
Friday, February 24th, 2012
Speaker: John Pardon (Stanford)
Title: Volumes of moduli spaces of flat bundles over a Riemann surface
Friday, March 2nd, 2012
Speaker: Jenya Sapir (Stanford)
Title: Hausdorff dimension of sets of curves on surfaces
Friday, March 9th, 2012
Speaker: No Seminar this week
Friday, March 16th, 2012
Speaker: Curt McMullen (Harvard)
Title: Cascades in the dynamics of surface foliations
Friday, March 23rd, 2012
No Seminar
Friday, April 6th, 2012:
Friday, April 13th, 2012:
Speaker: Tom Church (Stanford)
Title: A conjecture on stability in the unstable cohomology of moduli space
Friday, April 20th, 2012:
Speaker: Guillaume Dreyer (USC)
Title: Geometric properties of Anosov representations
Friday, April 27th, 2012:
Speaker: Tan Ser Peow (Singapore)
Title: A dilogarithm identity on moduli spaces of curves
Friday, May 4th, 2012:
Speaker: Kasra Rafi (Oklahoma)
Title: The Teichmuller space is semi-hyperbolic
Friday, May 11th, 2012:
Speaker: Thomas Koberda (Harvard)
Title: Generalizations of the Nielsen--Schreier Theorem
Friday, May 18th, 2012:
No Seminar
Friday, May 25th, 2012:
Speaker: Shinpei Baba (Caltech)
Title: Grafting Complex Projective Structures
Friday, June 15st, 2012:
Speaker: Scott Wolpert
Title: Infinitesimal deformations of nodal stable curves