Informal Geometry & Topology Seminar

All talks are held on Friday in 381-T, starting at 3:30 pm, unless otherwise noted.

Spring Quarter (2014):

Friday, April 18th, 2014

Speaker: Tian Yang

Title: Hyperbolic cone metrics on 3-manifolds with boundary

Friday, April 25th, 2014

Speaker Tian Yang

Title A deformation of Penner's simplicial coordinate

Friday, May 2, 2014

TBA

Winter Quarter (2013):

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, March 8, 2013

Speaker Harry Baik

Title: Groups acting on the circle with dense invariant laminations

Abstract: I propose a new way to look at the group actions on the circle via the number of transverse dense invariant laminations. As a motivational example, we characterize the Fuchsian groups in terms of the invariant laminations. Having infinitely many invariant laminations with some additional assumptions on the laminations guarantees that the given group is Fuchsian. From the ideas developed in the proof, we can also prove that having three invariant laminations with stronger assumptions gives the same result. The key ingredient is the convergence group theorem. The development of the theory was motivated by Thurston's universal circle construction for tautly foliated 3-manifold groups.

Fall Quarter (2012):

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

Title: Gap Distributions and Homogeneous Dynamics \

Friday, November 23, 2012

No Seminar

Friday, November 30, 2012

Speaker Alex Wright

Title: SL(2,R) orbit closures of translation surfaces.

Winter Quarter (2012):

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

Spring Quarter:

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