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

** Friday, January 16th, 2015**

**Speaker**: Emmanuel Breuillard

**Title**:Diophantine approximation on matrices and Lie groups.

Abstract: Almost two decades ago Kleinbock and Margulis introduced novel ideas from dynamics on homogeneous spaces to prove a long standing conjecture of Sprinzuk about diophantine approximation of a random point on a submanifold of $\R^n$. Kleinbock eventually showed that the diophantine exponent of a submanifold and that of its linear span are the same. In this talk I will investigate the natural generalization of these questions to submanifolds of matrices $M_{m,n}(\R)$. One result is that the diophantine exponents of a submanifold and its Zariski closure coincide. In the talk I will review the necessary background about homogeneous dynamics that leads to this analysis and describe applications to another well-known problem advertised by Sarnak in a different context, namely non-commutative diophantine approximation in Lie groups.

** Friday, September 26th, 2014**

**Speaker**: Yitwah Cheung (SFSU)

**Title**: A fundamental domain for SL(n,Z)

Abstract: In this talk I will present a fundamental domain for the action SL(n,Z) on the space of lattices SL(n,R)/SL(n,Z).
As an application, we show that Levy's constant for the exponential growth rate of best approximation denominators
can be realized as a ratio of two periods.
This is joint work with Nicolas Chevallier.

** Friday, October 3rd, 2014**

**Speaker**: Sara Maloni

** Title ** Combinatorial methods on actions on character varieties.

Abstract: In this talk we consider the SL(2,C)-character variety X of the four-holed sphere S, and the natural action of the mapping class group \MCG(S) on it. In particular, we describe a domain of discontinuity for the action of \MCG(S) on the relative character varieties X_{(a,b,c,d)}, which is the set of representations for which the traces of the boundary curves are fixed. Time permitting, in the case of real characters, we show that this domain of discontinuity may be non-empty on the components where the relative Euler class is non-maximal. (This is joint work with F. Palesi and S. P. Tan.)

** Friday, October 10th, 2014**

**Speaker**: Kathrynn Mann

** Title ** Representation spaces, flat bundles, and rigidity

Abstract:
Let S_g denote the closed, genus g surface. In this talk, I'll introduce you to the "representation space" Hom(pi_1(S_g), Homeo+(S^1)), equivalently, the space of flat circle bundles over the surface. The Milnor-Wood inequality gives a lower bound on the number of connected components of this space, but until very recently it was not known whether the bound was sharp. In fact, (in contrast to more traditional character varieties) we still don't know whether Hom(pi_1(S_g), Homeo+(S^1)) has finitely or infinitely many connected components!
I'll explain some of my recent work, which distinguishes new connected components of Hom(pi_1(S_g), Homeo+(S^1)) and identifies rigidity phenomena for certain "geometric" or "maximal" representations. We'll see that there are both parallels with, and fundamental differences between, Hom(pi_1(S_g), Homeo+(S^1)) and more familiar character varieties.

** Friday, October 17th, 2014**

**Speaker**: Anastasiia Tsvietkova (UC Davis)

** Title ** Hyperbolic links: diagrams, volume and the colored Jones polynomial

Abstract:
Since the introduction of quantum invariants into knot theory, there has
been a strong interest in relating them to the intrinsic geometry of a link
complement. For example, the Volume Conjecture claims that the volume
of a link is determined by its colored Jones polynomial. Another major task
in knot theory is to relate the geometry of a link to its combinatorial
picture, reflected in the link diagram. We will discuss how investigating the latter
question might help to approach the former one. In particular, I will show
how the upper bound for volume in terms of the twist number of a diagram
(by M. Lackenby, I. Agol and D. Thurston) can be rened for hyperbolic
links, and then expressed in terms of the coeffients of the colored Jones
polynomial for hyperbolic alternating links. This is a joint work with O.
Dasbach.

** Friday, October 31, 2014**

**Speaker**: Priyam Patel

** Title **: Effective Separability for Hyperbolic Surface and 3-Manifold Groups

Abstract: The fundamental groups of hyperbolic surfaces and 3-manifolds, referred to as surface groups and 3-manifold groups, respectively, have various algebraic finiteness properties. Two of these properties, residual finiteness and subgroup separability, have played an important role in the recent resolution of some outstanding conjectures in 3-manifold theory. We will explain how effective proofs of these properties can help us "quantify" separability and discuss the topological implications of such quantifications. We initially focus on the hyperbolic surface case and then discuss joint work with K. Bou-Rabee and M.F. Hagen extending effective separability results to hyperbolic 3-manifold groups using right-angled Artin groups.

** Friday, November 7, 2014**

**Speaker**: Inkang Kim (KIAS)

** Title ** : Gromov simplicial volume, Bounded cohomology and Rigidity

Abstract: I will discuss Gromov simplicial volume in terms of bounded cohomology and rigidity phenomena in
character variety.

** Friday, November 14, 2014**

**Speaker**: Kathy Lindsy

** Title ** : Horocycle flow orbits and lattice surface characterizations

Abstract: A translation surface is, roughly speaking, a surface made from a finite collection of polygons by gluing the edges of the polygons together according to a specific set of rules. An element of SL2R acts on a translation surface by affinely stretching each of the polygons that makes up the surface -- resulting in a new surface. The horocycle flow is the action of the one-parameter subgroup consisting of unipotent upper triangular matrices. How is the orbit of a translation surface under the horocycle flow related to the orbit of that surface under all of SL2R? It turns out that for any translation surface, after first rotating the surface by almost any angle, the horocycle orbit closure equals the SL2R orbit closure! This, in turn, leads to several new characterizations of lattice surfaces -- characterizations both in terms of the horocycle flow orbits and in terms of cylinder rank. These results are joint work with Jon Chaika.

** Friday, December 5, 2014**

**Speaker**: Jon Chaika

**Title**: Isomorphism and disjointness in interval exchange transformations and flows on flat surfaces.

**Abstract**: A basic question in dynamical systems is when are two systems isomorphic. Starting from rotations of the circle and flows on tori we will talk about the fact that typical interval exchanges and flows on flat surfaces are not isomorphic. In fact, they satisfy a stronger property called being disjoint. I will mention some consequences of these results and open questions. This includes joint work with Vaibhav Gadre and Pascal Hubert.

** 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 **

** No Seminar **

** Friday, May 9, 2014 **

** Speaker** Kim Inkang

** Title ** Kahler metric on the space of convex projective structures on surface

** Friday, May 16, 2014 **

** Speaker** Illya Gekhtman (U. Chicago)

** Title ** Patterson-Sullivan Theory for Subgroups of Mapping Class Groups and Orbit Counting in Teichmuller Space

** Friday, May 23, 2014 **

** No Seminar **

** Friday, May 30, 2014 **

**No Seminar **

** Thursday, June 5, 2014 (Note Special day and time)**

** Speaker** Tom Church

** 2:15p-3:15p in 383-N **

** Title ** Geometric spaces of geometric structures: geometry

** Friday, June 6, 2014 (The seminar will be in 383-N)**

** Speaker** Tom Church

** Title ** Geometric spaces of geometric structures: low-dimensional topology

** 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 Weilâ€“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.

** 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
\

** Friday, November 23, 2012 **

**No Seminar**

** Friday, November 30, 2012 **

**Speaker** Alex Wright

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

** 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

Last modified: Sat Jan 07 09:30:09 PST 2012