Informal Geometry & Topology Seminar

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

Winter Quarter (2015):

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.

Fall Quarter (2014):

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.

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

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

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

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.

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

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