| Time: Thursday 8/13, 5 pm |
Name: Baris Coskunuzer
Affiliation: Koc University
Title: Minimal Surfaces with Arbitrary Topology in H^2xR
Abstract: In this talk, we show that any open orientable
surface can be embedded in H^2xR as a complete area minimizing
surface. Furthermore, we will discuss the asymptotic Plateau problem
in H^2xR, and give a fairly complete solution.
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| Time : Tuesday 8/11, 2:15 pm |
Name: Stefan Friedl
Affiliation: University of Regensburg
Title: The Thurston norm via Fox calculus
Abstract: Given a 3-manifold whose fundamental group admits a
presentation with two generators and one relator we will show how one
can easily obtain the Thurston norm via Fox calculus. This is based on
joint work with Kevin Schreve and Stephan Tillmann.
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| Time : Thursday 8/13, 3:30 pm |
Name: David Futer
Affiliation: Temple University
Title: From triangulated 3-manifolds to generic few-relator groups
Abstract: Given a presentation of a group G with many more
generators than relations, where the relations are random long words,
we construct a 2-dimensional complex with nice geometry whose
fundamental group is G. This complex is built out of hyperbolic
polygons, glued by isometry along the edges, with a negative curvature
condition at the vertices. The entire construction is guided in a big
way by the study of ideal triangulations of 3-manifolds.
As a consequence of this ''geometric realization'' of the group, we
learn that G is hyperbolic and enjoys several other pleasant
group-theoretic properties. For instance, all finitely generated
subgroups are undistorted, hyperbolic, and separable. This is joint
work with Dani Wise.
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| Time : Friday 8/14, 11:45 am |
Name: Stavros Garoufalidis
Affiliation: Georgia Institute of Technology
Title: Evaluation of state integrals via Grothendieck residues
Abstract: Joint work with Rinat Kashaev. We will make a friendly introduction to state-integral invariants of ideally triangulated manifolds, and illustrate our results with computations.
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| Time : Thursday 8/13, 10:15 am |
Name: Eriko Hironaka
Affiliation: Florida State University
Title: Dilatations of pseudo-Anosov mapping classes
Abstract: I will talk about the minimum dilatation problem
for pseudo-Anosov mapping classes and some recent results for
pseudo-Anosov braid monodromies.
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| Time : Tuesday 8/11, 11:45 |
Name: BoGwang Jeon
Affiliation: Columbia University
Title: Hyperbolic 3-manifolds of bounded volume and trace field degree
Abstract: In this talk, I present my proof of the conjecture
that there are only a finite number of hyperbolic 3-manifolds of
bounded volume and trace field degree.
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| Time : Friday 8/14, 2:15 pm |
Name: Mustafa Kalafat
Affiliation: Tunceli University
Title: Constructing special 4-manifolds via hyperbolic 3-manifolds
Abstract: We use hyperbolic 3-manifold geometry to produce
4-manifolds with special structures. These are locally conformally
flat, self-dual and almost complex structures. We can construct these
4-manifolds by sketching their handşebody diagrams. If time permits,
we prove that the connected sum of two self-dual Riemannian
4-manifolds of positive scalar curvature is again self-dual of
positive scalar curvature, under a vanishing hypothesis. The proof
involves Kodaira-Spencer-Freedman deformation theory and Leray
Spectral Sequence. Again if time permits, we will discuss metrics on
the Quotients of Enriques Surfaces, and applications of the Geometric
Invariant Theory, Complex/Almost Complex and Kahler structures. This
is joint work with S. Akbulut.
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| Time : Wednesday 8/12, 11:45 pm |
Name: Effie Kalfagianni
Affiliation: Michigan State University
Title: Non orientable knot genus and the Jones polynomial
Abstract: I will talk on joint work with Christine Lee where
we use the Jones polynomial to estimate (and often calculate) the
non-orientable genus (i.e. the crosscut number) of alternating and
other families of knots.
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| Time : Wednesday 8/12, 9 am |
Name: Joanna Kania-Bartoszynska
Affiliation: National Science Foundation
Title: Structure of the Kauffman bracket skein algebra of a surface.
Abstract: The Kauffman bracket skein algebra of an orientable
surface is formed by taking linear combinations of isotopy classes of
links in the cylinder over that surface, and dividing by the Kauffman
bracket relations. We will discuss the structure of this algebra for
closed surfaces and for surfaces with boundary. The talk is based on
joint work with Charles Frohman.
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| Time : Wednesday 8/12, 5 pm |
Name: Rinat Kashaev
Affiliation: University of Geneva
Title: A hidden 4D structure of the Teichmüller TQFT
Abstract: The Teichmüller TQFT partition function of a shaped
triangulation X of a pseudo 3-manifold can written as an evaluation of
a shape independent tempered distribution, called kinematical kernel,
on a test function given by the tensor product of (shaped) quantum
dilogarithms.Remarkably, the kinematical kernel can be given an
interpretation of a partition function of a simple (generalized) TQFT
in four dimensions of the cone over X.
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| Time : Monday 8/10, 10:15 am |
Name: Mustafa Korkmaz
Affiliation: Middle East Technical University
Title: Arbitrarily long factorizations in mapping class groups
Abstract: On a compact oriented surface of genus $g$ with
$n\geq 1$ boundary components, $\delta_1, \delta_2,\ldots, \delta_n$,
we consider positive factorizations of the boundary multitwist
$t_{\delta_1} t_{\delta_2} \cdots t_{\delta_n}$, where $t_{\delta_i}$
is the positive Dehn twist about the boundary $\delta_i$. We prove
that for $g\geq 3$, the boundary multitwist $t_{\delta_1}
t_{\delta_2}$ can be written as a product of arbitrarily large number
of positive Dehn twists about nonseparating simple closed curves,
extending a recent result of Baykur and Van Horn-Morris, who proved
this result for $g\geq 8$. This fact has immediate corollaries on the
Euler characteristics of the Stein fillings of conctact three
manifolds. This is a joint work with Elif Dalyan and Mehmetcik Pamuk.
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| Time : Monday 8/10, 5 pm |
Name: Thang Le
Affiliation: Georgia Institute of Technology
Title: Kauffman bracket skein modules of 3-manifolds at roots of 1
Abstract: We extend the Kauffman bracket skein modules of
3-manifolds to marked 3-manifolds and show how the the
Chebyshev-Frobenius homomorphism appears naturally in this theory.
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| Time: Thursday 8/13, 11:45 am |
Name: Joseph Maher
Affiliation: CSI and GC, CUNY
Title: Random walks on weakly hyperbolic groups
Abstract: Let G be a group acting by isometries on a Gromov
hyperbolic space, which need not be proper. If G contains two
hyperbolic elements with disjoint fixed points, then we show that a
random walk on G converges to the boundary almost surely. This gives a
unified approach to convergence for the mapping class groups of
surfaces, Out(Fn) and acylindrical groups. This is joint work with
Giulio Tiozzo.
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| Time: Monday 8/10, 3:30 pm |
Name: Julien Marche
Affiliation: Université Pierre et Marie Curie
Title: Singular intersections on character varieties
Abstract: We study the singular intersections between a curve
in a 2-torus and the 1-dimensional sub-tori. Such a problem arises
when looking at rigidity of representations of the Dehn fillings of a
3-manifold with toric boundary.
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| Time: Wednesday 8/12, 2:15 pm |
Name: Sergei Matveev
Affiliation: Chelyabink State University
Title: Dijkgraaf-Witten Z_2 -invariants for orientable Seifert 3-manifolds
Abstract: We prove that all twice orientable Seifert
3-manifolds can be decomposed into two classes A and B such that
DW(M)=0 if M is in the class A and DW(M) =1/2 dim H^1 (M;Z_2) if M is
in the class B.
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| Time: Tuesday 8/11, 3:30 pm |
Name: Hitoshi Murakami
Affiliation: Tohoku University
Title: The colored Jones polynomials, the Chern-Simons
invariants, and the Reidemeister torsions of a knot
Abstract: We discuss a relation of the colored Jones
polynomials of a knot to the Chern-Simons invariants and the
Reidemeister torsions of its complement.
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| Time: Monday 8/10, 2:15 pm |
Name: Kate Petersen
Affiliation: Florida State University
Title: (P)SL(2,C) Representations of knot groups
Abstract: Representations of knot groups into groups such as
SU(2) and (P)SL(2,C) have many connections to 3-manifold invariants.
I'll discuss representations of knot groups into (P)SL(2,C), focusing
on two-bridge knots and an algorithm for determining 'geometric'
representations for a large class of knots including alternating
knots.
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| Time: Tuesday 8/11, 10:15 am |
Name: Alan Reid
Affiliation: University of Texas, Austin
Title: Determining hyperbolic 3-manifolds by geometric spectra.
Abstract: This talk will discuss to what extent closed
hyperbolic 3-manifolds can be determined by various geometric spectra
such as length spectra, and the set of pi_1-injective surfaces.
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| Time: Thursday 8/13, 9 am |
Name: Makoto Sakuma
Affiliation: Hiroshima University
Title: Mapping class group action on the space of geodesic
rays of a punctured hyperbolic surface
Abstract: For a hyperbolic punctured surface S of finite
area,consider the space, G, of geodesic rays emanating from
punctures. Then the mapping class group of S naturally acts on the
space G. In the first half of my talk, I will explain the role of the
action in the variations of McShane's identities for (i) punctured
surface bundles (Bowditch and Akiyoshi-Miyachi-Sakuma) and (ii)
2-bridge links (Lee-Sakuma). In the second half of my talk, I will
explain the following theorem proved by Bowditch, answering to a my
question. Theorem. The non-wandering set of the action of the mapping
class group on the space G has measure 0. I also hope to discuss the
mapping class group action on the space of "simple" geodesic rays.
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| Time: Monday 8/10, 11:45 am |
Name: Saul Schleimer
Affiliation: University of Warwick
Title: End invariants of splitting sequences
Abstract: Thurston introduced train tracks and geodesic
laminations as tools to study surface diffeomorphisms and Kleinian
groups. We'll start the talk with a relaxed introduction to these.
Then, in analogy with the end invariants of Kleinian groups and
Teichmüller geodesics, we will define the end invariants of an
infinite splitting sequence of train tracks. These end invariants
determine the set of laminations that are carried by all tracks in the
infinite splitting sequence. If there is time, we'll use these ideas
to sketch a new proof of Klarreich's theorem, determining the boundary
of the curve complex.
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| Time: Thursday 8/13, 2:15 pm |
Name: Henry Segerman
Affiliation: Oklahoma State University
Title: Veering Dehn surgery
Abstract: This is joint work with Saul Schleimer. Veering
structures on ideal triangulations of cusped manifolds were introduced
by Ian Agol, who showed that every pseudo-Anosov mapping torus over a
surface, drilled along all singular points of the measured foliations,
has an ideal triangulation with a veering structure. Any such
structure coming from Agol's construction is necessarily layered,
although a few non-layered structures have been found by randomised
search. We introduce veering Dehn surgery, which can be applied to
certain veering triangulations, to produce veering triangulations of a
surgered manifold. As an application we find an infinite family of
transverse veering triangulations none of which are layered. Until
recently, it was hoped that veering triangulations might be geometric,
however the first counterexamples were found recently by Issa, Hodgson
and me. We also apply our surgery construction to find a different
infinite family of transverse veering triangulations, none of which
are geometric.
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| Time : Tuesday 8/11, 9 am |
Name: Mehmet Haluk Sengun
Affiliation: University of Sheffield
Title: Cycle complexity of arithmetic hyperbolic 3-manifolds
Abstract: In joint work with N. Bergeron and A. Venkatesh, we
propose a conjecture which essentially says that homology classes in
arithmetic hyperbolic 3-manifolds can be represented by cycles of
small topological complexity. We prove the conjecture in special
cases using sophisticated machinery and some standard, but deep,
conjectures from number theory. As a corollary of the conjecture,
which was our original motivation for the work, we show that torsion
homology grows exponentially with respect to the volume.
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| Time: Wednesday 8/12, 10:15 am |
Name: Adam Sikora
Affiliation: SUNY BUffalo
Title: Skein Algebras of Surfaces
Abstract: For a surface F the space of links in F x [0,1]
modulo Kauffman bracket skein relations is called the skein algebra of
F, denoted by S(F). It is a non-commutative deformation of the
SL(2,C)-character variety in F and, at roots of unity, it is (almost)
the quantum Teichmuller space of F. Except for a few simplest
surfaces F, not much is known about the algebraic properties of
S(F). We are going to prove the following two fundamental properties
of skein algebras: 1. S(F) has no zero divisors, 2. Away from roots of
unity, the center of S(F) is composed of polynomials in knots parallel
to boundary components of F. We state analogous results for relative
skein algebras.
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| Time: Tuesday 8/11, 5 pm |
Name: Yasar Sozen
Affiliation: Hacettepe University
Title: Reidemeister torsion of Anasov representations
Abstract: This talks consists of two parts. In this first
part, using symplectic chain complex and pant-decompositon of closed
orientable hyperbolic surfaces, we present a formula for computing the
topological invariant Reidemeister torsion of such surfaces. The
second parts aims to prove that Reidemeister torsion is well defined
for PSL(n,R)-Anasov representations of closed orientable hyperbolic
surfaces. Using symplectic chain complex, we will also present a
formula to compute Reidemeister torsion of such representations.
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| Time: Friday 8/14, 3:30 pm |
Name: Roland van der Veen
Affiliation: University of Amsterdam
Title: Quantum invariant theory
Abstract: Three-dimensional hyperbolic geometry is the
geometry of the group SL(2,C). The aim of this talk is to explore what
happens to the geometry when one passes to quantum group. This is
relevant for understanding quantum knot invariants such as the Jones
polynomial. We illustrate our point of view using simple examples
coming from polyhedra and the Alexander polynomial.
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| Time: Wednesday 8/12, 3:30 pm |
Name: Andrei Vesnin
Affiliation: Sobolev Institute of Mathematics and Chelyabinsk State University
Title: Complexity and Turaev - Viro invariants of 3-manifolds.
Abstract: We will present recent results which demonstrate
how to use Turaev – Viro invariants to find Matveev’s complexity of
3-manifolds. The talk is based on joint results with E. Fominykh and
V. Turaev.
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| Time: Friday 8/14, 9 am |
Name: Tian Yang
Affiliation: Stanford University
Title: On type-preserving representations of the four-punctured sphere group
Abstract: We give counterexamples to a conjecture of Bowditch
that if a non-elementary type-preserving representation
$\rho:\pi_1(\Sigma_{g,n})\rightarrow PSL(2;\mathbb R)$ of a punctured
surface group sends every non-peripheral simple closed curve to a
hyperbolic element, then $\rho$ must be Fuchsian. The counterexamples
come from relative Euler class $\pm1$ representations of the
four-punctured sphere group. As a related result, we show that the
mapping class group action on each non-extremal component of the
character space of type-preserving representations of the
four-punctured sphere group is ergodic. The main tool we use is
Penner's lengths coordinates of the decorated character spaces defined
by Kashaev.
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| Time: Friday 8/14, 10:15 am |
Name: Christian Zickert
Affiliation: University of Maryland
Title: Coordinates for representations of 3-manifold groups
Abstract: We study the shape and Ptolemy varieties of a
compact 3-manifold M with a topological ideal triangulation. The
varieties give coordinates for representations of pi_1(M) in the sense
that each point determines a representation (up to conjugation). We
describe the varieties, how to compute them, and how to compute
invariants such as trace fields and complex volume.
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Funding is kindly provided by Gazi University
and the National Science Foundation (NSF).