| Jan 8 |
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| Jan 15 |
Kevin Walker |
MicroSoft |
0+1+1+1 dimensional TQFTs |
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| Jan 22 |
Hessam Hamidi Tehrani |
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On the linearity problem for mapping class groups |
Formanek and Procesi have demonstrated that Aut(F_n) is not linear for n >2. Their technique is to construct a family of nonlinear groups, which we call FP-groups, and then to embed one such group in Aut(F_3). We show that no FP-groups can be embedded in mapping class groups. Thus the methods of Formanek and Procesi fail in the case of mapping class groups, providing strong evidence that mapping class groups may in fact be linear. |
| Jan 29 |
Jason Manning |
UCSB |
Bushy pseudo-characters in geometric Group theory |
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| Feb 5 |
Jason Manning |
UCSB |
Bushy pseudo-characters in geometric Group theory cont. |
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| Feb 11, 1-2pm |
Will Kazez |
U. Georgia at Athens |
Convex decompositions of 3-manifolds |
I'll talk about joint work with Ko Honda and Gordana Matic. We've been constructing and classifying tight contact structures and studying their relation to taut foliations. |
| Feb 12 3-4pm |
Koya Shimokawa |
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Boundary slopes and crossing number of knots |
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| Feb 19 |
Sylvain Maillot |
UQAM |
Characterizations of Seifert-fibered 3-manifolds and orbifolds
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Orbifolds are topological spaces locally modelled on R^n modulo
finite groups, generalizing manifolds. A 3-orbifold is Seifert-fibered
if it is foliated by circles and intervals.
The main result of this talk is a characterization of
Seifert-fibered orbifolds with infinite fundamental group by
the presence of an infinite cyclic normal subgroup in their
fundamental group. I plan to discuss this result in the case of
manifolds. I will give motivation and present an outline of the
proof, focusing on the part that involves geometrizing open 3-manifolds. |
| Feb 26 |
Damian Heard |
Melbourne |
Hyperbolic Three-Orbifolds |
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| Mar 5 |
Joseph Maher |
UCSB |
Free Z_3 actions on the three-sphere are standard. |
PhD defense |
| Mar 12 |
Swatee Naik |
U. Nevada at Reno, visiting UC Irvine |
Torsion in the classical knot concordance |
We will discuss knots in the three-sphere which have
order 4 in the algebraic concordance group, but infinite
order in the knot concordance group.
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| April 2 |
MISHA Kapovich |
University of Utah |
Foliated Seifert Conjecture |
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April 9 |
Ko Honda |
USC |
On the finiteness of tight contact structures |
Abstract: Contact geometry, in dimension three, lies at the
intersection of many fields: symplectic geometry, 3- and 4-dimensional
topology, CR-geometry, dynamics, etc. Contact structures come in two
flavors: tight contact structures which tend to reflect the ambient
geometry of the 3-manifold, and overtwisted contact structures which are
flabby (homotopic in nature) and are relatively well-understood. In
this talk, I will explain the dichotomy of 3-manifolds that carry
finitely many tight contact structures vs. those that carry infinitely
many. This is joint work with Vincent Colin and Emmanuel Giroux.
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| April 16 |
Mohamed Ait Nouh |
UCSB |
Twisted satellite knots |
Let Kn be a n-twisted knot in the 3-sphere, obtained from K along C;
and M=S3 - intN(KUC). By Thurston Dehn filling theorem, M is either Seifert
fibred, toroidal, or hyperbolic. We study these cases separately, and give a
classification of satellite and twisted knots. In particular, we prove that if M
is hyperbolic an Kn is satellite, then n=+1 or -1 or Kn is a satellite of a
tunnel number one knot and n=+2 or -2. Moreover, we give an example of a
satellite twisted knot with M hyperbolic.
This is a joint work with Daniel Matignon (University of Provence) and Kimihiko
Motegi (Nihon University).
Mohamed, |
April 23 |
David Bachman |
Cal Poly SLO |
Non-parallel essential surfaces in knot complements. |
Abstract: If a knot, K, in thin position in S^3 has at least 1 thin level
then Thompson has shown that there is a planar, meridional, essential
surface in the complement of K. Bachman and Schleimer showed that this
result also holds for knots in B^3. After reviewing these proofs I will show
that if there are at least n thin levels then there must be at least n
non-parallel, planar, meridional, essential surfaces. As a corollary I will
show that it takes at least (n-1)/2 tetrahedra to make an ideal
triangulation of the complement of K.
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April 30 |
Kenneth Bromberg |
Cal tech |
Hyperbolic cone-manifolds, short geodesics and Schwarzian
derivatives |
Given a geometrically finite hyperbolic cone-manifold, with cone
singularity sufficiently short, we construct a one parameter family of
cone-manifolds decreasing the cone angle to zero. We also control the
geometry of this one parameter family via the Schwarzian derivative of the
projective boundary and the length of closed geodesics. |
May 7 |
Jim Hoste |
Pitzer College |
Trace fields of 2-bridge knots |
The fundamental group of a 2-bridge knot has a particularly nice
presentation, having only two generators and a single relation. For
certain families of 2-bridge knots, such as the torus knots, or the twist
knots, the relation takes on an especially simple form. Exploiting this
form allows one to gain information about the representations of the knot
group into $PSL(2,C)$. In joint work with Patrick Shanahan, we determine
the trace field for all twist knots and discuss the prospects of applying
these techniques to other families of 2-bridge knots with similar
presentations. |
May 14 |
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May 21 |
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May 28 |
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June 4 |
Michel Boileau |
Toulouse visiting UCSB |
Degree one maps between small 3-manifolds |
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