| Date | Speaker | Title and Abstract |
| Wednesday
Oct 4 |
Jean-Baptiste Meilhan UC Riverside |
Introduction to finite type
invariants |
| Wednesday
Oct 11 |
Jean-Baptiste Meilhan UC Riverside |
Introduction to finite type
invariants II After defining and studying last week the notion of Goussarov-Vassiliev invariants of knots and links, we show how similar finite type invariants theories can be developped for 3-manifolds. Next we introduce the notion of C_n-move, which gives a complete topological characterization of the information contained by Goussarov-Vassiliev knot invariants: Goussarov and Habiro showed indeed that two knots are related by a sequence of C_n-moves if and only if they are not distinguished by Goussarov-Vassiliev invariants of degree < k. We will consider here the case of links (where this equivalence is not true in general) and of string links (where this equivalence is a conjecture). |
| Wednesday
Oct 18 |
Derek Wise UC Riverside |
Higher electromagnetism and volumetric field theory |
| SATURDAY Oct 21, 10-11am, |
JiaJun Wang Berkeley/Columbia |
A combinatorial description of
$\widehat{HF}$ and $\widehat{HFK}$. Abstract:
Heegaard Floer homology is an invariant for closed three-manifold,
which also gives invariants for four-manifolds, knot and links, and
contact structures, etc. Conjecturally, Heegaard Floer homology is
equivalent to the Seiberg-Witten theory. We will give a combinatorial
description of the hat version Heegaard Floer homology of any closed
oriented three-manifold. Our algorithm also allows us to compute the
hat version of knot Floer homology (and link Floer homology) of a null
homologous link in an arbitrary three-manifold. This is joint work with
Sucharit Sarkar.
|
| SATURDAY Oct 21, 11:15-12:15pm |
Yi Ni Princeton University |
Knot Floer
homology detects fibred knots. Abstract: Knot
Floer homology is a knot invariant introduced by Ozsvath and Szabo, and
by Rasmussen. The Euler characteristic of knot Floer homology gives
rise to the Alexander polynomial of a knot, so many properties of
Alexander polynomial can be generalized to knot Floer homology. For
example, if a knot is fibred, then its knot Floer homology is "monic".
Ozsvath and Szabo conjectured that the converse of the previous fact is
also true, namely, if the knot Floer homology is monic, then the knot
is fibred. In this talk, we will discuss a proof of this conjecture,
based on the works of Paolo Ghiggini and of the speaker. A corollary is
that if a knot in S^3 admits a lens space surgery, then the knot is
fibred.
|
| Wednesday
Oct 25 |
Yeon Soo Yoon Hannam University |
Title: Mapping spaces and Cyclic maps In this talk, we consider the following problems; 1) In general, the path components of the mapping space almost never have the same homotopy type. Under what conditions, do they have the same homotopy type? 2) It is known that the evaluation fibration Omega X --> X^S1 --> X is a fiber homotopically trivial iff for any space B and any map g:Sigma B --> X, g is cyclic. Clearly, cat~(Sigma B) <= 1 for any suspension space \Sigma B. What is a necessary and sufficient condition to be for any space Z with cat~(Z) <= k and any map g:Z --> X, g is cyclic ? |
| Wednesday
Nov 1 |
Stefano Vidussi UC Riverside |
Symplectic 4-manifolds and
subgroup separability Abstract: In this talk I will overview some problems and results in the study of symplectic 4-manifolds. In particular I will discuss how the problem of classifying product symplectic manifolds can be reduced to some standard conjectures in 3-dimensional topology, leading to a complete solution for suitable cases. |
| Wednesday
Nov 8 |
Cornelia
Van Cott Indiana University |
Braid length and its relationship
to the number of braid strands Abstract: Every knot can be represented by infinitely many different braids. In 2004, Gittings discovered some surprising examples of knots for which these braid representatives become simpler as the number of strands is increased. We will study this occurrence and discuss several general relationships between braid length and the number of braid strands. |
| Wednesday Nov 15 |
Bob Pelayo Caltech |
Complexes of Seifert Surfaces
in S^3 Abstract: This talk focuses on Kakimizu's complexes of incompressible and minimal genus Seifert surfaces for a given link L. These simplicial complexes are defined using a disjointness property and are conjectured to be contractible. While global properties of these complexes are relatively scarce, many local properties have been discovered by Gabai, Sakuma, and Kakimizu. We will discuss these properties, as well as compute several explicit examples for certain classes of links. Further, we will utilize geometric concepts like minimal surfaces (those with mean curvature zero) to obtain diameter bounds on these complexes for hyperbolic links. |
| Wednesday Nov 22 |
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| Wednesday Nov 29 |
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| Wednesday Dec 6 |
Danny Stevenson UC Riverside |
Schreier theory for Lie 2-algebras The notion of a connection on a principal bundle is ubiquitous in geometry and physics. Recently, motivated by string theory, there has been an interest in generalisations of principal bundles, in which groups are replaced by groupoids. Developing the geometry of these generalised principal bundles, known as `gerbes', is an important problem. In the case of ordinary principal bundles, Atiyah gave an elegant formulation of the notion of a connection in terms of a splitting of an exact sequence of Lie algebras. In this talk we will present a classification theorem for extensions of `Lie 2-algebras' - certain categories whose sets of objects and morphisms have the structure of Lie algebras - and show how the geometry of gerbes can be understood in this framework. We will try to illustrate how these ideas could be put to use in studying bundles with structure group String(n). |
| Wednesday Dec 13 2pm-- at Serge 268 |
Danny Stevenson UC Riverside |
Schreier theory for Lie
2-algebras Continued. |
| Date | Speaker | Title and Abstract |
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