Contact: swissknots@math.unibe.ch
Program
Download the program as pdf.Wednesday | Thursday | Friday |
---|---|---|
09.30 – 10.20 A. Wand | ||
10.00 – 10.50 A. Pichon | coffee break | |
coffee break | 10.50 – 11.40 M. Golla | |
11.10 – 12.00 C. Livingston | 11.20 – 12.10 R. Zentner | 11.50 – 12.40 J. Hom |
14.00 – 14.50 P. Cahn | 14.00 – 14.50 A. Lobb | |
coffee break | coffee break | |
15.20 – 16.10 A. Conway | 15.20 – 16.10 H. Queffelec | |
16.20 – 17.10 M. Boileau | 16.20 – 17.10 M. Borodzik | |
18.00 Apero | 19.30 Dinner |
The talks on Wednesday and Thursday will take place in the ExWi building, room B7.
The talk on Friday will take place in the University's main building, room 101.
The conference dinner will take place in the restaurant Lokal at Militärstrasse 42, bus/tram station Breitenrain.
Charles Livingston:
Problems related to the 4-genus of knots and concordance
Wednesday 11.10 – 12.00, Exwi building, room B7
In this talk I will discuss a selection of open problems related to the concordance group of knots and the 4-genus. Topics include questions concerning torsion, symmetry properties of knots, and how the 4-genus behaves under connected sum.
Patricia Cahn:
Signatures of branched covers of the four-sphere via linking numbers in three-manifolds
Wednesday 14.00 – 14.50, Exwi building, room B7
We describe an algorithm for calculating the linking number of any two rationally null-homologous curves in a 3-fold dihedral branched cover of S^{3}. It is well known that every closed oriented three-manifold can be represented as such a cover. Therefore, our method computes the linking number of two curves in a 3-manifold whenever this number is defined. This work is a key ingredient in calculating signatures of dihedral covers of S^{4} with singular branching sets, using a formula of Kjuchukova. (Joint with Alexandra Kjuchukova).
Anthony Conway:
Computing the Blanchfield pairing of a link
Wednesday 15.20 – 16.10, Exwi building, room B7
The torsion part of the Alexander module of a link supports a hermitian form called the Blanchfield pairing. For knots, this pairing can be expressed using Seifert matrices. In this talk, I will explain how to compute the Blanchfield pairing of a link with non-zero Alexander polynomial. This is a joint work with Stefan Friedl and Enrico Toffoli.
Michel Boileau:
Cyclic branched covers of quasipositive links and L-spaces
Wednesday 16.20 – 17.10, Exwi building, room B7
Joint work with Steve Boyer (University of Quebec at Montreal) and Cameron McA. Gordon (University of Texas at Austin). We study when the n-fold cyclic cover of S^{3} branched over a strongly quasipositive link is an L-space. When the Alexander polynomial is monic we show that n ≥ 5 and that it is a non-trivial product of cyclotomic polynomials. Our results allow to calculate the smooth and topological 4-ball genera of, for instance, quasi-alternating oriented quasipositive links. They also allow to classify strongly quasipositive 3-strand pretzel links.
Anne Pichon:
The Lipschitz geometry of complex curve and surface singularities
Thursday 10.00 – 10.50, Exwi building, room B7
Let (X, 0) ⊂ (C^{n}, 0) be a germ of an analytic set. For all sufficiently small ε > 0
the intersection of X with the sphere S2n-1
ε of radius ε about 0 is transverse, and
X is locally "topologically conical," i.e., homeomorphic to the cone on its link
L_{ε} = X ∩ S2n-1
ε. However, it is in general not metrically conical: there are parts of
the link L_{ε} with non-trivial topology which shrink faster than linearly when ε tends
to 0. A natural problem is then to build classifications of the germs up to local
bi-Lipschitz homeomorphism, and what we call Lipschitz geometry of a singular
space germ is its equivalence class in this category.
There are different approaches for this problem depending on the metric one
considers on the germ. A germ (X,0) has actually two natural metrics induced
from any embedding in C^{n} with a standard euclidean metric: the outer metric is
defined by the restriction of the euclidean distance, while the inner metric is defined
by the infimum of lengths of paths in X.
I will start by reviewing the pioneering work of Pham and Teissier on Lipschitz
classification of germs of plane curves. Then I will present a joint work with Lev
Birbrair and Walter Neumann on bilipschitz classification of normal complex surface
singularities. It starts with a decomposition of a normal complex surface singularity
into its "thick" and "thin" parts. The former is essentially metrically conical, while
the latter shrinks rapidly in thickness as it approaches the origin. The thin part
is empty if and only if the singularity is metrically conical. Then the complete
classification consists of a refinement of the thin part into geometric pieces.
Raphael Zentner:
Irreducible SL(2,C)-representations of homology 3-spheres
Thursday 11.20 – 12.10, Exwi building, room B7
We prove that the splicing of any two non-trivial knots in the 3-sphere admits an irreducible SU(2)-representation of its fundamental group. Using a result of Boileau, Rubinstein and Wang, it follows that the fundamental group of any integer homology 3-sphere different from the 3-sphere admits irreducible representations of its fundamental group in SL(2,C). Our result uses instanton gauge theory and in particular holonomy perturbations of the flatness equation in an essential way.
Andrew Lobb:
Spacifying quantum knot invariants
Thursday 14.00 – 14.50, Exwi building, room B7
Khovanov cohomology is a knot invariant taking the form of a bigraded finitely generated abelian group. In fact, there is a nice way to associate a topological space to a knot, so that the cohomology of the space agrees with Khovanov cohomology – this space was constructed by Lipshitz and Sarkar. If you only care about knots in the 3-sphere, I'll tell you why you should care about this Khovanov space. I'll talk about the Khovanov space and some generalizations and extensions that I think are cool – for example current work on lifting the Lie algebra action on annular Khovanov cohomology to an action on an annular Khovanov space. This is joint work in various combinations with Dan Jones, Patrick Orson, and Dirk Schuetz.
Hoel Queffelec:
Braid group metrics from Khovanov-Seidel categorical action
Thursday 15.20 – 16.10, Exwi building, room B7
Khovanov and Seidel defined in 2000 a categorical action of the braid group on some category of modules over the zig-zag algebra, a particularly simple quotient of a path algebra. This action, that categorifies the Burau representation, turns out to be faithful, and, in a sense, provides a setup that should be thought of as a replacement for the root lattice in the study of Weyl groups. The richer structure of this categorified root lattice, and in particular the several gradings it can be endowed with, provides new tools to study the Artin-Tits braid groups. We study the metrics derived from measuring how much a given braid spreads two particular gradings, and relate them to word-length metrics in the positive braid generators or in the strongly quasi-positive braid generators. An upshot of our approach is that both studies can be run simultaneously on the same doubly-graded category: this allows us to prove a conjecture of Digne-Gobet relating dual atoms to usual atoms.
Maciej Borodzik:
Khovanov homology and periodic knots
Thursday 16.20 – 17.10, Exwi building, room B7
Given a periodic knot in R^{3} W. Politarczyk defined an equivariant version of Khovanov homology. Based on that, one can give a new obstruction for periodicity of knots in terms of standard Khovanov homology. This is a joint project with W. Politarczyk.
Andy Wand:
Filtering the Heegaard Floer contact invariant
Friday 9.30 – 10.20, Main building, room 101
The modern development of contact geometry in 3 dimensions has seen several (due to Giroux, Wendl, Latschev and Wendl, Hutchings, and others) invariants of contact structures meant in some sense to measure non-(Stein/symplectic)-fillability of the structure. We will discuss a new approach which uses Heegaard Floer homology to define an invariant with a similar aim, but which has several desirable properties lacking in earlier approaches. Time permitting, we will discuss some examples and applications. This is joint work with Kutluhan, Matic, and Van Horn-Morris.
Marco Golla:
Heegaard Floer homology and deformations of curve singularities
Friday 10.50 – 11.40, Main building, room 101
I will discuss a topological approach to the study of 1-parameter families of singular curves, using correction terms in Heegaard Floer homology. This is joint work with József Bodnár and Daniele Celoria.
Jennifer Hom:
Satellite knots and L-space surgeries
Friday 11.50 – 12.40, Main building, room 101
An L-space is a rational homology three-sphere with the simplest possible Heegaard Floer homology. Which knots admit L-space surgeries? We will give sufficient conditions for a satellite knot to admit an L-space surgery. Parts of this are joint work with Tye Lidman and Fery Vafaee.