Speakers:
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Sebastian Baader (University of Bern)
Marius Huber (University of Bern)
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| Title: |
Plane algebraic
curves, positive braids and Heegaard Floer
homology
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Description:
|
The main purpose
of this course is to study isolated singularities
of plane algebraic curves by knot theoretical
methods.
In the first lecture, we explain the dichotomy
between simple and non-simple singularities, which
is based on the difference between the topological
and analytical equivalence of singularities. We
will prove that all singularities of multiplicity
two are simple, and give an easy example of a
non-simple singularity of multiplicity four.
In the second lecture, we discuss links associated
with isolated singularities of plane curves, and,
more generally, positive braid links. As we will
see, the links associated with simple
singularities can be characterized as prime
positive braid links which admit a positive
definite Seifert form.
The third lecture focuses on the canonical fibre
surface of positive braid links. In particular, we
will see how these surfaces can be constructed by
an operation called positive Hopf plumbing. This
provides a simple description of their
monodromies.
The fourth lecture will be a research talk by
Marius Huber on the Floer homology of positive
fibred Pretzel knots. These admit an even simpler
Hopf plumbing structure than positive braid knots.
We describe a pair of mutant knots of this type
that cannot be distinguished by the hat version of
Floer homology. Moreover, we give a conjectural
picture on the Floer homology that implies
mutation invariance for this class of knots.
|
Date &
Time:
|
Tuesday, Jan. 31,
2017, 14:00-15:30
Wednesday, Feb. 1, 2017, 15:30-17:00
Monday, Feb. 6, 2017, 14:00-15:30,
Tuesday, Feb. 7, 2017, 14:00-15:30
|
Location:
|
Lecture Hall 1,
IPM Niavaran Building,
Niavaran Square, Tehran
|
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