On Mathematical Work of Maryam Mirzakhani [pdf]
Mathematical Research in Iran and the Concern
of Quality [pdf]
Discussions with Cedric Villani on Research
Life in Mathematics [pdf]
Related
Papers
Splicing Knot complements
Heegaard Floer homology of the 3-manifold which is
obtained by splicing a pair of knot complements may
be described in terms of the knot Floer complexes
associated with the two knots. This description may
then be used to show that if a homology sphere
contains an incompressible torus then its Heegaard
Floer groups are non-trivial.
Associated with the boundary of a sutured
3-manifold, together with A. Alishahi, we define
an algebra, which is generated over the integers
by variables which are in correspondence with the
sutures. The sutured Floer complex associated with
the sutured manifold is then defined as a chain
complex with coefficients in this algebra. We are
currently working on defining a corresponding
cobordism map.
Together with I. Setayesh, we have been exploring
the kappa ring of the Delign-Mumford
compactifiaction of the moduli space of curves with
markings. In particular, we have been able to
compute the asymptotic growth of the rank of this
ring.
In collaboration with A. Kamalinejad and N.
Bagherifard we have started the study of the link
between Heegaard Floer homology and the balanced
presentations of the fundamental group of a given
closed manifold.
I am a member of the organizing committee of the
annual conference "Frontiers in Mathematical
Sciences", which is a gathering of Iranian
Mathematicians.
Together with Meysam Nassiri, I co-organize
Meetings on Contemporary Mathematics at IPM. MCM is
organized 2 or 3 times each year, with the goal of
introducing active areas of contemporary research in
mathematics to the Iranian mathematics community.
