Braid loops with infinite monodromy on
the Legendrian contact DGA
Joint with Roger Casals.
arXiv:2101.02318.
Here is the Mathematica notebook associated with the paper.

fillings.nb,
a notebook containing computations of filling augmentations and
monodromy for Legendrian (1)closures of positive braids, as
described in the paper.

Topological strings, Dmodel, and knot
contact homology
Joint with Mina Aganagic, Tobias Ekholm, and Cumrun Vafa.
Adv. Theor. Math. Phys. 18
(2014), no. 4, 827956.
Here are the Mathematica notebooks associated with the paper.

An atlas of Legendrian knots
Joint with Wutichai Chongchitmate.
Exp. Math. 22 (2013), no. 1, 2637.
See here.

Combinatorial knot contact homology
and transverse knots
Adv. Math.
227 (2011), no. 6, 21892219.
The Mathematica packages used to compute transverse homology as
described in the paper are available for download:
 transverse.m, which calculates
the
full invariants in the noncommutative setting. In order to run this
package, the user first needs to install the noncommutative algebra
package NCAlgebra.
 transversecomm.m, which
calculates the abelianized versions of the invariants. This does not
require NCAlgebra to run.
 transverseexamples.nb,
an executable notebook containing the computations cited in Section 5.2
of the paper, except for the m(10_{145}) and 12n_{591}
knots.
Before executing this notebook (and the next one), first download
transverse.m. One can use
transversecomm.m instead, since the augmentationnumber calculations
use only the abelianized versions of the invariants, but for some
reason the calculations run much faster with transverse.m than with
transversecomm.m.
 trans1014512n591.nb, a
notebook containing the computations of augmentation numbers for the
m(10_{145}) and 12n_{591} knots.
Also available:
 AugmentationPolynomials.nb,
a notebook containing threevariable augmentation polynomials for
various small topological knots, including: all knots with 7 or fewer
crossings; the (2,3), (2,5), (2,7), (2,9), (3,4), and (3,5) torus knots; the
knots 8_{5}, 8_{15}, 8_{20}, 8_{21},
9_{42}, 10_{132}, and 10_{139}; and
connected sums of trefoils. These polynomials were obtained via Mathematica
(with the help of the above packages) and Macaulay2 and are presented
without proof; documentation can be provided upon request.
Revised JulyAugust 2013 (added 7_{4}, 7_{6},
7_{7}, 8_{5}, 8_{15}, and 9_{42}, and
corrected 8_{21}).

Transverse knots distinguished by
knot Floer homology
Joint with Peter
Ozsváth and Dylan
Thurston.
J. Symplectic Geom.
6 (2008), no. 4, 461490.
Here is a mirror of the C program cited in the
paper: TransverseHFK.c. To compile and
run it, type cc TransverseHFK.c followed by a.out at
the command prompt. To try the program on a different grid diagram,
first edit the file appropriately.

Framed knot contact homology
Duke Math. J.
141 (2008), no. 2, 365406.
Here are the Mathematica packages which compute the invariants
in
the paper. They are essentially soupedup versions of the
packages from “Knot and braid invariants from contact
homology I” below, with a few things removed. Currently they require
a braid input; if there's interest, I can
post updated versions which allow calculation in terms of a knot
diagram.
 framedDGA.m, which gives the
full
invariants in
the noncommutative category.
In order to run this package, the user first needs to install
the noncommutative algebra package NCAlgebra/NCGB, available
from http://www.math.ucsd.edu/~ncalg/.
 framedDGAcomm.m, which gives
the commutative
version of the invariants and does not require any additional packages.

Knot and braid invariants from contact
homology I
Geom. Topol.
9 (2005), 247297.
Here are the Mathematica notebooks and packages,
in various flavors, which compute the invariants used in the paper.
 DGA.nb, with the full
versions of the invariants (except linearized homology; see below).
In order to run this notebook, the user first needs to install
the noncommutative algebra package NCAlgebra/NCGB, available
from http://www.math.ucsd.edu/~ncalg/.
Instructions on how to use the code are included in the notebook.
 DGAabelian.m, which calculates
the invariants in the commutative setting, and does not require
NCAlgebra/NCGB.
For instructions, input the package and
type “?Instructions”.
 DGAlin.m, which calculates
linearized
knot contact homology.
For instructions, input the package and
type “?Instructions”.
This package requires the use of another package,
IntegerSmithNormalForm.m, which can be downloaded from the Mathematica
Information Center here.
