Adam Simon Levine

Brandeis University
Mathematics Department, Office 96-205
415 South Street
Waltham, MA 02453
E-mail: levinea at brandeis.edu
Telephone: (781) 736-3056

I am an NSF Mathematical Sciences Postdoctoral Research Fellow at Brandeis University. I study low-dimensional topology, specifically Heegaard Floer homology and its applications to concordance and other areas of knot theory. My curriculum vitae can be found here.


Papers


Thesis

My Ph.D. thesis is Applications of Heegaard Floer homology to knot and link concordance, supervised by Peter Ozsváth at Columbia University. It consists in large part of my first four papers, listed above. Here is a summary in sonnet form:

Our goal is one whose application's nice
For smooth four-manifold topology:
To tell if certain knots and links are slice
With bordered Heegaard Floer homology.

We seek concordance data that detect
Some links obtained by Whitehead doublings,
As well as knots we get when we infect
Along two of the three Borromean rings.

Some lengthy work with bordered Floer then proves
How τ for satellites like these is found.
We see, by this result and cov'ring moves,
That smooth slice disks our links can never bound.

The theorem's proved, the dissertation's done,
But all the work ahead has just begun.


Teaching

Spring 2012:

Math 15a - Applied Linear Algebra
Math 121b - Topology II

Fall 2011:

Math 15a - Applied Linear Algebra
Math 221a - Topology III

Past courses at Columbia University:

Calculus II - Summer 2007
Linear Algebra - Summer 2008