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

• Strong L-spaces and left-orderability (with Sam Lewallen)
[abstract] [pdf]

• A combinatorial spanning tree model for knot Floer homology (with John Baldwin)
[abstract] [pdf]

[abstract] [pdf] Journal of Topology, to appear.

• Knot doubling operators and bordered Heegaard Floer homology
[abstract] [pdf] Journal of Topology, to appear.

• On knots with infinite concordance order
[abstract] [pdf] Journal of Knot Theory and its Ramifications, to appear.

• Computing knot Floer homology in cyclic branched covers
[abstract] [pdf] Algebraic & Geometric Topology 8 (2008), 1163--1190.

### 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
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