Current Research

My research advisor is Ed Swartz.

I am currently studying the quotients of spheres by linear effective actions of abelian groups. I am particularly interested in finding the homology of these quotient spaces and their singular sets. My study of these spaces is facilitated by a number of combinatorial tools, especially matroids. In particular, the Poincare polynomials of these quotients can be obtained from certain Tutte polynomials of the associated matroid.

I have successfully computed the homology of any quotient of a sphere by the effective linear action of a torus. I also found the homology of the rational singular set of such an orbit space. A draft of my paper will appear here soon.

Slides from Selected Talks:

Quotients of Spheres and the Tutte Polynomial, Fall 2011
Cornell University Discrete Geometry and Combinatorics Seminar
Binghamton University Combinatorics Seminar

Finding Homology of Sphere Quotients , Fall 2009
Binghamton University Graduate Conference in Algebra and Topology (BUGCAT).

Living In a Quotient Space, Spring 2011
Binghamton University Undergraduate Math Club
Bard College Math, Computer Science, and Physics Seminar
EDGE Reunion Weekend

Matroids, Invariants, and Colorings, Spring 2010
Binghamton University Undergraduate Math Club
Bard College Math, Computer Science, and Physics Seminar

Lattices, Shellings, and Matroids- Oh My!, Spring 2010
Olivetti Club (weekly Cornell graduate student seminar)

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