Research Interests

My primary research focus is low-dimensional manifolds and knot theory. I am especially interested in invariants of 3-manifolds and knots that are constructed using gauge theory, including Floer homology and the Casson invariant, as well as many related invariants such as knot polynomials, signature, Khovanov homology.

Much of my recent work involves traceless character varieties of knots and links. The traceless character variety is the set of homomorphisms from the knot or link group to SU(2). There are also higher rank analogs, character varieties with a condition fixing the meridional conjugacy classes.

I also have been involved in several interdisciplinary projects related to engineering and climate science.

Below are my publications, some of which can be downloaded in pdf form.

Preprints and Publications


This webpage is under construction. Check back for updates. (In the meantime, many of the recent papers listed above are listed on the mathematics preprint arxiv.)
last updated 1/31/17

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