I am an associate professor in the Boston College math department, studying low-dimensional
I have particular interest in interactions between Heegaard Floer homology and Khovanov homology,
as well as applications of both theories to questions about braids, Dehn surgery, and concordance.
I co-organized this topical ICERM workshop (August 4-8, 2014), partially supported by my NSF CAREER grant. See videos of
some of the (excellent) talks here! (Under "Programs and Workshops 2014/Summer 2014")
Here is the website for MT855: Surfaces, braids, and homology-type invariants, Spring 2016. Here is the website for a graduate reading seminar on the Schoenflies conjecture and generalized property R, co-organized with John Baldwin, Peter Feller, and Josh Greene during spring 2015. Here is the website for MT831: Algebraic topology and low-dimensional topology, Fall 2014. Here is the website for MT855: Applications of homology-type invariants in low-dimensional topology, Spring 2014. Here is the syllabus for MT216: Intro to Abstract Math, Fall 2013. Here is the syllabus for MT808: Graduate Algebraic Topology, Fall 2011. Here is the website for MT210: Linear Algebra, Fall 2010. Here is the syllabus for MT105: CalculusII-AP, Fall 2009. Here is the syllabus for the undergraduate knot theory course I taught at Columbia, Fall 2008.
I directed Lisa Piccirillo in a summer research project on Khovanov homology in the Summer of 2011, funded by a BC URF. Here is the poster she created, summarizing her results.
I co-led a 10-week research program for undergraduates with Jason Behrstock at Columbia University in the Summer of 2008.
Some of the students' final papers:
Amy Cen, Summary of research on variants of the Tower of Hanoi