B.A., Boston University; M.A., Ph.D., Brown University
Science Center 370
Associate Professor of Mathematics
Research in algebraic topology, specifically calculus of functors and its applications to embeddings, including knots and links.
My area of research is algebraic topology, and more specifically calculus of functors. I have been applying this theory to the study of the rational homotopy type spaces of embeddings, and in particular to spaces of knots, links, and braids. I have also been trying to generalize finite type knot invariants to various embedding spaces, define multivariable manifold calculus and apply it to links and braids, and investigate Milnor invariants from the functor calculus viewpoint. I am coauthoring a graduate textbook on homotopy theory of cubical diagrams that underlie calculus of functors as an important technical tool.
I enjoy teaching across the curriculum, and am fortunate to have taught a variety of classes at Wellesley, including topology, abstract algebra, Galois theory, number theory, combinatorics, and others. I also designed a class on algebraic geometry and supervised independent studies on Hochschild homology, differential geometry, math behind Google, differential equations, and knot theory. Along with my colleague Stanley Chang, in 2007 I also organized and ran a “bootcamp” for some of our students who were going on to graduate school in mathematics. This program was designed to facilitate their transition to the culture and rigor of graduate school. We hope to expand this program in the future. In addition, I started the weekly math department student seminar series, which continues to run with great success.
In recent years, the mathematics department has been redesigning and strengthening its curriculum and has as a result succeeded in recruiting more majors and sending more students to excellent graduate programs in mathematics. I am fortunate to have joined the faculty at this time since my own professional goals coincide with this effort. I strive to blend the research and teaching parts of my job by introducing undergraduates to research mathematics. Teaching special topics courses, bringing mathematicians to give talks, supervising independent studies, summer research, and honors thesis are just some of the ways in which I try to convey to our students that mathematics is a vibrant, exciting research field.