As an undergraduate student at
Harvard University, Hutchings did an
REU project with
Frank Morgan at
Williams College that began his interest in the mathematics of soap bubbles. He finished his undergraduate studies in 1993, and stayed at Harvard for graduate school, earning his Ph.D. in 1998 under the supervision of
Clifford Taubes. After postdoctoral and visiting positions at
Stanford University, the
Max Planck Institute for Mathematics in
Bonn, Germany, and the
Institute for Advanced Study in
Princeton, New Jersey, he joined the UC Berkeley faculty in 2001. His work on circle-valued Morse theory (partly in collaboration with Yi-Jen Lee) studies torsion invariants that arise from circle-valued Morse theory and, more generally,
closed 1-forms, and relates them to the three-dimensional
Seiberg–Witten invariants and the Meng–Taubes theorem, in analogy with Taubes'
Gromov–Seiberg–Witten theorem in four dimensions. The main body of his work involves
embedded contact homology, or ECH. ECH is a holomorphic curve model for the
Seiberg–Witten Floer homology of a three-manifold, and is thus a version of Taubes's Gromov invariant for certain four-manifolds with boundary. Ideas connected to ECH were important in Taubes's proof of the
Weinstein conjecture for three-manifolds. Embedded contact homology has now been proven to be isomorphic to both
monopole Floer homology (Kutluhan–Lee–Taubes) and
Heegaard Floer homology (Colin–Ghiggini–Honda). Hutchings has also introduced a sequence of
symplectic capacities known as ECH capacities, which have applications to embedding problems for
Liouville domains. He won a
Sloan Research Fellowship in 2003. He gave an
invited talk at the
International Congress of Mathematicians in 2010, entitled "Embedded contact homology and its applications". In 2012, he became a fellow of the
American Mathematical Society. ==References==