- Professor, University of Nevada, Reno, 2009-present, Current teaching load: 15 credits/year (3+2)
- Core Mathematics Director, University of Nevada, Reno, 2008- 2014, Reduced teaching load: 6 credits/year (1+1)
- Visiting Researcher, McMaster University, April 2008
- Visiting Researcher, Indiana University, October 2007
- Associate Professor, University of Nevada, Reno, 2003- 2009
- General Member, Mathematical Sciences Research Institute, Berkeley, Ca, February 2001
- Visiting Scholar, University of California, Berkeley, March 2001
- Post Doctoral Visitor, Harvard University, September-November 2000
- Assistant Professor, University of Nevada, Reno, 1999-2003
- Visiting Assistant Professor, Swarthmore College, 1996-1999
- Britton Postdoctoral Fellow, McMaster University, Hamilton, Ontario, 1994-1996
- Visiting Researcher, Max Planck Institut für Mathematik, Bonn,
- Germany January-June 1995
- Visiting Assistant Professor, University of California, Irvine, 1992-1994
My research interests include low-dimensional topology, knot theory, symplectic geometry, and gauge theory, as well as various interdisciplinary areas.
Several current projects are related to traceless SU(2) character varieties of knots and links, as well as higher rank analogs. There are a variety of interesting ways to decompose knot complements along a surface, splitting it into tangles. The traceless character varieties of the tangles produce Lagrangian submanifolds in the traceless character variety of the splitting surface, which is symplectic. The Fukaya category of this symplectic space provides a very useful algebraic framework to study these situations. These character varieties are related to singular instanton knot Floer homology, Khovanov homology and Casson-Lin invariants.
- University of California, Berkeley B.A., Mathematics 1985
- University of California, Berkeley Ph.D., Mathematics 1992
- The Fukaya category of the pillowcase, traceless character varieties, and Khovanov Cohomology (with M. Hedden, M. Hogancamp, and P. Kirk), to appear in Trans. Amer. Math. Soc. Preprint at arXiv:1808.06957.
- A note on orderability and Dehn filling (with X. Zhang), Proc. Amer. Math. Soc. 147 (2019), 2815-2819. Preprint at arXiv:1807.00742.
- Holonomy perturbations in a cylinder, and regularity for traceless SU(2) character varieties of tangles (with P. Kirk), Quantum Topology , 9 (2018), no. 2, 349-418. Preprint at arXiv:15111.00308.
- The pillowcase and traceless representations of knot groups, II: A Lagrangian-Floer theory in the pillowcase (with M. Hedden and P. Kirk) , J. Symplect. Geom. 16 (2018), no. 3, 721-815. Preprint at arXiv:1501.00028.
- The SU(2) Casson-Lin invariant of the Hopf link (with H. Boden), Pacific J. Math. 285 (2016) , no. 2, 283-288. Preprint at arXiv:1601.06017.