department of mathematics
Ph.D. California Institute of Technology
Honors and Awards
- Liftoff Fellowship, Clay Mathematics Institute, 2000
- Alfred P. Sloan Doctoral Dissertation Fellowship, 1999 − 2000
My research is mainly focused on the topology and geometry of 3-dimensional manifolds.
These manifolds have striking geometric and combinatorial structures. One
goal of my research is to explore the connections between these structures and other
areas of mathematics, such as knot theory and geometric group theory.
- Immersed essential surfaces in hyperbolic 3-manifolds, Comm. Anal. Geom. 10 (2002), 275-290.
- Laminar branched surfaces in 3-manifolds, Geom. Topol. 6 (2002) 153-194.
- Boundary curves of surfaces with the 4-plane property, Geom. Topol. 6 (2002) 609-647.
- Heegaard surfaces and measured laminations, I: the Waldhausen conjecture, Invent. Math. 167, (2007), 135-177.
- Heegaard surfaces and measured laminations, II: non-Haken 3-manifolds, J. Amer. Math. Soc., 19 (2006) 625-657.