I am now an Assistant Professor at CSU Long Beach. For my new website click here.

My Research


I study low dimensional geometry and topology with an emphasis on knot theory.

The world in which we live is three dimensional. This basic fact implies that we live in some 3-manifold. In this way, the study of 3-manifolds illuminates the nature of the universe. Knotting phenomena in manifolds is so rich that a complete understanding of it would lead to a complete understanding of all 3-manifolds. The broad goal of my research is to study 3-manifolds via knots.

My recent research investigates the structure of 3-manifolds and the knots they contain by applying modern techniques such as thin position and distance in the curve complex to classical constructions such as Heegaard splittings, Dehn surgery and diagrammatic knot invariants.

Submitted Papers


Genus Bounds Bridge Number for High Distance Knots(with Marion Campisi, Jesse Johnson, Scott Taylor and Maggy Tomova) Submitted

Bridge distance, Heegaard genus, and Exceptional Surgeries(with Marion Campisi, Jesse Johnson, Scott Taylor and Maggy Tomova) Submitted

High Distance Bridge Surfaces(with Maggy Tomova and Michael Yoshizawa) Submitted

Bridge Number and Tangle Products to appear in Algebraic & Geometric Topology

A Decomposition Theorem for Higher Rank Coxeter Groups(with Ryan Ottman) to appear in Communications in Algebra

Width is not Additive(with Maggy Tomova) to appear in Geometry & Topology

Companions of the Unknot and Width Additivity(with Maggy Tomova) to appear in J. Knot Theory Ramifications

Bridge Number and Conway Products Algebr. Geom. Topol. 10: 789-823 (electronic), 2010.

Alternating Augmentations of Links J. Knot Theory Ramifications, 18 (2009), 67-73.