## Assistant Professor of Mathematics

Dylan P. Thurston, Assistant Professor of Mathematics, joined the Barnard faculty in 2005. Previously, he was a Benjamin Peirce Assistant Professor at Harvard University.

At Barnard and Columbia, Professor Thurston teaches courses in calculus, analysis, and symmetry. His research is in the area of low-dimensional topology, with special emphasis on finite-type invariants and geometric 3-manifold topology.

Professor Thurston is the organizer of the Columbia University Geometry/Topology seminar.

#### Selected Publications

"The Aarhus invariant of rational homology 3-spheres III: The relation with the Le-Murakami-Ohtsuki invariant," with D. Bar-Natan, S. Garoufalidis, and L. Rozansky, *Selecta Mathematica* (in press).

"Cluster algebras and triangulated surfaces. Part I: Cluster complexes," with S. Fomin and M. Shapiro, *Acta Mathematica*. (to appear).

"A random tunnel number one 3-manifold does not fiber over the circle," with N. Dunfield, *Geometry and **Topology*Vol. 10 (2006): 2431–2499.

"Two applications of elementary knot theory to Lie algebras and Vassiliev invariants," with D. Bar-Natan and T. Le,* Geometry and Topology* Vol. 7, No. 1 (2003): 1–31.

"The Aarhus invariant of rational homology 3-spheres I: A highly non-trivial flat connection on S3,” with D. Bar-Natan, S. Garoufalidis, and L. Rozansky, *Selecta Mathematica* (N.S.) Vol. 8, No. 3 (2002): 315–339.

"The Aarhus invariant of rational homology 3-spheres II: Invariance and universality," with D. Bar-Natan, S. Garoufalidis, and L. Rozansky, *Selecta Mathematica* (N.S.) Vol. 8, No. 3 (2002): 341-371.

"On the existence of finite type link homotopy invariants," with Blake Mellor, *J. Knot Theory Ramifications* Vol. 10, No. 7 (2001): 1025–1039.

"Wheels, wheeling, and the Kontsevich integral of the unknot," with D. Bar-Natan, S. Garoufalidis, and L. Rozansky, *Israel J. **Math*Vol. 119 (2000): 217–237.

Low dimensional topology