Department of Mathematics
David Rittenhouse Lab.
209 South 33rd Street
Philadelphia, PA 19104-6395.
8-7835 on campus
pcahn (at) math (dot) upenn (dot) edu
Office: DRL 4C7
and by appointment.
Penn In Touch
Courses In Touch
I am a Hans Rademacher Instructor of Mathematics
at the University of
Pennsylvania, working in low-dimensional and geometric
I received my PhD from Dartmouth
College in 2012, where my advisor was Vladimir Chernov.
I received my BA in Mathematics, and a minor in music, from Smith
College in 2006. I was a visiting scientist at the Max Planck Institute for
from January-August 2014. During the 2015-2016 academic year I
will return to the Max Planck Institute, and in fall 2016 I will
begin a tenure-track position at Smith College.
This spring I am teaching Math 560/730, a topics course on knot
theory and low-dimensional topology.
I am interested in geometric
and low-dimensional topology.
Intersections of Loops and the Andersen-Mattes-Reshetikhin Algebra, (with V. Chernov.) J. Lond. Math. Soc. (2) 87 (2013), no. 3, 785–801.
A Generalization of the Turaev Cobracket and the Minimal Self-Intersection Number of a Curve on a Surface. New York J. Math. 19 (2013), 253–283.
The Number of Framings of a Knot in a 3-Manifold, (with V. Chernov and R. Sadykov.) J. Knot Theory Ramifications. 23 (2014), 1450072 (9 pages).
Vassiliev Invariants of Virtual Legendrian Knots, (with A. Levi.) Pacific J. Math. 273 (2015), no. 1, 21-46.
The Classification of V-Transverse Knots and Loose Legendrians, (with V. Chernov.) Submitted.
Generalization of Turaev's Virtual String Cobracket. Submitted.
Deformation and Extension of Fibrations of Spheres by Great Circles, (with H. Gluck and H. Nuchi.)
Intersections of arcs and curves on surfaces.
On the classification of non-nullhomologous Legendrians (with B. Tosun.)
Math 560/730: Low-dimensional Topology (Spring 2015)
Math 420: Ordinary Differential
Equations (Fall 2012)
Math 32: The Shape of Space, Winter 2012: A course in intuitive geometry and topology for mathematics majors.
31: Topics in Algebra,
Fall 2010: A course in
introductory group and ring theory for mathematics majors.
Math 1: Calculus with Algebra, Fall 2009: An introductory calculus course beginning with a review of precalculus.
I play the double bass. I am currently a member of the Penn Symphony Orchestra.