- Contact

Department of Mathematics

David Rittenhouse Lab.

209 South 33rd Street

Philadelphia, PA 19104-6395.

(215) 898-7835

8-7835 on campus

pcahn (at) math (dot) upenn (dot) edu

Office: DRL 4C7 - Office Hours:

On leave from Penn.

Feel free to email me!

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I am a Hans Rademacher Instructor of Mathematics
at the University of
Pennsylvania, working in low-dimensional and geometric
topology.
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.

Next fall I will be teaching Math 500 (Topology) and Math 104
(Calculus). If you have questions about these courses please feel
free to email me or check out the websites from previous years at the
bottom of this page.

I will be at the Max Planck Institute for Mathematics in Bonn, Germany from January 1 until August 15, 2014.

I am interested in geometric
and low-dimensional topology.

The Classification of V-Transverse Knots and Loose Legendrians, (with V. Chernov.)

The Number of Framings of a Knot in a 3-Manifold, (with V. Chernov and R. Sadykov.) Submitted.

A
Generalization of Turaev's Virtual String Cobracket. Submitted.

Vassiliev Invariants of
Virtual Legendrian Knots, (with A.
Levi.) To appear in Pacific J. Math.

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.

Intersections
of Loops and the Andersen-Mattes-Reshetikhin Algebra,
(with
V. Chernov.) J. Lond. Math. Soc. (2) 87 (2013), no. 3, 785–801.

Undergraduate work:

Permutation Notations for
the Exceptional Weyl Group F_4,
(with R. Haas, A. G. Helminck, J. Li, and J. Schwartz.)
Involve, Vol. 5 (2012), No. 1,
81–89. (NCSU REU)

Color-Permuting
Automorphisms of Cayley Graphs, (with M.
Albert, J. Bratz, T. Fargus, N. Haber, E. McMahon, J. Smith, S.
Tekansik). Congressus Numerantium
190, November 2008, pp. 161-171. (Lafayette REU)

Unfolding
Smooth Prismatoids, (with N.
Benbernou and J. O'Rourke). (Preprint from summer research at Smith College).

Math 500: Topology (Fall 2013, Fall 2014)

Math 240: Calculus, Part III (Fall 2013)

Math 420: Ordinary Differential
Equations (Fall 2012)

Math 104: Calculus, Part I (Fall 2012, Spring 2013, Fall 2014, Spring 2015)

Math 32: The Shape of Space, Winter 2012: A course in intuitive geometry and topology for mathematics majors.

Math
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.