Patricia Cahn




  1. 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

  2. Office Hours:

    Calculus: Thursday 1-2, Friday 3-4
    Topology: Monday 4:20-5:20,
                    Tuesday 1-2
    And by appointment.

  3. Links:

    Penn AWM
    Blackboard
    MathSciNet
    Arxiv
    AMS
    AWM
    Penn In Touch
    Courses In Touch

Patricia Cahn

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.  I was a visiting scientist at the Max Planck Institute for Mathematics from January-August 2014.

This semester I am teaching Math 500 (Topology) and Math 104 (Calculus).


Next spring I will teach Math 560/730, a topics course on knot theory and low-dimensional topology. 



Research


I am interested in geometric and low-dimensional topology. 

Recent Publications:

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.

Submitted Preprints:

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

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.

In preparation:

Intersections of arcs and curves on surfaces.

Infinitesimal fibrations of spheres by great circles (with H. Gluck and H. Nuchi.)

On the classification of non-nullhomologous Legendrians (with B. Tosun.)



Teaching



At Penn:

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)

At Dartmouth:

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.


Music


I play the double bass. I am currently a member of the Penn Symphony Orchestra.