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:

    None (Summer)

  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.  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.




Research


I am interested in geometric and low-dimensional topology. 

Recent Publications:

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.


Preprints and submitted articles:

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

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

Deformation and Extension of Fibrations of Spheres by Great Circles, (with H. Gluck and H. Nuchi.)


In preparation:

Intersections of arcs and curves on surfaces.

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



Teaching


At Penn:

Math 560/730: Low-dimensional Topology (Spring 2015)

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.