Emily Peters

eep AT math DOT berkeley DOT edu

I graduated from the University of California, Berkeley this May. Next year I'll be a lecturer at the University of New Hampshire. In the meantime, I'm visiting MIT for the summer.

My research interests are planar algebras, subfactors, fusion categories and knots. My advisor was Vaughan Jones, and my dissertation was on "A planar algebra construction of the Haagerup subfactor."

Papers and Preprints

A planar algebra construction of the Haagerup subfactor: Preprint.

Skein Theory for the D_{2n} planar algebra (Joint with Scott Morrison and Noah Snyder): To appear in the Journal of Pure and Applied Algebra.

Research

My focus is on constructing planar algebras, and exotic subfactors. Planar algebras are a structure roughly equivalent to a pivotal category, in which certain diagrams in the plane are interpreted as morphisms. Subfactors of von Neumann algebras give an example of a planar algebra.

The simplest example of a planar algebra is the Temperley-Lieb algebra, which first arose in statistical mechanics. The planar algebra perspective on Temperley-Lieb helps explain why this algebra has close ties to both subfactors and knot theory (specifically, the Jones polynomial).

I'm particularly interested in using planar algebras to construct exotic subfactors. Exotic subfactors are those which don't come from previously studied algebraic objects, like groups, quantum groups, or rational conformal field theories. In my dissertation, I used planar algebras to construct the Haagerup subfactor, and also to find a non-standard embedding (I use this term loosely) of the Haagerup planar algebra in a graph planar algebra.

My current projects include

The extended Haagerup subfactor (Joint with Stephen Bigelow, Scott Morrison and Noah Snyder)
Constructing the D(2n) planar algebra and link invariants (Joint with Scott Morrison and Noah Snyder; there is a colorful summary of this work in the Handouts and Slides section below.)
Developing the Atlas of Subfactors, and classifying principal graphs up to Sqrt{5} (Joint with Scott Morrison and Noah Snyder)
Connecting Q-systems and planar algebras

If you'd like more details, check out my (now slightly outdated) research statement , read some blog posts about planar algebras, or email me!

Handouts and Slides

Planar Algebras and Knots: A poster from the AWM poster session at the 2009 Joint Math Meetings in DC.

Generators and Relations for the Haagerup planar algebra: Handout from my talk at the University of Toronto, December 12, 2008.

Planar algebras and the Haagerup subfactor, at the University of Tokyo operator algebras seminar, October 23, 2008. Beamer slides

Exceptional Tensor Categories in Subfactor Theory, at the MFO (Mathematisches Forschungsinstitut Oberwolfach) Arbeitsgemeinschaft on Algebraic structures in conformal field theories, April 4, 2007. Extended Abstract.

Teaching

At Berkeley, I've been the graduate student instructor for classes on calculus, linear algebra, linear algebra for math majors, and complex analysis.

I'm a former student and former and future staff member of the Hampshire College Summer Studies in Mathematics, a summer program for mathematically inclined high school students. As HCSSiM junior staff, I've taught topics including group theory, galois theory and knot theory.

What am I like as a teacher? Here's a full transcript (with illustrations!) of a talk on platonic solids which I gave at the Davis Math Circle in March 2007.