Peter Tingley


I graduated from UC Berkeley in May 2008, where my advisor was Nicolai Reshetikhin . As a grad student I worked on a number of projects, mostly related to the representation theory of quantum groups, and in particular quantum affine algebras. I am also interested in applications of representation theory to statistical mechanics. For anyone who is interested, here is my Thesis . For those who want something shorter, here is a synopsis of the main results. If you still want to know more, you can look at my CV and other application material.

As of July 2008, I am a research fellow at the University of Melbourne (Australia), where I am working with Arun Ram, mainly studying Hecke Algebras and Fock space.

Office: Richard Berry 147
Email: P.Tingley AT ms DOT unimelb DOT edu DOT au

Seminar:

student RTGC seminar, fall 2007

Special outdoor seminar, March 21, 2008

Teaching:

Math 54, summer 2004.

Lecture notes and other short expositions:

A minus sign that used to annoy me but now I know why it is there (notes on the Jones polynomial).

Constructing the R-matrix from the quasi R-matrix.

Three combinatorial models for affine sl(n) crystals, with applications to cylindric plane partitions. Hour version or half-hour version.

The half twist. Slides , Pictures.

Publications and preprints:

Tingley, Peter. A half-twist type formula for the R-matrix of a symmetrizable Kac-Moody algebra. Preprint.

Snyder, Noah and Tingley, Peter. The half twist to U_q(g) representations. Preprint.

Tingley, Peter. A formula for the R-matrix using a system of weight preserving endomorphisms. Preprint.

Kamnitzer, Joel and Tingley, Peter. The crystal commutor and Drinfeld's unitarized R-matrix. To appear in the Journal of Algebraic Combinatorics.

Kamnitzer, Joel and Tingley, Peter. A definition of the crystal commutor using Kashiwara's involution. To appear in the Journal of Algebraic Combinatorics.

Tingley, P. Three Combinatorial Models for Affine sl(n) Crystals, with Applications to Cylindric Plane Partitions. International Mathematics Research Notices (2007) Vol. 2007, Article ID rnm143, 40 pages. doi:10.1093/imrn/rnm143. Preprint.

Haxell, P.E., Luczak, T. and Tingley, P.W. Ramsey numbers for trees of small maximum degree. Special issue: Paul Erdos and his mathematics. Combinatorica 22 (2002), no 2, 287-320.

Djokociv, Dragomir and Tingley, Peter. Natural group actions on tensor products of three real vector spaces with finitely many orbits. Electron. J. Linear Algebra 8 (2001), 60-82 (electronic).

Other math related activities:

Since January 2007, I have written reviews for MathSciNet. These can be found here. Note: this site requires a subscription.

Other:

My wife Emily plays with zome tools.

My brother Martin works on global warming.

My father Daryl grows big pumpkins. hit counter