Peter Tingley

Over the last few years I have worked on a number of projects, mostly related to the representation theory of quantum groups, and in particular quantum affine algebras. For an overview of my work up to May 2008, here is a synopsis of my thesis. More updated information can be found in my CV and application package.

Office: 2-332
Email: ptingley@math.mit.edu

Seminars I organize/have organized:

• Pure maths student seminars, Melbourne 2009
• Algebra, Geometry and Topology seminar, Melbourne, semester 1, 2009;
• Student Representation theory geomerty and combinatorics seminar, Berkeley, Fall 2007
• Special outdoor seminar, Berkeley, March 21, 2008

Expository notes:

• Notes on Fock space.
• Explicit crystal maps between cylindric plane partitions, multi-partitions and multi-segments.
• 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.

Slides from talks:

• Some combinatorics related to affine sl(n) representation theory (Suny Albany Colloquium, Oct 30, 2009).
• Realizations of affine sl(n) crystals (given in Korea Sept 2009, and at MIT Oct 2009).
• 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:

• Savage, Alistair and Tingley, Peter. Quiver grassmannians, quiver varieties and the preprojetive algebra. Preprint.
• Tingley, Peter. Monomial crystals and partition crystals. Preprint.
• 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 for U_q(g) representations. Preprint.
• Tingley, Peter. Some results on the crystal commutor and affine sl(n) crystals (my thesis).
• 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. Journal of Algebraic Combinatorics. 29 Issue 3, p315, 2009.
• Kamnitzer, Joel and Tingley, Peter. A definition of the crystal commutor using Kashiwara's involution. Journal of Algebraic Combinatorics, 29 Issue 2, p261, 2009.
• Tingley, Peter. 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.
• While in Berkeley I taught some classes at the Oakland/East Bay math circle and the Davis math circle.
• I spent the 2005-2006 accademic year as an 8th grade math teacher at Frick middle school in Oakland California.

Other:

• My wife Emily plays with zome tools.
• My brother Martin drinks coffee.
• My father Daryl grows big pumpkins.