Talks, papers, and lecture notes

Foster group, Physics & Astronomy Department, Rice University

Curriculum Vitae of Matthew S. Foster

0. Recent Talks

1. Shock (ICTS Bangalore, 06-23-2023)

2. Fragile (Aspen, 12-12-2023)

2. Interference (Gainesville, 12-16-2023)

1. Papers on arXiv

2. Lecture notes

• Topological Materials Physics [Guest lecture]

Slides for a guest lecture in undergraduate solid state physics being taught at Rice in Spring 2017. This is an introduction to topological materials, mainly by way of the dimerized chain (Su-Schrieffer-Heeger) model.

"Modern" mathematical physics I: Mainly Lie algebra representation theory [Course notes]

These are course notes for a class being taught in Fall 2016 at Rice on Lie algebras and their representations. Most of the material will be standard, but the plan is for the presentation to be unabashedly applied, emphasizing visualization and algorithms at the expense of rigor and generality. I am following roughly the presentation in Robert Cahn's excellent Semi-simple Lie Algebras and Their Representations, available on the web here. The main difference is that I will work many examples and elaborate on various topics. All lecture notes will be posted here. These are intended to be complete enough for self study, and I hope they will prove generally useful for physics students that wish to learn this material. As the current course is being taught at the graduate level, I hope to cover some advanced topics by the end (some subset of Riemannian symmetric spaces and random matrix theory; classification of topological phases; affine Lie algberas, WZNW models, quantum equivalence; quantum groups, anyons, fusion and braiding rules).

1. Rotations, so(3) and su(2). [v2.1]
2. Lie groups as manifolds. SU(2) and the 3-sphere. [v1.5]
2A. SU(n), SO(n), and Sp(2n) Lie groups. [v1.5]
3. Introduction to su(3). [v1.7]
4. Killing form and commutation relations. [v1.6]
5. Roots and weights. [v2.0]
6. Cartan classification of Hamiltonians: The 10-fold way. [v1.2]
7. The classical and exceptional Lie algebras. [v1.5]
8. Highest-weight representations. [v2.5]
8b. Informal lecture--some applications. [v1.0]
9. Casimir, characters, dimension and strange formulae. [v1.8]
10. Spinor representations of SO(N). [rough notes]
11. Affine Lie algebra representation theory I. [rough notes]