The first two-ish weeks will be devoted to a crash course on linear algebra and related concepts that are important for the REU. A tentative schedule is below. Links to lecture notes will be provided as they become available. Note: while these sessions are referred to as lectures, they are expected to be more interactive.
Preliminaries can be found at this link.
Week 1 (June 5th to June 7th): The first few days are devoted to a crash course (of sorts) on linear algebra.
Wednesday, June 5th, 2024:
Morning: “Sophisticated” linear algebra and group theory.
Afternoon: Orthogonal, symmetric, Hermitian, and unitary matrices.
Thursday, June 6th, 2024:
Morning: The Spectral Theorem
Afternoon: Basic “axioms” of quantum mechanics.
Friday, June 7th, 2024:
Morning: Symmetric polynomials, characteristic polynomials, and different “bases” of symmetric polynomials.
Afternoon: Gaussian Unitary Ensemble, motivations from physics, and Wigner’s Semicircle Law.
Week 2 (June 10th to June 14th): For most of the week I will be attending a summer school, but there are still a few things going on with the REU.
Monday, June 10th, 2024:
Students are invited to attend the summer school that I will be at.
Tuesday, June 11th, 2024:
Since I am attending the summer school all day, two of the students will be asked to give (unsupervised) presentations to the group.
Wednesday, June 12th, 2024:
Morning: Nothing, as I am in summer school.
Afternoon: Lie algebras, classical matrix Lie algebras as examples, other examples of matrix Lie algebras.
Thursday, June 13th, 2024:
Since I am attending the summer school all day, the other two students will be asked to give (unsupervised) presentations to the group.
Friday, June 14th, 2024:
Morning: Nothing, as I am in summer school.
Afternoon: Symmetries in quantum mechanics as unitary representations, infinitesimal symmetries, perhaps with a focus on “electron spins” as an example of an \(SU(2)\)-representation.
Week 3 (June 17th to June 21st): This week will focus on applications of the linear algebra taught so far, with an emphasis on “super” things.
Monday, June 17th, 2024:
Morning: Bosons vs. Fermions.
Afternoon: Super linear algebra as a natural home for bosons and fermions.
Tuesday, June 18th, 2024:
All day: Supersymmetric quantum mechanics as a baby case of supersymmetry.
Wednesday, June 19th, 2024:
There is nothing scheduled due to the holiday.
Thursday, June 6th, 2024:
Morning: Super Lie algebras.
Afternoon: Superconformal Lie algebras in dimensions 2 and 3.
Friday, June 7th, 2024:
Nothing is scheduled for this day yet, but I anticipate things spilling over their allotted times and/or needing to reschedule, so this is our “free” day (which will likely fill up).