Contact Information:
I have left Penn, and am currently a software engineer at Google. You can reach me at jbandlow at gmail dot com.
Teaching:
For the spring semester of 2011, I taught Math 103. Course information, including complete lecture notes, are available below:
Research:
My research is in the field of algebraic combinatorics. In particular, I have spent a lot of time trying to understand the combinatorics of symmetric functions, including Macdonald polynomials, Hall-Littlewood polynomials, k-Schur functions, Grothendieck polynomials, Schubert polynomials, and other related objects.
Some Papers/Preprints:
Combinatorial expansions in K-theoretic bases (with Jennifer Morse).
The Murnaghan-Nakayama rule for k-Schur functions (with Anne Schilling and Mike Zabrocki).
A new proof of a theorem of Littlewood (with Michele D'Adderio).
On the uniqueness of promotion operators on tensor products of type A crystals (with Anne Schilling and Nicolas Thiéry).
A new characterization for the m-quasiinvariants of S_n and explicit basis for two row hook shapes (with Gregg Musiker).
Combinatorics of Macdonald polynomials and extensions (doctoral dissertation under the direction of Adriano Garsia).
Quasiinvariants of S_3 (with Gregg Musiker).
A Weight Preserving Bijection Between Schroeder Paths and Schroeder Permutations (with Eric Egge and Kendra Killpatrick).
An Area-to-Inv Bijection Between Dyck Paths and 312-avoiding Permutations (with Kendra Killpatrick).
Slides from recent talks:
A Murnaghan-Nakayama rule for k-Schur functions: FPSAC 2011 slides
A tour through symmetric funtion theory via the Murnaghan-Nakayama rule: Lehigh Colloquium slides
A Murnaghan-Nakayama rule for k-Schur functions: Affine Schubert Calculus Workshop slides.
Grothendieck expansions of symmetric polynomials: FPSAC 2010 slides
Sage Worksheets
Sage is an excellent open-source mathematical software system. Below are some presentations on Sage that I have given, in the Sage notebook format.
- Affine Schubert Calculus Workshop (July 2010)
- An Introduction To Algebraic Objects
- An Introduction To Symmetric Functions
Pictures
I've put some pictures I've taken on Flickr.