Graham Hawkes

hawkes@math.ucdavis.edu.

I am a fifth year graduate student in the department of mathematics at the University of California in Davis, working with Anne Schilling. My interests lie in various areas of enumerative and algebraic combinatorics. Frequently my work stems from viewing algebraic structures from a combinatorial viewpoint. This is often manifested in the search for the combinatorial backbone which supports a given algebraic phenomenon. More specifically I investigate subjects such as crystal bases (for Lie and super-Lie algebras), Coxeter groups (and their relation to symmetric functions), and pure enumeration (including tableaux and partitions).

Publications:

Crystal analysis of type C Stanley symmetric functions
Simple Surface Singularities, their Resolutions, and Construction of K3 Surfaces


Preprints:

Symmetric function theory at the border of types A and C
Characterization of queer Lie supercrystals
Generalized Staircase Tableaux: Symmetry and Applications
An Elementary Proof of the Hook Content Formula



Some sequences involving tableaux and partitions:

Lattice paths on the cube by inversion number
Young tableaux of arbitrary dimension
4-dimensional bounded totally symmetric partitions
5-dimensional totally symmetric partitions
6-dimensional totally symmetric partitions
All totally symmetric partitions




Teaching:

2015: MAT22A Linear Algebra
2016: MAT22A Linear Algebra
2017: MAT145 Combinatorics
2018: MAT22A Linear Algebra