Interests
I am primarily interested in number theory and algebraic geometry, especially arithmetic statistics. Broadly, all my research in arithmetic statistics thus far has been motivated by the Cohen–Lenstra heuristics. These projects are primarily concerned with computing various statistics of random groups arising in number theory, such as sandpile groups and class groups of orders in quadratic extensions.
I have also written a couple of research papers in enumerative and algebraic combinatorics, entirely on generalizations of Schützenberger's promotion map on posets.
Research
Articles in Preparation
- E. Hodges and A. Swaminathan, The average number of 3-torsion elements in class groups of orders in quadratic extensions of number fields, in preparation.
- E. Hodges, The distribution of cokernels of random Hermitian matrices with their pairings, in preparation.
Preprints
Publications
- G. Barkley, C. Defant, E. Hodges, N. Kravitz, and M. Lee, Bender–Knuth billiards in Coxeter groups, Forum of Mathematics, Sigma, 13 (2025). [journal] [arXiv]
- E. Hodges, The distribution of sandpile groups of random graphs with their pairings, Transactions of the American Mathematical Society, 377 (12 2024), 8769–8815. [journal] [arXiv]
- E. Hodges, On promotion and quasi-tangled labelings of posets, Annals of Combinatorics, 28 (2024), 529–554. [journal] [arXiv]