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

  1. E. Hodges and A. Swaminathan, The average size of 3-class groups of orders in quadratic extensions of number fields, in preparation.
  2. E. Hodges and A. Swaminathan, A parametrization of 3-class groups of quadratic rings over Dedekind domains, in preparation.
  3. E. Hodges, Cokernels of random Hermitian matrices with quadratic integer entries, in preparation.

Preprints

Publications

  1. 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]
  2. 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]
  3. E. Hodges, On promotion and quasi-tangled labelings of posets, Annals of Combinatorics, 28 (2024), 529–554. [journal] [arXiv]

Theses

  1. E. Hodges, 3-torsion in class groups of orders in number fields (Harvard senior thesis). [PDF]