I like research projects that let me count fun mathematical objects: plane trees, Young diagrams, graphs, root systems, matrices, even strands of RNA. My work bridges several mathematical worlds including: algebra, algebraic geometry, combinatorics, and molecular biology.
Some of these problems have let me to use 3D printing to visualize the objects I study. In Summer 2017, in collaboration with the SPEED program run by Swarthmore Media Services, two students and I put together a website to 3D print Cayley graphs of reflection groups.
The pictures on the left are illustrations of some of the objects I care about. The top one can be 3D printed, you can download the .stl file here. You can search for them in the papers below, or better yet, ask me about them!
If you are a student interested in working with me, check out these problems to get you started thinking about the sorts of things I think about.
Papers and preprints
The Containment Poset of Type A Hessenberg Varieties.
E. Drellich, Submitted.
Geometric combinatorics and computational molecular biology: Branching polytopes for RNA sequences.
E. Drellich, A. Gainer-Dewar, H. Harrington, Q. He, C. Heitsch, and S. Poznanovic
Algebraic and Geometric Methods in Discrete Mathematics. Contemporary Mathematics 685 (2017), 137-154.
Valid plane trees: Combinatorial models for RNA secondary structures with Watson-Crick base pairs.
F. Black, E. Drellich, and J. Tymoczko
Accepted to SIAM J. of Discrete Mathematics.
A module isomorphism between $H^*_T(G/P)\otimes H^*_T(P/B)$ and $H^*_T(G/B)$.
E. Drellich and J. Tymoczko
Communications in Algebra, 45, (2017), no.1, 17-28.
Monk's Rule and Giambelli's Formula for Peterson Varieties of All Lie Types.
Journal of Algebraic Combinatorics, 41 (2015), no. 2, 539-575.
Combinatorics of Equivariant Cohomology: Flags and Regular Nilpotent Hessenberg Varieties.
You can email me at edrelli1 (at) swarthmore.edu.