The only places that \(s_1s_2\cdots s_n\) appears as a subword of \(w_0\) are contained in the shaded boxes.

### A variety of combinatorial objects

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. Links to these projects along with photos and descriptions are on the coding page.

The pictures on the left are illustrations of some of the objects I care about. You can find more information about them in the papers below, or better yet, ask me about them!

### Research with students

Amaechi Abuah ('21), me, Charles Yang ('19), and Gabrielle Kerbel (MHC '20)

Algebraic Splines Research Group, Summer 2018.

In the summer of 2018, I worked with three students on algebraic splines. What can we say about splines over a general ring with unity? Does the supersmoothness property for polynomial splines extend to algebraic splines? What sorts of algorithms will work for finding splines over general rings?

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.

E. Drellich

Journal of Algebraic Combinatorics, ** 41** (2015), no. 2, 539-575.

Combinatorics of Equivariant Cohomology: Flags and Regular Nilpotent Hessenberg Varieties.

Doctoral Dissertation.