Chern forms on partial flag varieties
A conjectural new description of the Littlewood-Richardson rule
Two-row Springer fibers
Someday, hopefully: orbit harmonics and parking functions
Feel free to reach out at dorawood@mit.edu if these topics are of interest to you! Let's work together :)
What's this paper about?
The ubiquitous functions are fundamentally related to the complete graph . Postnikov and Shapiro generalized them to any graph by defining graphical parking functions. Just like classical parking functions, graphical parking functions can be studied from the perspective of representation theory. This article specializes to the case of complete bipartite graphs. Using a combinatorial lattice path model of Snider and Yan, we give a combinatorial proof of an analogue of a theorem of Berget and Rhoades.
with Ankur Moitra and Alex Postnikov. Uploaded to ArXiv (2026)
What's this paper about?
A beautiful, classical result of Knutson, Tao, and Klyachko answered a conjecture of Alfred Horn about eigenvalues of sums of matrices, giving a geometric and combinatorial proof via honeycombs. This proof makes use of (and historically motivated some) Lie theory, Schubert calculus, representation theory, etc... We reprove the result using only very down-to-earth tools (linear algebra, calculus, combinatorics) giving new insight into why honeycombs control eigenvalue spectra, with potential algorithmic applications.
What's this paper about?
Schur positivity is a phenomenon demonstrated by many important symmetric functions. In this paper, we are interested in key positivity, which generalizes Schur positivity to all (not necessarily symmetric) polynomials. We give a new theoretical framework for proving key positivity, and apply it to obtain three generalizations of important Schur positivity results.
I presented this paper at the Minnesota Combinatorics Seminar and Graduate Student Combinatorics Conference 2026, and presented a poster with Rosa at FPSAC 2026.
with Annie Guo. Submitted (2026)
What's this paper about?
Forest polynomials are beautiful recent objects, first introduced by Nadeau and Tewari in their study of the permutahedral variety. They have close connections with Schubert polynomials. We study the relationship between forest polynomials and Schubert polynomials through the lens of permutation pattern avoidance.
Important note: we found an error in our original work, and plan to upload a corrected version of the paper very soon.
with Guy Moshkovitz. Won Best Paper at Computational Complexity Conference 2026.
What's this paper about?
Our original motivation was a 'structure theorem' for non-surjective polynomials over finite fields, inspired by previous work of Thomas Karam. We ended up proving new bounds for arithmetic circuit complexity based on the geometry of their polynomial images.
with Son Nguyen and Joseph Vulakh. To appear in Electronic Journal of Combinatorics.
What's this paper about?
d-Complete posets were defined and studied by Proctor. They exhibit phenomena like hook length formulas and jdt-behavior, generalizing Young tableaux. We give the first purely combinatorial proof of the hook length formula for d-complete posets by defining a generalization of the celebrated RSK bijection.
with Chau Nguyen and Son Nguyen. To appear in Algebraic Combinatorics.
What's this paper about?
We give a new combinatorial interpretation of the Littlewood-Richardson coefficients which comes with two upshots: first, it provides a computationally efficient rule for computing TL-imminants of Jacobi-Trudi matrices, and second, it gives insight into the Lam-Postnikov-Pylyavskyy Schur log concavity conjecture (now proved fully by Speyer). Our interpretation has other fun combinatorics, like a nice interaction with Bender-Knuth involutions.
I co-presented a poster on this paper at FPSAC 2026.
Appeared in Electronic Journal of Combinatorics.
What's this paper about?
SEMs and CHMs are algebraically/geometrically motivated analogues of the usual monomials, defined and studied by Fomin and Postnikov in the context of quantum Schubert calculus. We show a cute fun fact: the number of single SEM Schubert polynomials is given by Fibonaccis, and the number of single CHM Schubert polynomials is given by powers of two.
with Guilherme Zeus Dantas e Moura and Ramanuja Kandalam. Appeared in Algebraic Combinatorics.
What's this paper about?
We prove that the cluster monomials of a graph Laurent phenomenon algebra (defined by Lam and Pylyavskyy) form a linear basis, and this linear basis is positive when the underlying graph is a tree. This result is an analogue of a celebrated theorem of Caldero and Kelly.
I co-presented a talk on this paper at JMM 2024.
with Nora Frankl. Appeared in Discrete and Computational Geometry.
What's this paper about?
This was my first official research paper! We study and solve several graphical variants of the infamous Unit Distance Problem, inspired by previous work of Kupavski and Frankl. These variants are of the form 'what if you count more complicated subgraphs than single edges in a unit distance graph?' It is surprising(!!) that this question is sometimes easier (sometimes much easier!) than the original Unit Distance Problem, even though it seems like it should be more complex.
As an undergrad, I was in a large research group mentored by Colin Adams. We published these two papers in hyperbolic knot theory:
Hyperbolic Knotoids (we extended the notion of hyperbolic volume from knots to "knotoids"). Published in European Journal of Mathematics, 2024.
Generalizations of Knotoids and Spatial Graphs (we generalized several knot invariants to a broader setting). Published by the Cambridge Philosophical Society, 2024.