HANNA MULARCZYK

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• Sign components of diagonal superspace coinvariants, with Nicolle González and John Lentfer. (2026). arXiv. Submitted.

  Abstract: We prove the sign-isotypic components of the coinvariant rings $R_n^{(2,1)}$ and $R_n^{(2,0)} \otimes R_n^{(0,1)}$ are isomorphic and show that the triply-graded multiplicity of this sign character is the Schr\"oder polynomial $S_n(q,t,a)$, divided by $1+a$. This settles the sign-character component of a conjecture of Zabrocki (2019) on a module for the Delta theorem and proves a conjecture of F. Bergeron (2020) on the multiplicity of the sign character of $R_n^{(2,1)}$. Finally, using a result of Hogancamp (2017), we enhance a recent result of Gorsky--Mellit (2026) which relates the Khovanov--Rozansky homology of the $(n,n+1)$-torus knot to $R_n^{(2,0)} \otimes R_n^{(0,1)}$, by showing that the associated Poincar\'e series for this knot can be computed from the sign component of $R_n^{(2,1)}$.

• Chute Move Posets are Lattices, with Ilani Axelrod-Freed, Colin Defant, Son Nguyen, and Katherine Tung. (2025). arXiv. Submitted.

  Abstract: For each permutation w, we consider the set PD(w) of reduced pipe dreams for w, partially ordered so that cover relations correspond to (generalized) chute moves. Settling a conjecture of Rubey from 2012, we prove that PD(w) is a lattice. To establish this result, we provide a global description of the partial order on PD(w) by showing that PD(w) is isomorphic to a poset consisting of objects called Lehmer tableaux. In addition, we prove that PD(w) is a semidistributive polygonal lattice whose polygons are all diamonds or pentagons.

• Lattice Paths and Pattern-Avoiding Uniquely Sorted Permutations. Discrete Mathematics & Theoretical Computer Science, vol. 22, no. 2, Permutation Patterns 2019, Special issues (August 31, 2021) dmtcs:6494. arXiv.

  Abstract: Defant, Engen, and Miller defined a permutation to be uniquely sorted if it has exactly one preimage under West's stack-sorting map. We enumerate classes of uniquely sorted permutations that avoid a pattern of length three and a pattern of length four by establishing bijections between these classes and various lattice paths. This allows us to prove nine conjectures of Defant.

From Dimers to Trimers.

• AMS Fall Sourtheastern Sectional Meeting, October 10, 2026; Kennesaw, GA
• The UC Berkeley Combinatorics Seminar, April 29, 2026; Berkeley, CA
• Graduate Student Combinatorics Conference at UIC; March 29, 2026; Chicago, IL

Cluster expansions, snake graphs, and continued fractions.

• Institute of Pure and Applied Math Seminar Series; April 23, 2024; Los Angeles, CA

What's the word on polyominoes?

• Yellow Pig Math Days III; July 17, 2023; Amherst, MA
• The MIT Pure Math Graduate Student Seminar; September 29, 2023; Cambridge, MA

• I am currently a teaching assistant and math mentor for MIT 18.821: Mathematics Project Laboratory.
• Since 2022, I have mentored at Girls' Angle.
• I am a 2026 National Museum of Mathematics MOST Fellow.
• In January 2026 and 2023, I mentored undergraduates through MIT's Directed Reading Program.
• In fall 2025, I was a teaching assistant for MIT 18.02: Multivariable Calculus.
• In summer 2024, I mentored high school students through MIT's mathroots.
• In fall 2020, I was a course assistant for Havard Math 155R: Combinatorics.

• One day I will link photos of some of my art and design projects here.
• I create a bi-monthly math comic called "Bea and the Sea" for The Girls' Angle Bulletin.
• The title font is IO by alphabet artist Nat Pyper. All letters are made from copies of the same two units.
• Accessibility.