Hanna Mularczyk

I'm a fourth year Mathematics PhD student at MIT, advised by Alexander Postnikov and supported by an NSF GRFP. My research interests are in enumerative and algebraic combinatorics, and currently I'm focused on partially ordered sets and tilings. My other creative interests are in printmaking, photography, and combinatorial art and design.

Research

Please click on the paper title to show or hide the abstract.

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

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.

Selected Talks

From Dimers to Trimers.

The UC Berkeley Combinatorics Seminar, April 29, 2026; Berkeley, CA
Graduate Student Combinatorics Conference at UIC; March 29, 2026; Chicago, IL
Geometry, Statistical Mechanics, and Integrability Reunion Conference; December 11, 2025; Lake Arrowhead, CA

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

Teaching and Outreach

Since 2022, I have mentored at Girls' Angle.
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.

Potpourri

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.

HANNA MULARCZYK