Amanda Burcroff

MIT School of Science Dean's & NSF Postdoctoral Fellow

MIT

she/her

Preprints

  1. Positivity of generalized cluster scattering diagrams, 2025. With Kyungyong Lee and Lang Mou.
  2. Broken lines and compatible pairs for rank 2 quantum cluster algebras, 2024. With Kyungyong Lee.
  3. On faces and Hilbert bases of Kostka cones, 2023.
  4. Realizable standard Young tableaux, 2023. With Igor Araujo, Alexander E. Black, Yibo Gao, Robert A. Krueger, and Alex McDonough.

Published Research

  1. Higher q-continued fractions, European Journal of Combinatorics 131, 104244, 2026. With Nicholas Ovenhouse, Ralf Schiffler, and Sylvester W. Zhang.
  2. Scattering diagrams, tight gradings, and generalized positivity, Proceedings of the National Academy of Sciences 122 (18), e2422893122, 2025. With Kyungyong Lee and Lang Mou.
         ○ FPSAC Extended Abstract. Séminaire Lotharingien de Combinatoire, 93B, 33, 2025.
  3. Quasiperiods of magic labeling quasipolynomials, Australasian Journal of Combinatorics 92 (2), pg 382–398, 2025. With Margaret Bayer, Tyrrell B. McAllister, and Leilani Pai.
  4. On Dyck path expansion formulas for rank 2 cluster variables, Algebraic Combinatorics 7(2), pg 529-553, 2024.
  5. Near classification of compact hyperbolic Coxeter d-polytopes with d+4 facets and related dimension bounds, European Journal of Combinatorics 120, 103957, 2024.
         ○ FPSAC Extended Abstract. Séminaire Lotharingien de Combinatoire 89B, 26, 2023.
  6. Unimodality and monotonic portions of certain domination polynomials. Discrete Mathematics, 346 (9), 113508, 2023. With Grace O'Brien.
  7. Sets arising as minimal additive complements in the integers. Journal of Number Theory, 247, pg 15-34, 2023. With Noah Luntzlara.
  8. Domination parameters of the unitary Cayley graph of ℤ/nℤ. Discussiones Mathematicae Graph Theory, 43 (1), pg 95-114, 2023.
  9. Tightness of domination inequalities for direct product graphs. Discrete Mathematics, 344 (9), 112495, 2021.
  10. Generalized Lyndon factorizations of infinite words. Theoretical Computer Science, 809, pg 30-38, 2020. With Eric Winsor.
  11. Pattern-avoiding permutation powers. Discrete Mathematics, 343 (11), 112017, 2020. With Colin Defant.
  12. (k, λ)-anti-powers and other patterns in words. The Electronic Journal of Combinatorics, 25, #4.41, 2018.

Other Work

  1. "Positivity in Cluster Algebras and Their Generalizations", my PhD thesis completed at Harvard University advised by Lauren Williams
  2. "On Compact Hyperbolic Coxeter Polytopes with Few Facets", my master's thesis completed at Durham University under the supervision of Pavel Tumarkin
  3. "Tropical Structures in Mirror Symmetry", an essay written for the University of Cambridge Part III Mathematics Program and set by Mark Gross (available upon request)
  4. "Johnson Schemes and Certain Matrices with Integral Eigenvalues", an expository paper written for the 2017 UChicago Math REU under the supervision of László Babai