7 papers
Chute Move Posets are Lattices
Ilani Axelrod-Freed, Colin Defant, Hanna Mularczyk +2
For each permutation , we consider the set of reduced pipe dreams for , partially ordered so that cover relations correspond to (generalized) chute moves. Se…
Some algebraic properties of ASM varieties
Ilani Axelrod-Freed, Hanson Hao, Matthew Kendall +2
Fulton's matrix Schubert varieties are affine varieties that arise in the study of Schubert calculus in the complete flag variety. Weigandt showed that arbitrary intersections of m…
Spectrum of random-to-random shuffling in the Hecke algebra
Ilani Axelrod-Freed, Sarah Brauner, Judy Hsin-Hui Chiang +2
We generalize random-to-random shuffling from a Markov chain on the symmetric group to one on the Type A Iwahori Hecke algebra, and show that its eigenvalues are polynomials in q w…
Quantitative Transversal Theorems in the Plane
Ilani Axelrod-Freed, João Pedro Carvalho, Yuki Takahashi
Hadwiger's theorem is a Helly-type theorem involving common transversals to families of convex sets instead of common intersections. Subsequently, Pollack and Wenger identified a n…
Measuring the Space of Metaplectic Whittaker Functions
Ilani Axelrod-Freed, Claire Frechette, Veronica Lang
Whittaker functions are special functions that arise in -adic number theory and representation theory. They may be defined on representations of reductive groups as well as thei…
Bisections of mass assignments using flags of affine spaces
Ilani Axelrod-Freed, Pablo Soberón
We use recent extensions of the Borsuk--Ulam theorem for Stiefel manifolds to generalize the ham sandwich theorem to mass assignments. A -dimensional mass assignment continuousl…