29 citations · 42 across the 12 of their papers we have counts for
14 papers
On the language of palindromic reduced words in a Coxeter group
Asilata Bapat
We prove that the language of palindromic reduced words in a Coxeter system is regular if and only if the Coxeter group is a direct product of a finite Coxeter group with finitely…
A sphere of spherical objects
Asilata Bapat, Anand Deopurkar, Anthony M. Licata
Given a Bridgeland stability condition on a 2-Calabi--Yau category, we define a simplicial complex that encodes the Harder--Narasimhan filtrations of spherical objects. For 2-Calab…
MatrixNet: Learning over symmetry groups using learned group representations
Lucas Laird, Circe Hsu, Asilata Bapat +1
Group theory has been used in machine learning to provide a theoretically grounded approach for incorporating known symmetry transformations in tasks from robotics to protein model…
Some remarks about the faithfulness of the Burau representation of Artin--Tits groups
Asilata Bapat, Hoel Queffelec
We discuss the extension of the faithfulness question for the Burau representation of braid groups to the case of Artin--Tits groups. We prove that the Burau representation is not…
Wigglyhedra
Asilata Bapat, Vincent Pilaud
Motivated by categorical representation theory, we define the wiggly complex, whose vertices are arcs wiggling around points on a line, and whose faces are sets of wiggly arc…
Computing the Matching Distance of 2-Parameter Persistence Modules from Critical Values
Asilata Bapat, Robyn Brooks, Celia Hacker +3
The exact computation of the matching distance for multi-parameter persistence modules is an active area of research in computational topology. Achieving an easily obtainable exact…
-deformed rational numbers and the 2-Calabi--Yau category of type
Asilata Bapat, Louis Becker, Anthony M. Licata
We describe a family of compactifications of the space of Bridgeland stability conditions of any triangulated category following earlier work by Bapat, Deopurkar, and Licata. We pa…
Spherical objects and stability conditions on 2-Calabi--Yau quiver categories
Asilata Bapat, Anand Deopurkar, Anthony M. Licata
Consider a 2-Calabi--Yau triangulated category with a Bridgeland stability condition. We devise an effective procedure to reduce the phase spread of an object by applying spherical…
Morse-based Fibering of the Persistence Rank Invariant
Asilata Bapat, Robyn Brooks, Celia Hacker +2
Although there is no doubt that multi-parameter persistent homology is a useful tool to analyse multi-variate data, efficient ways to compute these modules are still lacking in the…
A Thurston compactification of the space of stability conditions
Asilata Bapat, Anand Deopurkar, Anthony M. Licata
We propose compactifications of the moduli space of Bridgeland stability conditions of a triangulated category. Our construction arises from a viewing a stability condition as a me…
Recollement for perverse sheaves on real hyperplane arrangements
Asilata Bapat
We consider a hyperplane arrangement in defined over , and the associated natural stratification of . The category of perverse sheaves smoo…
The Bernstein-Sato -function of the Vandermonde determinant
Asilata Bapat, Robin Walters
The Bernstein-Sato polynomial, or the -function, is an important invariant of singularities of hypersurfaces that is difficult to compute in general. We describe a few different…
Torus actions and tensor products of intersection cohomology
Asilata Bapat
Given certain intersection cohomology sheaves on a projective variety with a torus action, we relate the cohomology groups of their tensor product to the cohomology groups of the i…
Lower central series of free algebras in symmetric tensor categories
Asilata Bapat, David Jordan
We continue the study of the lower central series of a free associative algebra, initiated by B. Feigin and B. Shoikhet (arXiv:math/0610410). We generalize via Schur functors the c…