Asilata Bapat

Research

Work in progress

A contracting flow on the stability manifold in type \(A\) (with Anand Deopurkar, Anthony Licata)
In progress.
Talks: QUACKS II 2022

The sphere of spherical objects (with Anand Deopurkar, Anthony Licata)
In progress.
Talks: Sydney 2024 (notes), Davis 2022 (slides), LAGOON 2022 (slides), AustMS 2021 (slides)

Papers

\(q\)-deformed rational numbers and the 2-Calabi–Yau category of type \(A_{2}\) (with Louis Becker, Anthony Licata)
Forum of Mathematics, Sigma, 11, e47 (2023).
Talks: Sydney 2024 (notes), BIMSA-YMSC 2024 (slides), Sydney 2022 (slides), MIT 2022 (slides), Paris 2022 (slides), ICERM 2022 (slides), DiTS 2021 (slides, video)

(pdf, arXiv)

Spherical objects and stability conditions on 2-Calabi–Yau quiver categories (with Anand Deopurkar, Anthony Licata)
Mathematische Zeitschrift 303, 13 (2023).
Talks: INI Cambridge 2024 (notes), FD Seminar 2022 (slides), GPRT seminar 2022 (notes)

(pdf, arXiv, journal)

Computing the matching distance of 2-parameter persistence modules from critical values (with Robyn Brooks, Claudia Landi, Celia Hacker, Barbara Mahler, Elisabeth Stephenson)
Preprint.

(arXiv)

Morse-based fibering of the persistence rank invariant (with Robyn Brooks, Claudia Landi, Celia Hacker, Barbara Mahler)
Research in Computational Topology 2 (2022), pp. 27–62

(arXiv, journal)

A Thurston compactification of the space of stability conditions (with Anand Deopurkar, Anthony Licata)
Submitted.
Talks: INI Cambridge 2024 (notes), FD Seminar 2022 (slides), DiTS 2021 (slides, video), AMS special session 2021 (slides), RepNet 2021 (video), UGA 2020 (slides), Mooloolaba 2020 (slides)

(pdf, arXiv)

Recollement for perverse sheaves on real hyperplane arrangements
Journal of Algebra, 568 (2021), pp. 61–90
Talks: Melbourne 2018 (notes)

(pdf, arXiv, journal)

The strong topological monodromy conjecture for Coxeter hyperplane arrangements (with Robin Walters)
Mathematical Research Letters 24 (2017), no. 4, 947–954
Talks: JMM 2017 (slides)

(pdf, journal)

Torus actions and tensor products of intersection cohomology
Pacific Journal of Mathematics 276 (2015), pp. 19–34
Talks: AMS special session 2017 (slides)

(pdf, arXiv, journal)

Lower central series of free algebras in symmetric tensor categories (with David Jordan)
Journal of Algebra, 373 (2013), pp. 299–311

(pdf, arXiv, journal)

Not for publication

Equivariant cohomology and the localization theorem
Topic proposal (expository).

(pdf)

The Bernstein-Sato \(b\)-function of the Vandermonde determinant (with Robin Walters)
Preprint (not for publication).

(arXiv)

Code

Categorical braid group actions (with Anand Deopurkar)
This sage code computes the braid group action on the triangulated category of complexes of projective modules over the zig-zag algebra of a quiver.

(github)