Shreya Arya

Hans Rademacher Instructor of Mathematics

University of Pennsylvania

smarya@upenn.edu

Office: DRL 3N8D

Welcome to my homepage. I obtained my Ph.D. in Mathematics at Duke University with Sayan Mukherjee and Ezra Miller in 2024.

Currently, I am a postdoc at Penn, working with Robert Ghrist.

I am interested in geometry, topology and category theory and its applications to statistics, computer science and mathematical physics.

You can find my thesis here. It was awarded the Rudin Prize for Outstanding PhD Dissertation at Duke University.

Research

Kan approximations of the persistent homology transform
with J. Curry
2025
abstract arXiv
We develop a functorial framework for approximating the persistent homology transform using Kan extensions.
Learning with frustration: Torsor CNNs
with D. Li, R. Ghrist
NeurIPS Workshop on Symmetry and Geometry in Neural Representations, 2025
abstract arXiv
We introduce Torsor CNNs, a framework connecting discrete gauge theory to group synchronization for learning on graphs with local symmetries.
Decomposing the persistent homology transform of star-shaped objects
with Giunti, Hickok, Kanari, McGuire, Turner
To appear in La Matematica, 2024
abstract arXiv
We provide a decomposition theorem for the persistent homology transform of star-shaped objects.
The Gromov-Wasserstein distance between spheres
with Auddy, Edmonds, Lim, Mémoli, Packer
Foundations of Computational Mathematics, 2024
abstract arXiv
We compute the Gromov-Wasserstein distance between spheres of different dimensions.
A sheaf-theoretic construction of shape space
with J. Curry, S. Mukherjee
Foundations of Computational Mathematics, 2024
abstract arXiv
We construct shape space using sheaf theory, providing a categorical framework for understanding spaces of geometric objects and their deformations.
Fuzzy type theory
with G. Coraglia, P. North, S. O'Connor, A. Tenorio, H. Riess
2023
abstract
We develop a type theory with semantics in categories enriched in categories of fuzzy sets, in analogy with Martin-Löf type theory and its interpretation in categories.
Dimensionality reduction for k-distance applied to persistent homology
with J.-D. Boissonnat, K. Dutta, M. Lotz
Journal of Applied and Computational Topology, 2021 · SoCG 2020
abstract paper
We show that dimensionality reduction via random projections preserves k-distance and thus persistent homology.

Recent Talks & Upcoming Travel

Upcoming
May 2026
Statistics and Stochastics for Sheaves, Shapes, Stratified and Sub-Riemannian Structures, Oberwolfach
Dec 2025
NeurIPS, San Diego
Recent
March 2025
AMS Southeastern Sectional, Clemson
Feb 2025
Geometry-Topology Seminar, Penn
Oct 2024
AMS Eastern Sectional, Albany
Nov 2023
Math Physics Seminar, UC Boulder
Oct 2023
AATRN Seminar (video)
April 2023
Statistics of Shapes and Geometry of Shape Spaces, MPI Leipzig

Teaching

Penn
Fall 2025 MATH 5000 Geometry-Topology Instructor
Spring 2025 MATH 2400 Linear Algebra & Differential Equations Instructor
Fall 2024 MATH 3200 Computational Methods in Mathematics Instructor
Fall 2024 MATH 1410 Multivariable Calculus Instructor
Duke
Spring 2024 MATH 202 Multivariable Calculus for Economists TA
Spring 2022 MATH 112L Calculus II Instructor
Summer 2022 MATH 219 Multivariable Calculus TA
Spring 2021 MATH 112L Calculus II Instructor
Summer 2021 MATH 230 Probability TA
Summer 2020 MATH 260 Python Programming in Math TA
Fall 2019 MATH 111L Laboratory Calculus I TA

Service

Fall 2026 Co-organizer, Trimester Program on Geometric Statistics, Hausdorff Institute Bonn
2021–2023 Co-director, SWiM at Duke (with I. Daubechies, D. Buck)
2022–2023 Co-president, AWM Chapter at Duke

Other

Identity Types in Context, guest post on the n-Category Café with G. Coraglia.