Research projects
Manifold reconstruction from Morse critical points
With Vidit Nanda · University of Oxford · July 2026–present
- Study the critical points of height functions across different directions.
- Investigate how much geometric information their critical-point data preserves.
- Identify conditions under which an embedded manifold can be reconstructed.
Symmetry-invariant kernels for molecular shape spaces
With Marina Meilă · University of Waterloo / Vector Institute · March–October 2026
- Study group actions and quotient-space models of molecular configurations.
- Explore symmetry-invariant kernels and representations for shape comparisons.
- Evaluate invariance computationally under selected permutation and dihedral transformations.
Manifold cohomology estimation
With Jürgen Jost and Marzieh Eidi · Max Planck Institute · July 2025–February 2026
- Estimate cohomological features of manifolds from finite point clouds.
- Investigate spectral scale selection using Hodge-Laplacian information.
- Experiment with witness complexes and landmark selection to manage computational cost.
Earlier reading
Topological data analysis
Directed reading with Herbert Edelsbrunner: computational topology, stability, persistent homology, and persistence modules. · 2024–2025
Geometric formalisms of mechanics
Directed reading with Thomas Strobl and Hadi Nahari: differential geometry, Dirac structures, and singular Riemannian foliations. · 2024
Publications
Persistent Patterns in Eye Movements: A Topological Approach to Emotion Recognition
Preprint · 2025 · Arsha Niksa, Hooman Zare, Ali Shahrabi, Hanieh Hatami, Mohammadreza Razvan
arXiv ↗
Effects of Roughness on Rarefied Gas Flow in a Microfluidic Channel with Porous Walls
19th Fluid Dynamics Conference · 2021 · Arsha Niksa, Amirreza Soheili, Vahid Bazargan
Publication ↗