A combinatorial framework for discrete vector bundles with connection is introduced on simplicial complexes, with discrete curvature, gauge transformations, and flat connections computing twisted de Rham cohomology.
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Introduces tangential Bayes denoiser for Riemannian Gaussian mixtures on manifolds via spectral Laplace-Beltrami approximation, with nearly Bayes risk in low noise and minimax optimality on the circle.
Generalizes Landau-Ginzburg models of Dubrovin-Zhang form to Dynkin type A, develops a pole-collision comparison on Hurwitz space strata, and proves a prepotential structural result plus the Ma-Zuo conjecture for arbitrary rank and dimension.
An open-sourced Unified Autonomy Stack fuses LiDAR, radar, vision and inertial data with sampling-based planning and control barrier functions to deliver resilient autonomy on aerial and ground robots in challenging real-world settings.
The thesis constructs the étale fundamental group via the étale topology and recovers it alongside topological and motivic versions through Tannakian duality.
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Nonparametric Riemannian Empirical Bayes, and Denoising Measurements on Manifolds
Introduces tangential Bayes denoiser for Riemannian Gaussian mixtures on manifolds via spectral Laplace-Beltrami approximation, with nearly Bayes risk in low noise and minimax optimality on the circle.
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Landau-Ginzburg models of generalised Dubrovin-Zhang form and pole collision: Dynkin-type A
Generalizes Landau-Ginzburg models of Dubrovin-Zhang form to Dynkin type A, develops a pole-collision comparison on Hurwitz space strata, and proves a prepotential structural result plus the Ma-Zuo conjecture for arbitrary rank and dimension.
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The Unified Autonomy Stack: Toward a Blueprint for Generalizable Robot Autonomy
An open-sourced Unified Autonomy Stack fuses LiDAR, radar, vision and inertial data with sampling-based planning and control barrier functions to deliver resilient autonomy on aerial and ground robots in challenging real-world settings.
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\'Etale Fundamental Groups -- a geometric and topological approach to fundamental groups in algebraic geometry
The thesis constructs the étale fundamental group via the étale topology and recovers it alongside topological and motivic versions through Tannakian duality.