Investigating generative models defined on Riemannian manifolds and discrete geometric structures. Current focus includes score-based diffusion processes on curved spaces, conformal generative modeling on triangulated surfaces, and Laplacian-based kernels on cellular complexes.

Reading Lou et al. (Scaling Riemannian Diffusion Models)
Reading Dorobantu et al. (Conformal Generative Modeling on Triangulated Surfaces)
Reading Alain et al. (Gaussian processes on cellular complexes)

Semester-long directed study on knot sliceness and 4-manifold topology, centered on Lisa Piccirillo’s 2020 proof that the Conway knot is not slice. Worked through the geometric and algebraic techniques underlying the argument, including constructions in smooth 4-manifold theory, and presented findings in a formal talk.
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Built a custom 3D transformation system from scratch in Processing using 4×4 homogeneous matrices, implementing translation, rotation (X/Y/Z), scaling, and hierarchical composition via a matrix stack.
Developed both orthographic and perspective projection routines, manually performing world-to-screen coordinate transformations without relying on built-in OpenGL functions.
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Implemented a neural network pipeline to reconstruct 3D geometry from a single 2D silhouette image using voxel-based representations. Designed a 2D CNN encoder to map 128×128 inputs to a 512D latent space and a 3D transpose-convolution decoder to generate a 32³ occupancy grid. Extracted meshes using Marching Cubes and evaluated performance on ModelNet10 and ShapeNet datasets.
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Developed a website-based AI art critic using the OpenAI API and LangChain to provide structured, technique-focused feedback grounded in composition, perspective, lighting, and form. Additionally explored computer vision techniques for image analysis using TensorFlow.
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A collection of algorithmic artworks developed in Processing, exploring structure, symmetry, and emergent form. Many pieces are generated using iterative dynamical systems, including Julia sets and hyperbolic transformations, and rendered via log-density mapping techniques.
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