Semester-long directed study on graph theory and topological graph embeddings, focusing on the Tutte polynomial, chromatic polynomial, graph colorability, and the Heawood conjecture. Explored how classical obstructions to planarity such as K₅ and K_3,3 relate to embeddings on higher-genus surfaces, and presented the connection between Euler characteristic, genus, and surface colorability in a formal talk.
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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 an algorithmic trading bot as a solo team for IMC Prosperity 4, a competitive market-making and strategy challenge. Designed and tuned trading logic for two simulated products using order book signals, moving averages, trend estimation, inventory-aware fair value models, and position-limited bid/ask placement.
Placed as a finalist in the top 10% of participants, finishing around the 91st percentile overall.
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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 an AI-powered vision system for Alzheimer’s care integrating real-time face recognition (InsightFace), object detection (YOLOv8), and context-aware narration. Built a multimodal pipeline with camera input, voice interaction, and OpenAI-based orchestration to provide environmental awareness, identity recognition, routine assistance, and emotional support.
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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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