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Joshua Tan

Personal photo - Joshua Tan

Joshua Tan

Doctoral Student


Geometry, topology, category theory, artificial intelligence, complex systems


I apply geometry and topology to artificial intelligence. Concretely, this means using geometric language and thinking to unify different parts of AI, from reactive architectures in robotics to learning algorithms such as neural networks to the design of complex systems. You can find out more at my project page.

I am currently working with David Spivak and Andrea Censi on category theory for co-design problems, a broad class of optimization problems. I also work with Sokwoo Rhee and other members of NIST on hybrid indicator frameworks for smart cities.

Previously, as part of an NSF fellowship program, I worked with David Spivak and his lab at MIT on applied category theory, specifically on categorical approaches to data integration and to complex systems modeling. During my M.S., I worked with Misha Gromov on the mathematical foundations of AI.

Before math, I worked in robotics at ScazLab, where I helped program robots in several human-robot-interaction experiments.

Before robots, I studied art history at Yale, where I wrote my senior thesis on the sublime.

I am collecting my thoughts and questions into a summary of my research (the first version was my master’s thesis); any suggestions would be greatly appreciated! The paper is modeled on this paper by Andreas Holmstrom.