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Over the last century, logical and computational phenomena, in addition to physical ones, have provided mathematics with significant inspirations and been studied intensively. However, the very foundations of logic and computation have not been established in a mathematically satisfactory fashion. My research is concerned with this fundamental problem. 

A suitable mathematical foundation of logic and computation enables one to not only study them with the elegance, the durability and the universality of pure mathematics but also apply it to other fields of mathematics and beyond, furnishing new ideas and techniques. I am particularly interested in applying my novel foundational frameworks to (higher) categories, (algebraic) topology, functional analysis, probability, geometric groups and type systems.

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