Over the last century, logical and computational phenomena, in addition to physical ones, have provided mathematics with significant inspirations and been studied intensively. Nevertheless, logic or computation has not been captured in a mathematically satisfactory manner. I am concerned with this fundamental problem, and one of my goals is to establish the very foundation of mathematics in a syntax-free fashion via mathematics of physics, logic and computation, in which the three fields are unified yet distinguished by a single framework.

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A suitable foundation of physics, logic, computation and mathematics 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 foundational framework to (algebraic) topology, geometry, (functional) analysis, (higher) category theory, logic and type theory.