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Mathematical Logic Foundations

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Mathematical Logic Foundations

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Research Frontiers in Homotopy Type Theory Foundations

Investigates the connection between type theory and homotopy theory, treating types as topological spaces with higher-dimensional structure.

Synthetic Higher Categorical Structures in Type Theory
Computational Decidability of Homotopic Equivalences
Univalence and Its Constructive Computational Limits
Higher Inductive Types Beyond Classical Cohomology
Cubical Type Theory and Computational Canonicity
Infinity-Groupoids as Native Type-Theoretic Objects
Formal Verification Through Homotopy-Invariant Proofs
Non-Wellfounded Coinductive Structure in Dependent Types
Modalities and Cohesive Homotopy Type Theory
Computational Realizability of Higher Categorical Constructions

All Mathematical Logic & Foundations PhD categories