Georges Gonthier - Computer Proofs - Teaching Computers Mathematics, and Conversely
Explore computer-assisted mathematical proofs, from the four-color puzzle to homotopy type theory. Learn how computer science methods enhance mathematical language, leading to new insights and advancements in formal proofs.
A Fibrational Framework for Modal Dependent Type Theories
Explore modal extensions of homotopy type theory, their frameworks, and applications in real-cohesive and differential-cohesive HoTT. Gain insights into fibrational frameworks for modal type theories.
Formalization of Infinity Category Theory
Explore ∞-category theory's formalization, unifying mathematics, computer science, and physics. Learn synthetic reasoning and the Yoneda Lemma in this advanced mathematical seminar.
From HoTT to HOTT - Exploring Homotopy Type Theory
Explore the evolution from Homotopy Type Theory (HoTT) to Higher-Order Type Theory (HOTT) in this insightful lecture by Michael Shulman.
Formalizing the ∞-Categorical Yoneda Lemma
Explore the first formalization of ∞-category theory's Yoneda lemma using Rzk, a new proof assistant for synthetic ∞-category theory, paving the way for advanced mathematical proofs.
Homotopy Type Theory for Sewn Quilts
Explore PieceWork, an innovative programming language for quilt design inspired by Homotopy Type Theory. Learn how computational methods can enhance diversity in sewn designs and bridge programming theory with quilting craft.
Internal Parametricity Without an Interval
Explore internal parametricity in type theory without explicit geometry. Learn about a simple extension to Martin-Löf type theory and its implications for parametricity and canonicity.
A Fibrational Framework for Modal Simple Type Theories
Explore modal extensions of homotopy type theory, focusing on fibrational frameworks for modal simple type theories and their applications in topology, geometry, and spectra.
Discrete and Codiscrete Modalities in Cohesive HoTT
Explore discrete and codiscrete modalities in Cohesive Homotopy Type Theory, examining their applications in topology, differential geometry, and synthetic formalizations of mathematical concepts.
Compact Ordinals in Homotopy Type Theory and Univalent Foundations - Lecture
Explore compact ordinals in Homotopy Type Theory and Univalent Foundations with Martín Escardó's in-depth mathematical lecture at CIRM's thematic meeting.