Triposes and Gödel's Dialectica Interpretation
Exploring semantic presentation of Gödel's Dialectica interpretation using triposes, addressing previous work and suggesting solutions to related questions in mathematical logic.
Two Observations on Intuitionistic Logic and Arithmetic
Explore intuitionistic logic and arithmetic through finite type formalisation and negative translations. Gain insights into extensional and intensional models, decidable atomic formulas, and equality at higher types.
Refinement Type Systems and Martin Lof Type Theory
Explores refinement type systems, their connection to Martin-Lof type theory, and various notions of comprehension. Discusses recent work on functors as type refinement systems and Isbell duality theorem.
On B-adic Representation of Irrational Numbers
Explore b-adic representation of irrational numbers with Lars Kristiansen, delving into advanced mathematical concepts and their applications in number theory and analysis.
Erik Palmgren: A Constructive Examination of a Russell Style Ramified Type Theory
Exploration of ramified type theory in Martin-Löf type theory, examining functional reducibility and its applications in constructive mathematical analysis. Introduces an intuitionistic ramified type theory.
First Order Concatenation Theory vs First Order Number Theory
Comparative analysis of first-order concatenation theory and number theory, exploring similarities, differences, and extensions with bounded quantifiers in string-based structures.
Matthias Baaz - Fast Cut Elimination in Intuitionistic Logic
Explores elementary procedure for eliminating prenex cuts in intuitionistic logic, with implications for classical logic. Discusses surprising results in quantifier-based cut elimination.
Anton Freund- Bachmann Howard Fixed Points
Explores dilators, Bachmann-Howard fixed points, and their construction. Presents the equivalence between well-founded fixed points and ∏11-comprehension in mathematical logic.
The Absorption Law for Slow Provability
Explore the absorption law for slow provability, its simple proof, and application to Heyting Arithmetic's provability logic in this mathematical lecture by Albert Visser.
Reverse Mathematics of Caristi's Fixed Point Theorem and Ekeland's Variational Principle
Explore the mathematical strengths of Caristi's fixed point theorem and Ekeland's variational principle, examining their implications in complete separable metric spaces and their connections to various axiom systems.
An Overview Over Least Fixed Points in Weak Set Theories
Explore least fixed points in weak set theories, comparing standard constructions and their implications in Kripke Platek Set Theory extensions without the powerset axiom.
Hugo Herbelin- Investigations into Cubical Type Theory
Exploration of a variant of cubical type theory with type-based equality, direct coercion, and primitive composition, aiming for a parametricity translation to identity type theory.
Michael Rathjen - Opening and Introduction
Explore the foundations of mathematics in this lecture on types, sets, and constructions, delving into fundamental concepts that shape our understanding of mathematical structures.
Ulrich Kohlenbach: Extraction of Information from Proofs
Explore proof mining techniques and their applications in mathematics, focusing on extracting computational content from nonconstructive proofs in analysis and ergodic theory.
Ulrich Kohlenbach - Extraction of Information from Proofs
Explore proof theory and its applications in mathematics, focusing on extracting computational content from nonconstructive proofs for practical problem-solving.
Thierry Coquand- Constructive Algebra
Explore constructive algebra with Thierry Coquand, delving into foundational concepts and innovative approaches within the Types, Sets and Constructions program.
Modular Forms, Elliptic Polylogarithms and Feynman Integrals
Explores advanced mathematical concepts in Feynman integrals, focusing on epsilon-form solutions, modular forms, and elliptic polylogarithms, with applications in number theory and physics.
Johannes Brödel- From Elliptic Multiple Zeta Values to Modular Graph Functions
Explore the connection between elliptic multiple zeta values and modular graph functions in this advanced mathematics lecture by Johannes Brödel.
Stephan Stieberger - Single Valued Multiple Zeta Values and String Amplitudes
Explores the connection between real and complex iterated integrals in mathematics and their applications to open and closed string scattering amplitudes in physics, using single-valued projections.
Modular Graph Functions and Non Holomorphic Modular Forms
Explore non-holomorphic modular forms in string theory, their properties, and connections to mixed motives and L-functions. Gain insights into advanced mathematical concepts in physics.
Graphical Hyperlogarithms
Explore graphical hyperlogarithms, a generalization of iterated integrals related to cell zeta values. Learn about their graphical representation and coaction formula in subquotient graphs.