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1
Type Theory, Constructive Mathematics and Geometric Logic
01 May 2023 - 05 May 2023 • CIRM (Marseille Luminy), France
Organizer:
CIRM – Centre International de Rencontres Mathématiques
Abstract:
The debate between Hilbert and Brouwer, which took place at the beginning of the 20th century, is without doubt one of the most important events in the history of foundations of mathematics. In that debate Brouwer rejected transcendent proof methods and insisted on the exclusive use of intuitionist (or constructive) arguments for a conceptually correct development of mathematics. Hilbert, on the contrary, viewed these transcendental and non-effective proofs as the very essence of mathematical thinking. He introduced proof theory in the hope to justify these transcendent methods by purely effective means. While Gödel’s second incompleteness theorem is generally said to contravene Hilbert’s hopes, it is remarkable that Gödel himself insisted on the fact that his result does not contradict at all Hilbert’s program. In fact, the impact of Gödel’s result on Hilbert’s program was the topic of a discussion between Gödel, Herbrand and Neumann about the fundamental question of the scope of constructive mathematics. Recent results in different fields of mathematics, such as proof theory, type theory, constructive algebra and categorical logic, shed new light on this question. For instance, proof theory seems to indicate precise limits to intuitionistic type theory, while on the other hand the Univalence Axiomallows for a rather unexpected extension of constructive methods. The goal of this workshop is precisely to bring together experts in these different fields to evaluate the impact of those new results on foundations of mathematics.
Event listing ID:
1502993
Related subject(s):
2
QPL 2023 — 20th International Conference on Quantum Physics and Logic
17 Jul 2023 - 21 Jul 2023 • Institut Henri Poincaré in Paris, France
Abstract:
The 20th International Conference on Quantum Physics and Logic (QPL 2023) will take place from 17 July to 21 July 2023 at Institut Henri Poincaré in Paris, France. Quantum Physics and Logic is an annual conference that brings together academic and industry researchers working on mathematical foundations of quantum computation, quantum physics, and related areas. The main focus is on the use of algebraic and categorical structures, formal languages, type systems, semantic methods, as well as other mathematical and computer scientific techniques applicable to the study of physical systems, physical processes, and their composition. Work applying quantum-inspired techniques and structures to other fields (such as linguistics, artificial intelligence, and causality) is also welcome.
Abstract submission deadline:
01 Mar 2023
Event listing ID:
1543436
3
XVII International Luminy Workshop in Set Theory
09 Oct 2023 - 13 Oct 2023 • CIRM (Marseille Luminy), France
Organizer:
CIRM – Centre International de Rencontres Mathématiques
Event listing ID:
1503103
4
Ecology, epidemiology and evolution
23 Oct 2023 - 27 Oct 2023 • CIRM (Marseille Luminy), France
Organizer:
CIRM – Centre International de Rencontres Mathématiques
Event listing ID:
1503145


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Last updated: 8 February 2023