FOMUS: Foundations of Mathematics: Univalent Foundations and Set Theory - What are Suitable Criteria for the Foundations of Mathematics?
- https://www.mathematik.hu-berlin.de/de/events/fomus-2016
- FOMUS: Foundations of Mathematics: Univalent Foundations and Set Theory - What are Suitable Criteria for the Foundations of Mathematics?
- 2016-07-18T00:00:00+02:00
- 2016-07-23T23:59:59+02:00
- Wann 18.07.2016 00:00 bis 23.07.2016 23:59
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iCal
The FOMUS workshop will be held at the Center for Interdisciplinary Research of Bielefeld University from the 18th to the 23rd of July. Within this framework approximately 80 graduate students, junior researchers and leading experts will gather in order to investigate and discuss suitable foundations for mathematics and their qualifying criteria, with an emphasis on HoTT/Univalent Foundations and set theory. This interdisciplinary workshop, designed as a hybrid between summer school and research conference, is aimed at students and researchers from the fields of mathematics, philosophy and computer science.
Zermelo-Fraenkel axioms are widely assumed to be the foundation of mathematics within the mathematical practice of set theory. However, an increasing number of researchers are currently working on the Univalent Foundations as an alternative foundation of mathematics. This relatively young approach is based on Homotopy Type Theory, which is a link between Martin Löf's intuitionistic type theory and the homotopy theory from topology.
The workshop will be opened with an introduction to these two different foundational theories, with an emphasis on the less popular homotopy type theory, and then progress into indepth panel discussions and (research) talks. With regard to the philosophical discipline of mathematics, the formal requirements of the foundations of mathematics, their limitations and their naturality will be examined. Recently, it has become increasingly important to formalise mathematics by computer-aided formal proof systems, such as Coq. With this in mind, it will be investigated which foundation is most suitable for the changing needs of mathematical practice.
This workshop can be seen as the continuation of the event on Formal Mathematics, held at the University of Bonn in March 2015.
Organisers: Balthasar Grabmayr, Deborah Kant, Lukas Kühne, Deniz Sarikaya
This workshop is organised with the generous support of the Association for Symbolic Logic (ASL), the Association of German Mathematicians (DMV), the Berlin Mathematical School (BMS), the Center of Interdisciplinary Research (ZiF), the Fachbereich Grundlagen der Informatik of the German Informatics Society (GI) and the German Society for Analytic Philosophy (GAP).
The workshop will be opened with an introduction to these two different foundational theories, with an emphasis on the less popular homotopy type theory, and then progress into indepth panel discussions and (research) talks. With regard to the philosophical discipline of mathematics, the formal requirements of the foundations of mathematics, their limitations and their naturality will be examined. Recently, it has become increasingly important to formalise mathematics by computer-aided formal proof systems, such as Coq. With this in mind, it will be investigated which foundation is most suitable for the changing needs of mathematical practice.
This workshop can be seen as the continuation of the event on Formal Mathematics, held at the University of Bonn in March 2015.
Organisers: Balthasar Grabmayr, Deborah Kant, Lukas Kühne, Deniz Sarikaya
This workshop is organised with the generous support of the Association for Symbolic Logic (ASL), the Association of German Mathematicians (DMV), the Berlin Mathematical School (BMS), the Center of Interdisciplinary Research (ZiF), the Fachbereich Grundlagen der Informatik of the German Informatics Society (GI) and the German Society for Analytic Philosophy (GAP).