Krzysztof Bielas: From Quantum-Mechanical Lattice of Projections to Smooth Structure of R^4
Channel: International Center for Formal Ontology
Date: 30/03/2020

The conference "Category Theory in Physics, Mathematics and Philosophy" took place 16-17.11.2017 in Warsaw.



Krzysztof Bielas (Division of Astrophysics and Cosmology, Institute of Physics, University of Silesia): From Quantum-Mechanical Lattice of Projections to Smooth Structure of R^4


Recently it was shown that mathematical formalism of quantum mechanics provides a unique way of thinking not only about real numbers in general, but also about the issue of exotic smoothness. The main point of departure is a set of complete Boolean algebras contained in the quantum-mechanical lattice of projections, used to build various Boolean-valued models of ZFC, thus universes for mathematics in the usual sense. As each of them provides its own notion of real numbers, it gives a rather unique opportunity for considering exotic smoothness questions. It is not a surprise that an important step in the construction is a mapping between Boolean algebras and structures built upon reals, such as manifold covers. The present work aims at a categorical perspective on this subject.



Organizers:
- International Center for Formal Ontology, Faculty of Administration and Social Sciences, Warsaw University of Technology,
- Copernicus Center for Interdisciplinary Studies,
- Center for Theoretical Physics, Polish Academy of Sciences,
- Institute of Mathematics, Academy of Sciences of the Czech Republic.

Website of the conference in English: http://www.icfo.ans.pw.edu.pl/en/?page_id=1855
Website of the conference in Polish: https://www.ans.pw.edu.pl/Nauka/Konferencje/2017/Teoria-kategorii-w-fizyce-matematyce-i-filozofii