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Grant GA18-07776S     1.1.2018 - 31.12.2020
Grantor: Czech Science Foundation

Higher structures in algebra, geometry and mathematical physics


It has been gradually realized that various deep problems in algebra, geometry and mathematical physics, particularly in string theory, involve previously unknown higher structures. Over the years, this originally esoteric concept has become widely recognized, with parallel breakthroughs in the foundations of derived algebraic geometry and topology, category theory, representation theory and other seemingly unrelated fields. Our project aims to increase
the understanding of the topics mentioned above, by combining the expertise of the team members in different but tightly interlaced areas of mathematics and mathematical physics. More specifically, the project aims at topics such as the terminality conjecture for spaces relevant for string field theory, higher Lie algebras and gauge theory, M-branes, Penrose-Ward transform, Adams-Novikov spectral sequence, Riemann surfaces, and related issues. The common background of these themes are operads, higher category theory and homological algebra, combined with the standard methods of differential and algebraic geometry.

 Main investigator:

Markl Martin

 Participating institutions:

Institute of Mathematics, AS CR