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Workshop on Supergeometry and Bracket Structures in Mathematics and Physics...

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The Fields Institute

222 College St

Toronto, ON M5S 3E6

Canada

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Supergeometry was originally developed as a unifying language describing bosonic and fermionic degrees of freedom and particularly supersymmetry. In the last decades, supergeometric language has merged with methods coming from homological and homotopical algebra, with the concept of Q-manifolds coming to the fore. Symbolically, the equation Q2=H ("supersymmetry algebra") characteristic for the previous period has been replaced by the "homological" equation Q2=0. In the same time, the idea of "brackets" that in differential geometry had long been associated primarily with Lie brackets, has greatly expanded to include
Poisson structures and their generalizations, Lie algebroids and related structures, and various homotopy versions of Lie and Poisson brackets (such as L-, S-, and P-algebras), as well as further generalizations and mixture of all the above. This variety of bracket structures has developed either in
supergeometric context from the start or rely on supergeometric methods as a tool. Particularly important is the description of concepts such as an L--morphism or a Lie algebroid morphism in terms of the unifying notion of a Q-morphism. On the other hand, the definition of the latter can be treated as an integrability or flatness condition, interpreted e.g. a classical equation of motion for Poisson sigma-models and leading to a generalization of curvature in fiber bundles. Besides the role as a powerful unifying language, supergeometry has developed itself in recent decades and in connection with other active areas such as geometry of moduli spaces or cluster algebras.

The workshop will touch on the mentioned topics as well as derived geometry, Batalin-Vilkovisky formalism and topological quantum field theory, Poisson structures and their relatives; complex supergeometry, super Riemann surfaces and super moduli spaces, generalized geometry, and others. It will give a platform for exchange of ideas and interaction for researchers in mathematics and mathematical physics coming from different backgrounds.


Organizing Committee

Alexander Odesskii - Brock University
Ekaterina Shemyakova - University of Toledo
Theodore Voronov - University of Manchester

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Date and Time

Location

The Fields Institute

222 College St

Toronto, ON M5S 3E6

Canada

View Map

Refund Policy

Refunds up to 7 days before event

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