Universität Augsburg
Institut für Mathematik

Siegel der Universität Augsburg

 

Augsburger Mathematisches Kolloquium

 

Dr. Enno Keßler
Max-Planck Institut für Mathematik, Bonn

 
spricht am
 
Dienstag, 22. November 2022
 
um
 
17:30 Uhr
 
im
 
Raum 2004 (L1)
 
über das Thema:
 

»Supergeometric Generalizations of Harmonic Maps and J-holomorphic Curves«

Abstract:
The Dirichlet Action Functional for maps from a surface to a Riemannian target manifold is conformally invariant. Hence it can be used as a tool to study the Teichmüller space of complex structures on the surface. Furthermore, if the target manifold is almost Kähler J-holomorphic curves are an interesting class of minimizers of the Dirichlet action with many important applications in symplectic geometry. The two-dimensional non-linear supersymmetric sigma model is an extension of the Dirichlet action by spinorial fields. Its supersymmetry properties require that the spinorial fields are anti-commutative. In this talk, I want to show how geometry can be extended to supergeometry which contains dimensions with anti-commuting coordinates and motivate supergeometric generalizations of Riemann surfaces, harmonic maps and J-holomorphic curves. This yields a supergeometric understanding of the two-dimensional non-linear supersymmetric sigma model, its symmetries and critical points.

 

Hierzu ergeht herzliche Einladung.
Prof. Dr. Maxim Smirnov
 

Kaffee, Tee und Gebäck eine halbe Stunde vor Vortragsbeginn im Raum 2006 (L1).



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