# Main Results

the interpretation of the symmetries of the two-dimensional non-linear supersymmetric sigma model in terms of the geometry of super Riemann surfaces and their infinitesimal deformations, [6,11]

definition of super J-holomorphic curves, the construction of their moduli space as well as its compactification in genus zero, [1,2,5]

construction of an operadic structure on the moduli spaces of stable SUSY curves, [3]

regularity and symmetries of Dirac-harmonic maps with gravitinos, [4,8,9]

# Publications

[1]

E. Keßler, A. Sheshmani, and S.-T. Yau,

*Torus Actions on Moduli Spaces of Super Stable Maps of Genus Zero*, (2023).[2]

E. Keßler, A. Sheshmani, and S.-T. Yau,

*Super*, Math. Ann.*J*-Holomorphic Curves: Construction of the Moduli Space**383**, 1391 (2022).[3]

E. Keßler, Y. I. Manin, and Y. Wu,

*Moduli Spaces of SUSY Curves and Their Operads*, (2022).[4]

J. Jost, E. Keßler, R. Wu, and M. Zhu,

*Geometry and Analysis of the Yang-Mills-Higgs-Dirac Model*, J. Geom. Phys.**182**, 104669 (2022).[5]

E. Keßler, A. Sheshmani, and S.-T. Yau,

*Super Quantum Cohomology i: Super Stable Maps of Genus Zero with Neveu-Schwarz Punctures*, (2020).[6]

E. Keßler,

*Supergeometry, Super Riemann Surfaces and the Superconformal Action Functional*(Springer, Berlin, 2019).[7]

J. Jost, E. Keßler, J. Tolksdorf, R. Wu, and M. Zhu,

*From Harmonic Maps to the Nonlinear Supersymmetric Sigma Model of Quantum Field Theory: At the Interface of Theoretical Physics, Riemannian Geometry and Nonlinear Analysis*, Vietnam J. Math.**47**, 39 (2019).[8]

J. Jost, E. Keßler, J. Tolksdorf, R. Wu, and M. Zhu,

*Symmetries and Conservation Laws of a Nonlinear Sigma Model with Gravitino*, J. Geom. Phys.**128**, 185 (2018).[9]

J. Jost, E. Keßler, J. Tolksdorf, R. Wu, and M. Zhu,

*Regularity of Solutions of the Nonlinear Sigma Model with Gravitino*, Comm. Math. Phys.**358**, 171 (2018).[10]

E. Keßler, The Super Conformal Action Functional on Super Riemann Surfaces, PhD thesis, Universität Leipzig, 2017.

[11]

J. Jost, E. Keßler, and J. Tolksdorf,

*Super Riemann Surfaces, Metrics and Gravitinos*, Adv. Theor. Math. Phys.**21**, 1161 (2017).[12]

E. Keßler and J. Tolksdorf,

*The Functional of Super Riemann Surfaces – a “Semi-Classical” Survey*, Vietnam J. Math.**44**, 215 (2016).[13]

E. Keßler,

*Super Riemann Surfaces and the Super Conformal Action Functional*, in*Quantum Mathematical Physics: A Bridge Between Mathematics and Physics*, edited by F. Finster, J. Kleiner, C. Röken, and J. Tolksdorf (Birkhäuser, Basel, 2016), pp. 401–419.