The research interests of Nikolai included the field of (formal) deformation quantization as introduced in Bayen et al. as well as related topics of symplectic differential geometry and Hamiltonian mechanics. In his work he focused on a detailed study of different results on classification in the framework of deformation quantization. The method of Fedosov for the construction of star products and adaptions thereof to the specific additional structure of the symplectic manifold also played an important role in his work. In his diploma thesis he generalized the concept of ordering prescriptions. This work was continued in his doctoral thesis. He was able to provide a general formulation of Fedosov’s construction. Recently, he concentrated on a better understanding of phase space reduction in the framework of deformation quantization.

His most recent publications are:

Bordemann, M., Neumaier, N., Waldmann, S., Weiss, S.:Deformation Quantization of Surjective Submersions and Principal Fibre Bundles. Crelle Journal für die reine u. angew. Math. 639, 1-39 (2010).

Neumaier, N., Waldmann, S.: Deformation Quantization of Poisson Structures Associated to Lie Algebroids. SIGMA 5, 074, 29 pages (2009). Contribution to the Special Issue on Deformation Quantization.
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