Jonas Schnitzer
PostDoc at the University of Pavia
PostDoc at the University of Pavia
Email: jonaschristoph.[lastname]@unipv.it
My research interest is centered around Poisson geometry and deformation quantization, understood in a broad sense, and its application to (mathematical) physics.
A Poisson manifold is a smooth manifold \( M \) equipped with a Lie bracket \( \{ \cdot, \cdot \} \) on the smooth functions \( C^\infty(M) \), which is derivative in both slots. Examples of Poisson manifolds include dual spaces of finite-dimensional real Lie algebras and symplectic manifolds. Poisson manifolds can be considered as singular symplectic manifolds.
A deformation quantization of a Poisson manifold \( (M, \{ \cdot, \cdot \}) \) is a formal associative deformation of the pointwise product of smooth functions along the direction of the Poisson bracket. This is referred to as a star product \( \star \) on \( C^\infty(M)[[\hbar]] \), and is defined as follows:
Here, \( f, g \in C^\infty(M) \), and the individual terms of the expansion \( \star = \sum_{k \geq 0} \hbar^k C_k \) are given by bidifferential operators.
I work on semi-local models of poisson-related geometries, such as Jacobi bundles and Dirac structures, quantization of Poisson manifolds and the interplay of (semi-)local approximations and quantization. Moreover, I am interested in symmetries in Poisson geometry as well as reduction theory combined with quantizations. Recently, I got interested in graded (symplectic) geometry and its interplay with quantization.
I did my undergraduate education at the University of Würzburg, where I received my B.Sc. (2010-2014, thesis supervisor: Knut Hüper) and my M.Sc. (2014-2016, thesis advisors: Chiara Esposito, Stefan Waldmann). I received my Ph.D. under the supervision of Luca Vitagliano at the University of Salerno (IT). Here you can find my thesis. After that, I did a PostDoc in the differential geometry group at the mathematical institute of the University of Freiburg. At the moment, I am a PostDoc in the Mathematical Physics group at the University of Pavia under the supervision of Michele Schiavina. You can find my full CV here.
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