Mathematisches Seminar

Dr. Alessandro Malusà, University of Saskatchewan and PIMS (Pacific Institute for the Mathematical Sciences): "Hyper-Kähler quantisation"

14.01.2020 von 14:15 bis 15:45

LMS 4 - Raum 312 - Diskussionsraum


Geometric quantisation is a construction that mimics and extends those of canonical quantisation. The process starts with a symplectic manifold equipped with a particular type of Hermitian line bundle; the outcome is a certain Hilbert space constructed through the additional data of what is called a polarisation, typically a Lagrangian foliation or a Kähler structure. A rather common question in this setting is how to obtain such additional data and how the result depends on it.
An interesting question, somehow complementary to this problem, is how to approach the quantisation of a hyper-Kähler space: in that case, a whole family of equally good symplectic forms is given without a specific preference, while the problem of finding a polarisation is inessential since each comes with its own Kähler structure. In a recent work with Jørgen Andersen and Gabriele Rembado, soon to appear as a preprint, we address this question in the case of a hyper-Kähler vector space, thus obtaining a Hilbert space for each symplectic form and a natural identification between them in the form of a flat connection.
Time permitting, I will also discuss our main motivation, namely from quantisation problems on the hyper-Kähler moduli space of flat SL(n,C)-connections over a closed Riemann surface.
Einladende: C. Meneses, H. Weiß

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