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November 17, 2014
Monday, November 17
Graduate Seminar
Time: 11:20
Speaker: Baran Serajelahi (Western)
Title: "n-plectic quantization"
Room: MC 106

Abstract: In this talk I will discuss results obtained with Tatyana Barron. We suggest a way to quantize, using Berezin-Toeplitz quantization (also refered to as Kahler quantization), a compact hyperkahler manifold (equipped with a natural 3-plectic form), or a compact integral Kahler manifold of complex dimension n regarded as a (2n-1)-plectic manifold. In each of these cases the n-plectic structure is derived from the symplectic structure, so it is intuitively clear that we should be able to obtain a quantization by way of the usual Kahler quantization of the symplectic form. We show that the quantization has reasonable semiclassical properties. I will begin by giving an overview of the idea of quantization and in particular I will discuss the necessary background from Berezin-Toeplitz quantization. I will then review the main results of Berezin-Toeplitz quantization (due to Martin Bordemann, Eckhard Meinrenken, Martin Schlichenmaier, which can be found in their paper “Toeplitz Quantization of Kahler Manifolds and gl(N), N--> \infty Limits”) that we have generalized. Finally I will review our results and indicate the proofs.