Description coming soon...
Meetings will take place simultaneously in person in Hannover and Potsdam and also on Zoom, to allow for interaction between the participants in different places. Therefore, online participation of single individuals is possible (and welcome!)
The format of the seminar allows for some flexibility. This means that the program can also be modified en route and eventually adapted to better encompass the interests of the participants.
Time: Mondays, 14:15-15:45, Berlin Time (GMT+2).
Speaker: Fabrizio Zanello (Univeristy of Potsdam)
References: Sections 1 and 2 in [1], Sections 5.2 and 6.1 in [14].
Basic notions on Poisson manifolds, symplectic manifolds as a special case, detailed example of coadjoint representation of a Lie algebra.
Definition of star product, equivalence of star products, example of the standard star product on the cotangent space of n-dimensional euclidean space, brief overview on the existence and classification of star products.
Speaker: Fabrizio Zanello (University of Potsdam)
References: Sections 1,2,3 in [4] and Section 6.2.2 in [14]
Basic definition of Hochschild cohomology of an associative algebra;
Proof of the classification theorem for star products on symplectic manifolds.
Speaker: Arne Hofmann (Leibniz University Hannover)
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F. Bayen, M. Flato, C. Frondsal, A. Lichnerowicz, D. Sternheimer, "Deformation theory and quantization I. Deformations of symplectic structures", Annals of Physics, Volume 111, Issue 1, 1978, Pages 61-110.
F. Bayen, M. Flato, C. Frondsal, A. Lichnerowicz, D. Sternheimer, "Deformation theory and quantization II. Physical applications", Annals of Physics, Volume 111, Issue 1, 1978, Pages 111-151.
S. Beentjes, "An Introduction to Deformation Quantization: After Kontsevich" (Bachelor thesis), available online here.
M. Bertelson, M. Cahen, S. Gutt, "Equivalence of star products", Class. Quantum Grav. 14 (1997) A93–A107.
P. Chen, V. Dolgushev, "A Simple Algebraic Proof of the Algebraic Index Theorem", available online here.
G. Dito, D. Sternheimer, "Deformation Quantization: Genesis, Developments and Metamorphoses", Deformation Quantization: Proceedings of the Meeting of Theoretical Physicists and Mathematicians, Strasbourg, May 31 - June 2, 2001, edited by Gilles Halbout, Berlin, Boston: De Gruyter, 2002, pp. 9-54.
B. Fedosov, "Deformation Quantization and Index Theory", Wiley, 1995.
B. Fedosov, "Pseudo-differential operators and deformation quantization", In: Landsman, N.P., Pflaum, M., Schlichenmaier, M. (eds) Quantization of Singular Symplectic Quotients. Progress in Mathematics, vol 198. Birkhäuser, Basel (2001), https://doi.org/10.1007/978-3-0348-8364-1_5.
S. Gutt, "An explicit *-product on the cotangent bundle of a Lie group", Letters in Mathematical Physics 7 (1983), no. 3, 249-258.
A. C. Hirshfeld, P. Henselder, "Deformation quantization in the teaching of quantum mechanics", American Journal of Physics 70 (2002), no. 5, 537-547.
A. C. Hirshfeld, P. Henselder, "Star products and quantum groups in quantum mechanics and field theory", Annals of Physics 308 (2003), no. 1, 311-328.
R. Nest, B. Tsygan, "Algebraic index theorem", Commun. Math. Phys. 172, 223-262 (1995).
J. Nestruev, "Smooth Manifolds and Observables", Graduate Texts in Mathematics, vol. 220, Springer Nature Switzerland, Cham 2020.
J. Schnitzer, "Poisson Geomery and Deformation Quantization" (lecture notes), available online here.
S. Waldmann, "Poisson-Geometrie und Deformationsquantisierung: Eine Einführung", Springer Berlin, Heidelberg 2007.
A. Weinstein, "Deformation quantization", Astérisque, tome 227 (1995), Séminaire Bourbaki, exp. no 789, p. 389-409, available online here.