I will survey the theory of associative ℤ≥ 0-graded algebras presented by n generators and n(n-1)/2 quadratic relations and satisfying the so-called Poincare-Birkhoff-Witt condition (PBW-algebras). We will consider examples of such algebras depending on two continuous parameters (namely, on an elliptic curve and a point on this curve) which are flat deformations of the polynomial ring in n variables. We will discuss geometry of the corresponding Poisson structures. Diverse properties of these algebras and Poisson structures will be described, together with their relations to integrable systems, deformation quantization, moduli spaces and other directions of modern investigations.
|Thu, Feb 19
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||Fri, Feb 27
Recording of all of the lectures of the Master Class will be available on the FieldsLive Video Archive.
In the spirit of the Geometric Structures Laboratory we encourage the audience to ask questions and to engage in a meaningful dialogue with the speaker.
While the Master Class is designed especially for graduate students and other young researchers who wish to have greater exposure to the Poisson structures arising from elliptic algebras, senior researchers will also benefit from the lectures. All are welcome to attend.
This Master Class is organized by Victor Mouquin and Alberto Garcia-Raboso. Should you have any question, please contact them.
The image in the header of this page is taken from this webpage.