Seminar
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| Location: | SLMath: Eisenbud Auditorium, Online/Virtual |
Combinatorial deformation quantization via the Koszul complex
In the first part of this talk I will explain part of the theoretical backdrop for a combinatorial approach to deformations of path algebras of quivers with relations — the main idea being that of replacing the bar resolution of the algebra by a smaller projective resolution obtained from a reduction system. This allows one to study the problem of deforming associative structures on a "smaller model", closer to a given presentation by generators and relations. In the case of a
polynomial algebra, this "smaller resolution" is minimal and hence isomorphic to the Koszul resolution.
In the second part I will discuss the applications to deformation quantization, including a review of Kontsevich's universal quantization formula, highlighting similarities and differences with the above-mentioned combinatorial approach. Time permitting I will also mention the resulting progress on the problem of strict quantizations, as well as a brief discussion of some remaining open questions.