BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Alexei Yu. Pirkovskii (HSE Moscow) DTSTART:20230329T190000Z DTEND:20230329T200000Z DTSTAMP:20260420T053237Z UID:NYC-NCG/127 DESCRIPTION:Title: Nonformal deformations of algebras of holomorphic functions\nby Alex ei Yu. Pirkovskii (HSE Moscow) as part of Noncommutative geometry in NYC\n \n\nAbstract\nFormal deformations of associative algebras are by now class ical and relatively well-studied objects. They were introduced by Gerstenh aber in 1964\, and they are interesting especially because of their relati on to deformation quantization. By contrast\, the theory of nonformal defo rmations is now at a much earlier stage of development. Roughly\, a gener al feature of all existing approaches to nonformal deformations\, which di stinguishes them from formal deformations\, is that the role of the "base" ring is now played by a certain algebra of functions (continuous\, or smo oth\, or holomorphic...) rather than by the algebra of formal power series . This makes nonformal deformations quite attractive from the physical poi nt of view\, because they allow evaluating the deformed star product at co ncrete nonzero values of the deformation parameter (Planck's constant). In this talk\, our main objects will be nonformal (or\, more exactly\, holom orphic) deformations of the algebras of holomorphic functions on the polyd isc and on the ball in $\\mathbb{C}^n$. We will discuss some properties of such deformations and their relation to formal deformations. If time perm its\, we will compare our approach to holomorphic deformations with S. Wal dmann's approach\, which is better adapted to deformation quantization\, b ut which applies only to some proper subalgebras of the algebras of holomo rphic functions.\n LOCATION:https://researchseminars.org/talk/NYC-NCG/127/ END:VEVENT END:VCALENDAR