QUANTIZING DISCRETE STRUCTURES

Speaker(s)

ANDRE KORNELL

Affiliation

New Mexico State University, Las Cruces, USA

Language of the talk

English

Date

April 22, 2026, 5:15 p.m.

Information about the event

IMPAN - Room 405 & zoom

Title in Polish

QUANTIZING DISCRETE STRUCTURES

Seminar

North Atlantic Noncommutative Geometry Seminar

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A discrete structure consists of any number of sets and any number of maps and relations on those sets. This talk concerns a uniform approach to the quantization of classes of discrete structures. In other words, we extend classes of discrete structures to classes of discrete quantum structures. A quantum structure is discrete if its underlying quantum spaces are discrete in the sense of Podleś and Woronowicz. Examples will range from elementary discrete quantum structures such as quantum relations and quantum maps to interesting discrete quantum structures such as quantum metric spaces and quantum groups. Particular attention will go to the distinction between discrete quantum groups and discrete quantum groups of Kac type, which are both quantizations of groups. In each case, we quantize a class of discrete structures by reinterpreting a definition of that class in the category of hereditarily atomic von Neumann algebras and quantum relations in the sense of Weaver. This talk will emphasize the approach itself, as well as its motivation and its basis in a few simple principles.

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