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Noncommutative Geometry and Topology in Prague
A brief introduction to canonical extensions with some applications
Speaker’s name:
Tomáš Jakl
Speaker’s affiliation:
Czech Academy of Sciences
Place:
This talk will take place in the blue seminar room, back building, Žitná 25.
It will also be broadcast on Zoom:
https://cesnet.zoom.us/j/91975183920?pwd=SGdlRUhLS21HUnVFTXBKcE1vYXlrQT09
Meeting ID: 919 7518 3920
Passcode: 102707
It will also be broadcast on Zoom:
https://cesnet.zoom.us/j/91975183920?pwd=SGdlRUhLS21HUnVFTXBKcE1vYXlrQT09
Meeting ID: 919 7518 3920
Passcode: 102707
Date:
Tuesday, 2. May 2023 - 16:00 to 17:00
Abstract:
Canonical extensions are an algebraic approach to extensions of topo-algebraic dualities to structures with additional operations. It originates in the work of Jónsson and Tarski who described a representation of topological duals of Boolean algebras with modal operations. The theory of canonical extensions was later generalised to distributive lattices, posets, proximity lattices, coherent categories and more.
In this talk I will overview the basics of the theory of canonical extensions for distributive lattices or, equivalently, I will give an algebraic presentation of Priestley duality. Time permitting, I will also show some applications of canonical extensions to the theory of structural limits.
In this talk I will overview the basics of the theory of canonical extensions for distributive lattices or, equivalently, I will give an algebraic presentation of Priestley duality. Time permitting, I will also show some applications of canonical extensions to the theory of structural limits.