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SUMMARY:Nesta van der Schaaf (University of Edinburgh)
DTSTART;VALUE=DATE-TIME:20240301T110000Z
DTEND;VALUE=DATE-TIME:20240301T120000Z
DTSTAMP;VALUE=DATE-TIME:20240522T214729Z
UID:TheoryCSBham/5
DESCRIPTION:Title: Ordered Locales\nby Nesta van der Schaaf (University of Edinburgh
) as part of University of Birmingham theoretical computer science seminar
\n\nLecture held in LG23\, Computer Science.\n\nAbstract\nOrder and topolo
gy both abound in mathematics\, often even together. Combined\, they form
the notion of an ordered topological space. How can this notion be suitabl
y generalised to the theory of point-free topology? In this talk we will d
iscuss one possibility\, based on the so-called Egli-Milner relation. To k
eep the talk accessible\, we start with an introduction to the definition
of locales and describe their adjunction with topological spaces. After th
at\, we show how this adjunction can be extended to certain categories of
ordered spaces and the newly introduced ordered locales. To finish the tal
k we highlight some ongoing work. First\, we describe how we are using the
se techniques to study aspects of relativity theory. In particular\, we de
scribe ingredients for a "causal boundary" construction\, and show how "do
mains of dependence" can be recovered as a natural Grothendieck topology o
n ordered locales. Lastly\, time permitting\, we discuss an "internal" gen
eralisation of ordered locales. (Based on joint work with Chris Heunen and
Prakash Panangaden.)\n
LOCATION:https://researchseminars.org/talk/TheoryCSBham/5/
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