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比利时vs摩洛哥足彩 ,
university of california san diego

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colloquium

prof. fay dowker

imperial college london

combinatorial geometry: a tale of two signatures

abstract:

can a purely combinatorial object be approximated by a continuum geometry? i will describe evidence that the answer is "yes''  if that object is a transitive directed acyclic graph, otherwise known as a discrete order, otherwise known as a causal set. in which case, the approximating continuum geometry must be pseudo-riemannian with a "lorentzian'' signature of $(-, +, +, \ldots, +)$. i will, along the way, explain the crucial difference between riemannian and lorentzian geometry: in the former case the geometry is local and in the latter the geometry is, if not actually nonlocal then teetering on the edge of being nonlocal.  if there is time i will describe a model of random orders called transitive percolation, which is the lorentzian analogue of the erdős-renyi random graph and is an interesting toy model for a physical dynamics of discrete space-time.

host: david meyer

february 14, 2024

4:00 pm

apm 6402

research areas

mathematical physics

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