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DTSTART:20260308T070000
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DTSTART;TZID=America/Toronto:20260505T093000
SEQUENCE:0
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URL:https://uwaterloo.ca/pure-mathematics/events/phd-defence-2
SUMMARY:PhD Defence
CLASS:PUBLIC
DESCRIPTION:JENNIFER ZHU\, UNIVERSITY OF WATERLOO\n\n_Categorical Limits o
 f Quantum Graphs and Possibilities Induced by\nQuantumPseudometrics_\n\nQu
 antum graphs and quantum pseudometrics as defined by Kuperberg and\nWeaver
  have roots in quantum errorcorrection but have since been\ndeveloped as s
 ubjects in their own right. The motivation for the first\nhalf of thisthes
 is is to build an infinite quantum graph from finite\nquantum graphs. The 
 latter have been subjected to fargreater scrutiny\ndue to their connection
 s to categorical quantum theory\, while the\nformer have been somewhatnegl
 ected. To be precise\, we define and take\nthe categorical (co)limit of qu
 antum graphs by developing a newnotion\nof morphism compatible with previo
 us notions but carrying less\nbaggage. The inspiration for the secondhalf 
 follows from the\n(unpublished) theorem that pure states on a von Neumann 
 algebra\n\\mathcal{M} are givenby maximal filters in the projection lattic
 e of\n\\mathcal{M}. Upon the observation that points in a metric space$(X\
 ,\nd)$ with topology $\\tau$ are also given by maximal filters $\\tau$ and
 \nthat quantum pseudometrics provide anotion of distance between\nprojecti
 ons in $B(\\ell^2) \\overline{\\otimes} \\mathcal M$\, we are led\nto a no
 tion ofdistance $f$ between pure states induced by these\nquantum pseudome
 trics. Also this function $f$ does not satisfythe\ntriangle inequality\, w
 e make some parallels between it and David\nLewis's conception of ``possib
 le worlds.''\n\nMC 2009
DTSTAMP:20260501T150214Z
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