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DTSTART:20240310T070000
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DTSTART;TZID=America/Toronto:20250127T143000
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URL:https://uwaterloo.ca/pure-mathematics/events/pure-math-department-collo
 quium-5
SUMMARY:Pure Math Department Colloquium
CLASS:PUBLIC
DESCRIPTION:MICHAEL CHAPMAN\, NYU (COURANT INSTITUTE)\n\nSubgroup Tests and
  the Aldous-Lyons conjecture\n\nThe Aldous-Lyons conjecture from probabili
 ty theory states that every\n(unimodular) infinite graph can be (Benjamini
 -Schramm) approximated by\nfinite graphs. This conjecture is an analogue o
 f other influential\nconjectures in mathematics concerning how well certai
 n infinite\nobjects can be approximated by finite ones\; examples include 
 Connes'\nembedding problem (CEP) in functional analysis and the soficity\n
 problem of Gromov-Weiss in group theory. These became major open\nproblems
  in their respective fields\, as many other long standing open\nproblems\,
  that seem unrelated to any approximation property\, were\nshown to be tru
 e for the class of finitely-approximated objects. For\nexample\, Gottschal
 k's conjecture and Kaplansky's direct finiteness\nconjecture are known to 
 be true for sofic groups\, but are still wide\nopen for general groups.\n\
 nIn 2019\, Ji\, Natarajan\, Vidick\, Wright and Yuen resolved CEP in the\n
 negative. Quite remarkably\, their result is deduced from complexity\ntheo
 ry\, and specifically from undecidability in certain quantum\ninteractive 
 proof systems. Inspired by their work\, we suggest a novel\ninteractive pr
 oof system which is related to the Aldous-Lyons\nconjecture in the followi
 ng way: If the Aldous-Lyons conjecture was\ntrue\, then every language in 
 this interactive proof system is\ndecidable. A key concept we introduce fo
 r this purpose is that of a\nSubgroup Test\, which is our analogue of a No
 n-local Game. By providing\na reduction from the Halting Problem to this n
 ew proof system\, we\nrefute the Aldous-Lyons conjecture.\n\nThis talk is 
 based on joint work with Lewis Bowen\, Alex Lubotzky\, and\nThomas Vidick.
 \n\nMC 5501\n\n2:30pm - 3:30pm
DTSTAMP:20260504T225235Z
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