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DTSTART:20260308T070000
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DTSTART:20251102T060000
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DTSTART;TZID=America/Toronto:20260604T143000
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URL:https://uwaterloo.ca/combinatorics-and-optimization/events/algebraic-an
 d-enumerative-combinatorics-seminar-theodore
SUMMARY:Algebraic and Enumerative combinatorics seminar - Theodore\nMorriso
 n-Satisfiability thresholds of linear equations over a\ncommutative ring
CLASS:PUBLIC
DESCRIPTION:SPEAKER:\n Theodore Morrison\n\nAFFILIATION:\n University of Wa
 terloo\n\nLOCATION:\n MC 5479\n\nABSTRACT:The satisfiability threshold of 
 a random constraint\nsatisfaction problem (CSP) is the density of constrai
 nts at which a\nrandom CSP instance transitions from being satisfiable to\
 nunsatisfiable with high probability. Much of the research on well\nknown 
 CSPs\, including the $k$-SAT problem\, $k$-XORSAT problem\,\nhypergraph co
 louring\, and systems of linear equations\, has focused on\ndetermining sa
 tisfiability thresholds.\n\nIn this talk we consider systems of linear equ
 ations over finite\ncommutative rings as CSPs\, and build on the work of A
 yre\, Coja-Oghlan\,\nGao\, and Müller\, who determined the satisfiability
  threshold for\nrandom linear equations over a finite field. We determine 
 when the\nsatisfiability threshold is linear in the number of variables\, 
 and\nshow that any linear threshold over a principal ideal ring coincides\
 nwith the (unique) linear threshold over fields. We also determine the\nsa
 tisfiability threshold for some examples of non-principal ideal\nrings.\n\
 nThis is joint work with Jane Gao.\n\nTHERE WILL BE A PRE-SEMINAR PRESENTI
 NG RELEVANT BACKGROUND AT\nBEGINNING GRADUATE LEVEL STARTING AT 1:30PM IN 
 MC 5417.
DTSTAMP:20260523T134455Z
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