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DTSTART:20240310T070000
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DTSTART:20231105T060000
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DTSTART;TZID=America/Toronto:20240604T100000
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TRANSP:TRANSPARENT
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URL:https://uwaterloo.ca/pure-mathematics/events/number-theory-seminar-123
SUMMARY:Number Theory Seminar
CLASS:PUBLIC
DESCRIPTION:GAUREE WATHODKAR (UNIVERSITY OF MISSISSIPPI)\n\n_Partition regu
 larity in commutative rings._\n\nLet A ∈ Mm×n(Z) be a matrix with integ
 er coefficients. The system\nof equations A⃗x = ⃗0 is said to be parti
 tion regular over Z if\nfor every finite partition Z \\ {0} = ∪ri =1Ci\,
  there exists a\nsolution ⃗x ∈ Zn\, all of whose components belonging 
 to the same\nCi. For example\, the equation x + y − z = 0 is partition r
 egular. In\n1933 Rado characterized completely all partition regular matri
 ces. He\nalso conjectured that for any partition Z \\ {0} = ∪ri =1Ci\, t
 here\nexists a partition class Ci that contains solutions to all partition
 \nregular systems. This conjecture was settled in 1975 by Deuber. We\nstud
 y the analogue of Rado’s conjecture in commutative rings\, and\nprove th
 at the same conclusion holds true in any integral domain.\n\nMC5403
DTSTAMP:20260505T001722Z
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