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SUMMARY:Gabriela Laboska (Northwestern University)
DTSTART:20260430T180000Z
DTEND:20260430T190000Z
DTSTAMP:20260423T034446Z
UID:OLS/207
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OLS/207/">So
 me Computabiity-theoretic and Reverse-mathematical Aspects of Partition Re
 gularity over Algebraic Structures</a>\nby Gabriela Laboska (Northwestern 
 University) as part of Online logic seminar\n\nInteractive livestream: htt
 ps://zoom.us/j/122323340\n\nAbstract\nAn inhomogeneous system of linear eq
 uations over a ring $R$ is partition\nregular if for any finite coloring o
 f $R$\, the system has a monochromatic\nsolution. In 1933\, Rado showed th
 at an inhomogeneous system is partition\nregular over $\\mathbb{Z}$ if and
  only if it has a constant solution.\nFollowing a similar approach\, Bysze
 wski and Krawczyk showed that the\nresult holds over any integral domain. 
 In 2020\, Leader and Russell\ngeneralized this over any commutative ring $
 R$\, with a more direct\nproof than what was previously used. In this talk
 \, we analyze a theorem by Straus from a computability-theoretic and rever
 se-mathematical point of view. Straus' theorem has been\nused directly or 
 as a motivation to many of the results in this area.\n
LOCATION:https://researchseminars.org/talk/OLS/207/
URL:https://zoom.us/j/122323340
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