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DTSTART:19700308T020000
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UID:mathcal-11@shafikov.ca
DTSTAMP:19980119T070000Z
SUMMARY:Cycle systems and h-vectors of matroids (Anton Dochtermann - Texas State University)
DTSTART;TZID=America/Toronto:20260511T153000
DTEND;TZID=America/Toronto:20260511T163000
DESCRIPTION:The h-vector of a matroid is an important invariant that has been the subject of intense study in recent years. A still open conjecture of Stanley posits that the h-vector of a matroid is a pure O-sequence\, meaning that it can be obtained by counting faces of a pure multicomplex. Merino established Stanley's conjecture for the case of cographic matroids via chip-firing on graphs and the notion of a G-parking function. Inspired by these constructions\, we introduce the notion of a "cycle system" for a matroid M - a family of circuits of M with overlap properties that mimic cut-sets in a graph. A choice of cycle system on M defines a collection of integer sequences that we call "coparking functions"\, which we show are in bijection with the set of bases of M. This leads to a proof of Stanley's conjecture for the case of matroids that admit cycle systems\, which\, for instance\, include graphic matroids of cones as well as $K_{3\,3}$-minor free graphs. Joint work with Scott Corry\, Solis McClain\, David Perkinson\,
 and Lixing Yi.
LOCATION:MC 108
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BEGIN:VEVENT
UID:mathcal-25@shafikov.ca
DTSTAMP:19980119T070000Z
SUMMARY:Homological algebra and poset versions of the Garland method (Eric Babson - University of California, Davis)
DTSTART;TZID=America/Toronto:20260525T153000
DTEND;TZID=America/Toronto:20260525T163000
DESCRIPTION:Garland introduced a vanishing criterion for characteristic zero cohomology groups of locally finite and locally connected simplicial complexes based on the spectral gaps of the graph Laplacians of face links which has turned out to be effective in a wide range of examples.  This talk provides a homological algebra version of this method and a class of posets which provide examples including simplicial and cubical.  The former gives Garland’s original vanishing theorem while the latter gives a structure on generators rather than vanishing of cohomology. Random complexes provide examples and a conjecture. 
LOCATION:MC 108
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BEGIN:VEVENT
UID:mathcal-46@shafikov.ca
DTSTAMP:19980119T070000Z
SUMMARY:TBA (Colin Crowley - University of Oregon)
DTSTART;TZID=America/Toronto:20260615T153000
DTEND;TZID=America/Toronto:20260615T163000
DESCRIPTION:TBA
LOCATION:MC 108
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