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DTSTART:20231105T020000
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RDATE:20241103T020000
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UID:calendar.25998.field_event_date_2.0@math.wustl.edu
CREATED:20240304T160935Z
DESCRIPTION:Abstract: A spline is an assignment of polynomials to the verti
ces of a graph whose edges are labeled by ideals, where the difference of
two adjacent polynomials must belong to the corresponding ideal. The set
of splines forms a ring. We consider spline rings where the underlying gra
ph is the Cayley graph of a symmetric group generated by a collection of t
ranspositions. \n\nThese rings generalize the GKM construction for equivar
iant cohomology rings of regular semisimple Hessenberg varieties. These co
homology rings carry two actions of the symmetric group $S_n$ whose graded
characters are both of general interest in algebraic combinatorics.\n\nIn
this dissertation presentation, we generalize the graded $S_n$-represent
ations from the cohomologies of the above varieties to splines on Cayley g
raphs of $S_n$, give a combinatorial characterization of when graded piec
es of one $S_n$-representation is trivial, and compute the first degree p
iece of both graded characters for all generating sets.\n\nAdvisors: Marth
a Precup and John Shareshian
DTSTART;TZID=America/Chicago:20240402T150000
DTEND;TZID=America/Chicago:20240402T170000
LAST-MODIFIED:20240327T195001Z
SUMMARY:Thesis Defense: Splines on Cayley Graphs of the Symmetric Group
URL;TYPE=URI:https://math.wustl.edu/events/thesis-defense-splines-cayley-gr
aphs-symmetric-group
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