BEGIN:VCALENDAR
VERSION:2.0
PRODID:icalendar-ruby
CALSCALE:GREGORIAN
X-WR-CALNAME:Combinatorics Seminar: The $(1\,2)$-bosonic-fermionic coinvari
 ant ring
X-WR-TIMEZONE:Pacific Time (US & Canada)
BEGIN:VEVENT
DTSTAMP:20260719T070513Z
UID:tag:localist.com\,2008:EventInstance_47677824106046
DTSTART:20241007T210000Z
DTEND:20241007T220000Z
DESCRIPTION:John Lentfer\, UC Berkeley\n\nTitle: The (1\,2)-bosonic-fermion
 ic coinvariant ring\n\nAbstract: In 1994 Haiman introduced the ring of dia
 gonal coinvariants\, which is a quotient of a polynomial ring in two sets 
 of commutative variables by invariants of the diagonal action of the symme
 tric group.Recently\, there has been much interest in studying a more gene
 ral class of coinvariant rings with k sets of n commutative (bosonic) vari
 ables and j sets of n anticommutative (fermionic) variables\; denote this 
 ring by $R_n^{(k\,j)}$.\nWe will focus on the coinvariant ring $R_n^{(1\,2
 )}$\, with one set of bosonic and two sets of fermionic variables.\nBy int
 erpolating between the modified Motzkin path basis for $R_n^{(0\,2)}$ of K
 im--Rhoades (2022) and the super-Artin basis for $R_n^{(1\,1)}$ conjecture
 d by Sagan--Swanson (2024) and proven by Angarone et al. (2024)\, we propo
 se a monomial basis for $R_n^{(1\,2)}$.\nWe use the proposed basis to give
  combinatorial formulas for its conjectural Hilbert series and Frobenius s
 eries.\nWe will explain how our work on $R_n^{(1\,2)}$ relates to the Thet
 a conjecture and recent work of Iraci\, Nadeau\, and Vanden Wyngaerd (2023
 ).
GEO:34.022409;-118.291027
LOCATION:Kaprielian Hall (KAP)\, 167
SUMMARY:Combinatorics Seminar: The $(1\,2)$-bosonic-fermionic coinvariant r
 ing
URL;VALUE=URI:https://calendar.usc.edu/event/combinatorics-seminar-the-12-b
 osonic-fermionic-coinvariant-ring
CATEGORIES:Lecture / Talk / Workshop
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