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CATEGORIES:Exhibits
DESCRIPTION:Speaker: Patricia Klein (Texas A&M University)\n\nTitle: Alt
ernating sign matrix varieties\n\nAbstract: \n\nMatrix Schubert varieties\,
introduced by Fulton in the '90s\, are affine varieties that "live above"
Schubert varieties in the complete flag variety. They have many desirable a
lgebro-geometric properties\, such as irreducibility\, Cohen--Macaulayness\
, and easily-computed dimension. They also enjoy a close connection with th
e symmetric groups and have multidegrees that can be computed from pleasing
combinatorial formulas. \n\nAlternating sign matrix (ASM) varieties\, intr
oduced by Weigandt just several years ago\, are generalizations of matrix S
chubert varieties in two senses: (1) ASM varieties are unions of matrix Sch
ubert varieties\, and (2) the defining equations of ASM varieties are deter
mined by ASMs\, which are generalizations of permutation matrices. ASMs hav
e a rich history in enumerative combinatorics as the focus of the ASM conje
cture\, and they appear in statistical mechanics as the 6-vertex lattice mo
del. Although ASMs have a robust combinatorial underpinning and although th
eir irreducible components are matrix Schubert varieties\, they are neverth
eless much more difficult to get a handle on than matrix Schubert varieties
themselves. In this talk\, we will define ASMs\, compare and contrast them
with matrix Schubert varieties\, and state some open problems. \n\nThis ta
lk includes work by four undergraduates: Hao and Kendall as well as MIT's o
wn Axelrod-Freed and Luo.
DTEND:20220914T211500Z
DTSTAMP:20240725T034501Z
DTSTART:20220914T201500Z
LOCATION:MIT - Math Dept.\, // MIT Building 2\, Room 132
SEQUENCE:0
SUMMARY:MIT-Harvard-MSR COMBINATORICS SEMINAR
UID:tag:localist.com\,2008:EventInstance_41013639271159
URL:https://calendar.mit.edu/event/mit-harvard-msr_combinatorics_seminar_62
34
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