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UID:30219dc0-4931-46f8-98c8-8a46217f5387
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X-WR-CALNAME:IAS Special Year
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UID:b73fbdd1-f586-4223-9c0a-8941fdb6eb2e
DTSTAMP:20201202T034544Z
CREATED:20170614T200303Z
DESCRIPTION:During the 2020-2021 academic year\, the School will have a spe
cial\nprogram on Geometric and Modular Representation Theory. Geordie\nWil
liamson of the University of Sydney will be the Distinguished\nVisiting Pr
ofessor.\n\nConfirmed senior participants for Term I: George Lusztig\, Rap
hael\nRouquier Term II: Simon Riche\, Raphael Rouquier\, Catharina Stroppe
l\n\nSEMINAR PAGE [/math/sp/geometric_modular_reptheory/seminar]\n\nRepres
entation theory began with the work of Frobenius in the late\n19th century
and soon grew to play an important role in the\ndevelopment of modern mat
hematics. The second half of the last century\nsaw the introduction of pow
erful new geometric techniques. Some of the\ndeepest results in representa
tion theory are obtained via geometric\nmeans\, via the passage to algebra
ic geometry and the use of D-modules\,\nperverse sheaves and weights. More
recently\, techniques of higher\nrepresentation theory have provided new
techniques and impetus from\nalgebra and higher category theory.\n\nA focu
s of this special year will be on modular representations (i.e.\nrepresent
ations in positive characteristic). Here experience suggests\nthat simple
questions (e.g. understanding simple representations) can\nbe extremely di
fficult. The subject has been dominated for the last\nthirty years by conj
ectures stating that the story should be 'the\nsame' as over the complex n
umbers\, where 'classical' tools of\ngeometric representation theory provi
de the answer. However recent\nresults suggest that the story is more comp
licated\, and one is in need\nof new conjectures. It seems likely that bot
h algebraic and geometric\ntools will be necessary to make progress. One m
ight hope that a better\nunderstanding of pure characteristic p phenomena
(e.g. Frobenius\ntwist\, Steenrod operations\, relatively simple structure
of motives...)\nwill become essential to further understanding.\n\nAnothe
r focus of this special year will be to achieve a better\nunderstanding of
derived equivalence. This notion has grown into a\nunifying principle thr
oughout representation theory: from attempts to\ncategorify counting conje
ctures in finite group theory\, through the\nrepresentation theory of real
Lie groups\, to the local geometric\nLanglands program. A better understa
nding of these equivalences and\ntheir consequences seems guaranteed to le
ad to further progress.\n\nWorkshops for the year will be Fall: November 1
6-20\, 2020(virtual)\n[/math/sp/geometric_modular_reptheory/wrdgrt] and Sp
ring: March 29-\nApril 2\, 2021. More information to come.\n\nAny question
s? Please email sy@ias.edu and in the subject line\nreference the name and
dates of the special year.\n\nTO JOIN OUR MAILING LIST PLEASE SEND AN EMA
IL TO:\nSPECIAL_YEAR-SUBSCRIBE@MATH.IAS.EDU\n\nTO UNSUBSCRIBE TO OUR MAILI
NG LIST PLEASE SEND AN EMAIL TO:\nSPECIAL_YEAR-UNSUBSCRIBE@MATH.IAS.EDU\n
\n
DTSTART;TZID=America/New_York:20200901T090000
DTEND;TZID=America/New_York:20210430T090000
LAST-MODIFIED:20200907T224550Z
LOCATION:
SUMMARY:Special Year on Geometric and Modular Representation Theory
URL:https://www.ias.edu/math/sp/geometric_modular_reptheory
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