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SUMMARY:Eloise Hamilton (University of Cambridge)
DTSTART:20220407T123000Z
DTEND:20220407T133000Z
DTSTAMP:20260422T215144Z
UID:AGGITatE2022/1
DESCRIPTION:Title: Stability within instability\nby Eloise Hamilton (University of C
ambridge) as part of AGGITatE Days 2022: Algebraic Groups and Geometric In
variant Theory at Essex\n\nLecture held in NTC 2.01.\n\nAbstract\nGiven th
e linear action of a reductive group G on a projective variety X\, Geometr
ic Invariant Theory (GIT) produces an open locus inside X\, called the sem
istable locus\, which has two important properties. Firstly\, it admits a
quotient which is projective. Secondly\, the cohomology of the quotient ca
n be computed inductively in terms of that of X. This talk is guided by th
e following question: within the unstable locus\, namely the complement of
the semistable locus\, is there a suitable notion of "stability" such tha
t the associated "stable" locus also satisfies these same two properties?
I will explain how a recent generalisation of GIT\, called Non-Reductive G
IT\, can be used to give a positive answer to this question\, and illustra
te the resulting notions of "stability" in the case of rank 2 Higgs bundle
s.\n
LOCATION:https://researchseminars.org/talk/AGGITatE2022/1/
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SUMMARY:Frances Kirwan (University of Oxford)
DTSTART:20220407T133000Z
DTEND:20220407T143000Z
DTSTAMP:20260422T215144Z
UID:AGGITatE2022/2
DESCRIPTION:Title: GIT and Chow quotients\nby Frances Kirwan (University of Oxford)
as part of AGGITatE Days 2022: Algebraic Groups and Geometric Invariant Th
eory at Essex\n\nLecture held in NTC 2.01.\n\nAbstract\nWhen a reductive g
roup G acts linearly on a projective variety X\, Mumford's geometric invar
iant theory (GIT) provides a 'GIT quotient' which depends on the linearisa
tion of the group action with respect to an ample line bundle on X. The 'C
how quotient' (due to Kapranov and others) is independent of the choice of
linearisation but is often more difficult to understand geometrically. Th
e aim of this talk is to explore the relationship between these constructi
ons and related constructions for non-reductive group actions.\n
LOCATION:https://researchseminars.org/talk/AGGITatE2022/2/
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BEGIN:VEVENT
SUMMARY:Jesus Martinez-Garcia (University of Essex)
DTSTART:20220407T150000Z
DTEND:20220407T160000Z
DTSTAMP:20260422T215144Z
UID:AGGITatE2022/3
DESCRIPTION:Title: Computational Geometric Invariant Theory via Sagemath\nby Jesus M
artinez-Garcia (University of Essex) as part of AGGITatE Days 2022: Algebr
aic Groups and Geometric Invariant Theory at Essex\n\nLecture held in NTC
2.01.\n\nAbstract\nI will discuss a (pseudo-)algorithmical way to describe
(semi/poly-)stable points in GIT problems. I will describe the method and
apply it to the study of moduli problems whose elements are naturally rep
resented as points in projective space and the group acting on it is simpl
e. However\, the method is easily generalised to other settings (such as p
roducts of grassmannians\, semi-simple groups). In our particular situatio
n of groups on projective space\, I will demonstrate the algorithmical nat
ure by running some Sagemath code. I will also discuss applications to the
description of the K-moduli of Fano 3-folds. This is joint work with Patr
icio Gallardo\, Han-Bom Moon and David Swinarski.\n
LOCATION:https://researchseminars.org/talk/AGGITatE2022/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gerhard Röhrle (Ruhr-Universität Bochum)
DTSTART:20220408T080000Z
DTEND:20220408T090000Z
DTSTAMP:20260422T215144Z
UID:AGGITatE2022/4
DESCRIPTION:Title: Overgroups of regular unipotent elements in reductive groups\nby
Gerhard Röhrle (Ruhr-Universität Bochum) as part of AGGITatE Days 2022:
Algebraic Groups and Geometric Invariant Theory at Essex\n\nLecture held i
n NTC 2.01.\n\nAbstract\nThere is a long and remarkable history of the stu
dy of the subgroup structure of reductive algebraic groups. This in partic
ular involves overgroups of special elements. I shall report on recent joi
nt work with Michael Bate and Ben Martin where we study reductive subgroup
s H of a reductive linear algebraic group G such that H contains a regular
unipotent element of G. We show that under suitable hypotheses\, such sub
groups are G-irreducible in the sense of Serre\; this means such H are not
contained in a proper parabolic subgroup of G. This work generalizes prev
ious results of Malle\, Testerman and Zalesski. Time permitting I shall in
dicate analogous results for Lie algebras and for finite groups of Lie typ
e.\n
LOCATION:https://researchseminars.org/talk/AGGITatE2022/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Theodoros Papazachariou (University of Essex)
DTSTART:20220408T090000Z
DTEND:20220408T100000Z
DTSTAMP:20260422T215144Z
UID:AGGITatE2022/5
DESCRIPTION:by Theodoros Papazachariou (University of Essex) as part of AG
GITatE Days 2022: Algebraic Groups and Geometric Invariant Theory at Essex
\n\nLecture held in NTC 2.01.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/AGGITatE2022/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Martin (University of Aberdeen)
DTSTART:20220408T103000Z
DTEND:20220408T113000Z
DTSTAMP:20260422T215144Z
UID:AGGITatE2022/6
DESCRIPTION:by Benjamin Martin (University of Aberdeen) as part of AGGITat
E Days 2022: Algebraic Groups and Geometric Invariant Theory at Essex\n\nL
ecture held in NTC 2.01.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/AGGITatE2022/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alastair Litterick (University of Essex)
DTSTART:20220408T113000Z
DTEND:20220408T123000Z
DTSTAMP:20260422T215144Z
UID:AGGITatE2022/7
DESCRIPTION:Title: Overgroups of regular unipotent elements in reductive groups\nby
Alastair Litterick (University of Essex) as part of AGGITatE Days 2022: Al
gebraic Groups and Geometric Invariant Theory at Essex\n\nLecture held in
NTC 2.01.\n\nAbstract\nThere is a long and remarkable history of the study
of the subgroup structure of reductive algebraic groups. This in particul
ar involves overgroups of special elements. I shall report on recent joint
work with Michael Bate and Ben Martin where we study reductive subgroups
H of a reductive linear algebraic group G such that H contains a regular u
nipotent element of G. We show that under suitable hypotheses\, such subgr
oups are G-irreducible in the sense of Serre\; this means such H are not c
ontained in a proper parabolic subgroup of G. This work generalizes previo
us results of Malle\, Testerman and Zalesski. Time permitting I shall indi
cate analogous results for Lie algebras and for finite groups of Lie type.
\n
LOCATION:https://researchseminars.org/talk/AGGITatE2022/7/
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