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SUMMARY:Eloise Hamilton (University of Cambridge)
DTSTART:20220407T123000Z
DTEND:20220407T133000Z
DTSTAMP:20260404T131142Z
UID:AGGITatE2022/1
DESCRIPTION:Title: Stability within instability\nby Eloise Hamilton (Universi
ty of Cambridge) as part of AGGITatE Days 2022: Algebraic Groups and Geome
tric Invariant Theory at Essex\n\nLecture held in NTC 2.01.\n\nAbstract\nG
iven the linear action of a reductive group G on a projective variety X\,
Geometric Invariant Theory (GIT) produces an open locus inside X\, called
the semistable locus\, which has two important properties. Firstly\, it ad
mits a quotient which is projective. Secondly\, the cohomology of the quot
ient can be computed inductively in terms of that of X. This talk is guide
d by the following question: within the unstable locus\, namely the comple
ment of the semistable locus\, is there a suitable notion of "stability" s
uch that the associated "stable" locus also satisfies these same two prope
rties? I will explain how a recent generalisation of GIT\, called Non-Redu
ctive GIT\, can be used to give a positive answer to this question\, and i
llustrate the resulting notions of "stability" in the case of rank 2 Higgs
bundles.\n
LOCATION:https://stable.researchseminars.org/talk/AGGITatE2022/1/
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SUMMARY:Frances Kirwan (University of Oxford)
DTSTART:20220407T133000Z
DTEND:20220407T143000Z
DTSTAMP:20260404T131142Z
UID:AGGITatE2022/2
DESCRIPTION:Title: GIT and Chow quotients\nby Frances Kirwan (University of O
xford) as part of AGGITatE Days 2022: Algebraic Groups and Geometric Invar
iant Theory at Essex\n\nLecture held in NTC 2.01.\n\nAbstract\nWhen a redu
ctive group G acts linearly on a projective variety X\, Mumford's geometri
c invariant theory (GIT) provides a 'GIT quotient' which depends on the li
nearisation of the group action with respect to an ample line bundle on X.
The 'Chow quotient' (due to Kapranov and others) is independent of the ch
oice of linearisation but is often more difficult to understand geometrica
lly. The aim of this talk is to explore the relationship between these con
structions and related constructions for non-reductive group actions.\n
LOCATION:https://stable.researchseminars.org/talk/AGGITatE2022/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jesus Martinez-Garcia (University of Essex)
DTSTART:20220407T150000Z
DTEND:20220407T160000Z
DTSTAMP:20260404T131142Z
UID:AGGITatE2022/3
DESCRIPTION:Title: Computational Geometric Invariant Theory via Sagemath\nby
Jesus Martinez-Garcia (University of Essex) as part of AGGITatE Days 2022:
Algebraic Groups and Geometric Invariant Theory at Essex\n\nLecture held
in NTC 2.01.\n\nAbstract\nI will discuss a (pseudo-)algorithmical way to d
escribe (semi/poly-)stable points in GIT problems. I will describe the met
hod and apply it to the study of moduli problems whose elements are natura
lly represented as points in projective space and the group acting on it i
s simple. However\, the method is easily generalised to other settings (su
ch as products of grassmannians\, semi-simple groups). In our particular s
ituation of groups on projective space\, I will demonstrate the algorithmi
cal nature 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 wi
th Patricio Gallardo\, Han-Bom Moon and David Swinarski.\n
LOCATION:https://stable.researchseminars.org/talk/AGGITatE2022/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gerhard Röhrle (Ruhr-Universität Bochum)
DTSTART:20220408T080000Z
DTEND:20220408T090000Z
DTSTAMP:20260404T131142Z
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 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
particular involves overgroups of special elements. I shall report on rec
ent joint work with Michael Bate and Ben Martin where we study reductive s
ubgroups H of a reductive linear algebraic group G such that H contains a
regular unipotent element of G. We show that under suitable hypotheses\, s
uch subgroups are G-irreducible in the sense of Serre\; this means such H
are not contained in a proper parabolic subgroup of G. This work generaliz
es previous results of Malle\, Testerman and Zalesski. Time permitting I s
hall indicate analogous results for Lie algebras and for finite groups of
Lie type.\n
LOCATION:https://stable.researchseminars.org/talk/AGGITatE2022/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Theodoros Papazachariou (University of Essex)
DTSTART:20220408T090000Z
DTEND:20220408T100000Z
DTSTAMP:20260404T131142Z
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://stable.researchseminars.org/talk/AGGITatE2022/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Martin (University of Aberdeen)
DTSTART:20220408T103000Z
DTEND:20220408T113000Z
DTSTAMP:20260404T131142Z
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://stable.researchseminars.org/talk/AGGITatE2022/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alastair Litterick (University of Essex)
DTSTART:20220408T113000Z
DTEND:20220408T123000Z
DTSTAMP:20260404T131142Z
UID:AGGITatE2022/7
DESCRIPTION:Title: Overgroups of regular unipotent elements in reductive groups\nby Alastair Litterick (University of Essex) as part of AGGITatE Days 2
022: Algebraic Groups and Geometric Invariant Theory at Essex\n\nLecture h
eld in NTC 2.01.\n\nAbstract\nThere is a long and remarkable history of th
e study of the subgroup structure of reductive algebraic groups. This in p
articular involves overgroups of special elements. I shall report on recen
t joint work with Michael Bate and Ben Martin where we study reductive sub
groups H of a reductive linear algebraic group G such that H contains a re
gular unipotent element of G. We show that under suitable hypotheses\, suc
h subgroups are G-irreducible in the sense of Serre\; this means such H ar
e not contained in a proper parabolic subgroup of G. This work generalizes
previous results of Malle\, Testerman and Zalesski. Time permitting I sha
ll indicate analogous results for Lie algebras and for finite groups of Li
e type.\n
LOCATION:https://stable.researchseminars.org/talk/AGGITatE2022/7/
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