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SUMMARY:Sira Gratz (University of Glasgow)
DTSTART;VALUE=DATE-TIME:20210224T131500Z
DTEND;VALUE=DATE-TIME:20210224T141500Z
DTSTAMP;VALUE=DATE-TIME:20210514T205146Z
UID:AarHomAlg/1
DESCRIPTION:Title: Grassmannians\, Cluster Algebras and Hypersurface Singularities\nby
Sira Gratz (University of Glasgow) as part of Aarhus Homological Algebra S
eminar\n\n\nAbstract\nGrassmannians are objects of great combinatorial and
geometric beauty\, which arise in myriad contexts. Their coordinate rings
serve as a classic example of cluster algebras\, as introduced by Fomin a
nd Zelevinsky at the start of the millennium\, and their combinatorics is
intimately related to algebraic and geometric concepts such as to represen
tations of algebras and hypersurface singularities. At the core lies the i
dea of generating an object from a so-called "cluster" via the concept of
"mutation".\n\nIn this talk\, we offer an overview of Grassmannian combina
torics in a cluster theoretic framework\, and ultimately take them to the
limit to explore the a priori simple question: What happens if we allow in
finite clusters? In particular\, we introduce the notion of a cluster alge
bra of infinite rank (based on joint work with Grabowski)\, and of a Grass
mannian category of infinite rank (based on joint work with August\, Cheun
g\, Faber and Schroll).\n
LOCATION:https://researchseminars.org/talk/AarHomAlg/1/
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SUMMARY:Rosanna Laking (University of Verona)
DTSTART;VALUE=DATE-TIME:20210310T131500Z
DTEND;VALUE=DATE-TIME:20210310T141500Z
DTSTAMP;VALUE=DATE-TIME:20210514T205146Z
UID:AarHomAlg/2
DESCRIPTION:Title: Mutation and minimal inclusions of torsion classes\nby Rosanna Lakin
g (University of Verona) as part of Aarhus Homological Algebra Seminar\n\n
\nAbstract\nTorsion pairs are fundamental tools in the study of abelian ca
tegories\, which contain important information related to derived categori
es and their t-structures. In this talk we will consider the lattice of t
orsion classes in the category of finite-dimensional modules over a finite
-dimensional algebra\, with a particular focus on the minimal inclusions o
f torsion classes.\n\nIt was shown by Adachi\, Iyama and Reiten that minim
al inclusions of functorially finite torsion classes correspond to irreduc
ible mutations of associated two-term silting complexes in the category of
perfect complexes. In this talk we will explain how minimal inclusions o
f arbitrary torsion classes correspond to irreducible mutations of associa
ted two-term cosilting complexes in the unbounded derived category.\n\nThi
s talk will be based on joint work with Lidia Angeleri Hügel\, Jan Stovic
ek and Jorge Vitória.\n
LOCATION:https://researchseminars.org/talk/AarHomAlg/2/
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SUMMARY:Karin Baur (University of Leeds)
DTSTART;VALUE=DATE-TIME:20210317T131500Z
DTEND;VALUE=DATE-TIME:20210317T141500Z
DTSTAMP;VALUE=DATE-TIME:20210514T205146Z
UID:AarHomAlg/3
DESCRIPTION:Title: Orbifold diagrams and skew group categories\nby Karin Baur (Universi
ty of Leeds) as part of Aarhus Homological Algebra Seminar\n\n\nAbstract\n
Alternating strand diagrams (as introduced by Postnikov) on the disk have
been used in the study of the coordinate ring of the Grassmannian. In part
icular\, they give rise to clusters of the Grassmannian cluster algebras (
Scott) or to cluster-tilting objects of the Grassmannian cluster categorie
s of Jensen-King-Su (Baur-King-Marsh). On the other hand\, orbifolds have
also been related to cluster structures as Paquette-Schiffler (or Chekhov-
Shapiro for a geometric approach). Here we introduce orbifold diagrams as
quotients of symmetric Postnikov diagrams and show how to associate quiver
s with potentials to them. This is joint work with Andrea Pasquali (Stuttg
art) and Diego Velasco (Cali).\n
LOCATION:https://researchseminars.org/talk/AarHomAlg/3/
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SUMMARY:Ilke Canakci (Vrije Universiteit Amsterdam)
DTSTART;VALUE=DATE-TIME:20210421T121500Z
DTEND;VALUE=DATE-TIME:20210421T133000Z
DTSTAMP;VALUE=DATE-TIME:20210514T205146Z
UID:AarHomAlg/4
DESCRIPTION:Title: Infinite friezes\nby Ilke Canakci (Vrije Universiteit Amsterdam) as
part of Aarhus Homological Algebra Seminar\n\n\nAbstract\nFrieze patterns\
, introduced by Coxeter\, are infinite arrays of numbers where neighbourin
g numbers satisfy a local arithmetic rule. Under a certain finiteness assu
mption\, they are in one-to-one correspondence with triangulations of poly
gons [Conway–Coxeter] and they come from triangulations of annuli in an
infinite setting [Baur–Parsons–Tschabold]. In this talk\, we will disc
uss a relationship between pairs of infinite friezes associated with a tri
angulation of the annulus and explore how one determines the other in an e
ssentially unique way. We will also consider module categories associated
with triangulated annuli where infinite friezes may be recovered using a h
omological formula. This is joint work with Karin Baur\, Karin Jacobsen\,
Maitreyee Kulkarni\, and Gordana Todorov.\n
LOCATION:https://researchseminars.org/talk/AarHomAlg/4/
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BEGIN:VEVENT
SUMMARY:Jorge Vitoria (University of Cagliari)
DTSTART;VALUE=DATE-TIME:20210426T110000Z
DTEND;VALUE=DATE-TIME:20210426T120000Z
DTSTAMP;VALUE=DATE-TIME:20210514T205146Z
UID:AarHomAlg/5
DESCRIPTION:Title: Hearts for commutative noetherian rings: derived equivalences and torsio
n pairs\nby Jorge Vitoria (University of Cagliari) as part of Aarhus H
omological Algebra Seminar\n\n\nAbstract\nThe structure of the category of
modules over a commutative noetherian ring R and of its derived category
is largely controlled by the prime spectrum of R. In this talk we discuss
how this control extends to the structure of hearts of t-structures in th
e derived category. We will focus in particular on hearts arising from her
editary torsion pairs in Mod(R). These turn out to be Grothendieck catego
ries which are derived equivalent to R and such that part of the lattice o
f torsion pairs can be studied using the prime spectrum of R. This talk i
s based on joint work with Sergio Pavon.\n
LOCATION:https://researchseminars.org/talk/AarHomAlg/5/
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SUMMARY:Susan J. Sierra (University of Edinburgh)
DTSTART;VALUE=DATE-TIME:20210505T121500Z
DTEND;VALUE=DATE-TIME:20210505T131500Z
DTSTAMP;VALUE=DATE-TIME:20210514T205146Z
UID:AarHomAlg/6
DESCRIPTION:Title: The Poisson spectrum of the symmetric algebra of the Virasoro algebra\nby Susan J. Sierra (University of Edinburgh) as part of Aarhus Homologi
cal Algebra Seminar\n\n\nAbstract\nLet W be the Witt algebra of polynomial
vector fields on the punctured\ncomplex plane\, and let Vir be the Viraso
ro algebra\, the unique nontrivial central\nextension of W. We discuss wor
k in progress with Alexey Petukhov to analyse\nPoisson ideals of the symme
tric algebra of Vir. We focus on understanding\nmaximal Poisson ideals\, w
hich can be given as the Poisson cores of maximal\nideals of Sym(Vir) and
of Sym(W). We give a complete classification of maximal\nideals of Sym(W)
which have nontrivial Poisson cores. We then lift this\nclassification to
Sym(Vir)\, and use it to show that if $\\lambda \\neq 0$\, then $(z-\n\\la
mbda)$ is a maximal Poisson ideal of Sym(Vir).\n
LOCATION:https://researchseminars.org/talk/AarHomAlg/6/
END:VEVENT
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SUMMARY:Man-Wai Cheung (Harvard University)
DTSTART;VALUE=DATE-TIME:20210510T110000Z
DTEND;VALUE=DATE-TIME:20210510T120000Z
DTSTAMP;VALUE=DATE-TIME:20210514T205146Z
UID:AarHomAlg/7
DESCRIPTION:Title: Tropical disks counting\, stability conditions in symplectic geometry an
d quiver representations\nby Man-Wai Cheung (Harvard University) as pa
rt of Aarhus Homological Algebra Seminar\n\n\nAbstract\nBridgeland develop
ed stability scattering diagrams relating scattering diagrams with quiver
representations. Scattering diagrams were developed as a machinery in mirr
or symmetry. Together with Travis Mandel\, we associate tropical disks cou
nting with\nquiver representations by using the stability scattering diagr
ams.\nNext\, together with Yu-Wei Fan and Yu-Shen Lin\, we look at the sta
ble objects for the $A_2$ quiver. It is known that the derived Fukaya-Seid
el category of the rational elliptic surface is the derived category of th
e $A_2$ quiver. We made use of the relation and corresponded the special L
agrangian with the stable objects in the derived category of coherent shea
ves.\n
LOCATION:https://researchseminars.org/talk/AarHomAlg/7/
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