BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Sira Gratz (University of Glasgow) DTSTART:20210224T131500Z DTEND:20210224T141500Z DTSTAMP:20260404T095356Z UID:AarHomAlg/1 DESCRIPTION:Title: Grassmannians\, Cluster Algebras and Hypersurface Singularities\nby Sira Gratz (University of Glasgow) as part of Aarhus Homological Al gebra Seminar\n\n\nAbstract\nGrassmannians are objects of great combinator ial and geometric beauty\, which arise in myriad contexts. Their coordinat e rings serve as a classic example of cluster algebras\, as introduced by Fomin and Zelevinsky at the start of the millennium\, and their combinator ics is intimately related to algebraic and geometric concepts such as to r epresentations of algebras and hypersurface singularities. At the core lie s the idea of generating an object from a so-called "cluster" via the conc ept of "mutation".\n\nIn this talk\, we offer an overview of Grassmannian combinatorics in a cluster theoretic framework\, and ultimately take them to the limit to explore the a priori simple question: What happens if we a llow infinite clusters? In particular\, we introduce the notion of a clust er algebra of infinite rank (based on joint work with Grabowski)\, and of a Grassmannian category of infinite rank (based on joint work with August\ , Cheung\, Faber and Schroll).\n LOCATION:https://stable.researchseminars.org/talk/AarHomAlg/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Rosanna Laking (University of Verona) DTSTART:20210310T131500Z DTEND:20210310T141500Z DTSTAMP:20260404T095356Z UID:AarHomAlg/2 DESCRIPTION:Title: Mutation and minimal inclusions of torsion classes\nby Rosann a Laking (University of Verona) as part of Aarhus Homological Algebra Semi nar\n\n\nAbstract\nTorsion pairs are fundamental tools in the study of abe lian categories\, which contain important information related to derived c ategories and their t-structures. In this talk we will consider the latti ce of torsion classes in the category of finite-dimensional modules over a finite-dimensional algebra\, with a particular focus on the minimal inclu sions of torsion classes.\n\nIt was shown by Adachi\, Iyama and Reiten tha t minimal inclusions of functorially finite torsion classes correspond to irreducible mutations of associated two-term silting complexes in the cate gory of perfect complexes. In this talk we will explain how minimal inclu sions of arbitrary torsion classes correspond to irreducible mutations of associated two-term cosilting complexes in the unbounded derived category. \n\nThis talk will be based on joint work with Lidia Angeleri Hügel\, Jan Stovicek and Jorge Vitória.\n LOCATION:https://stable.researchseminars.org/talk/AarHomAlg/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Karin Baur (University of Leeds) DTSTART:20210317T131500Z DTEND:20210317T141500Z DTSTAMP:20260404T095356Z UID:AarHomAlg/3 DESCRIPTION:Title: Orbifold diagrams and skew group categories\nby Karin Baur (U niversity of Leeds) as part of Aarhus Homological Algebra Seminar\n\n\nAbs tract\nAlternating strand diagrams (as introduced by Postnikov) on the dis k have been used in the study of the coordinate ring of the Grassmannian. In particular\, they give rise to clusters of the Grassmannian cluster alg ebras (Scott) or to cluster-tilting objects of the Grassmannian cluster ca tegories of Jensen-King-Su (Baur-King-Marsh). On the other hand\, orbifold s have also been related to cluster structures as Paquette-Schiffler (or C hekhov-Shapiro for a geometric approach). Here we introduce orbifold diagr ams as quotients of symmetric Postnikov diagrams and show how to associate quivers with potentials to them. This is joint work with Andrea Pasquali (Stuttgart) and Diego Velasco (Cali).\n LOCATION:https://stable.researchseminars.org/talk/AarHomAlg/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Ilke Canakci (Vrije Universiteit Amsterdam) DTSTART:20210421T121500Z DTEND:20210421T133000Z DTSTAMP:20260404T095356Z UID:AarHomAlg/4 DESCRIPTION:Title: Infinite friezes\nby Ilke Canakci (Vrije Universiteit Amsterd am) as part of Aarhus Homological Algebra Seminar\n\n\nAbstract\nFrieze pa tterns\, introduced by Coxeter\, are infinite arrays of numbers where neig hbouring numbers satisfy a local arithmetic rule. Under a certain finitene ss assumption\, they are in one-to-one correspondence with triangulations of polygons [Conway–Coxeter] and they come from triangulations of annuli in an infinite setting [Baur–Parsons–Tschabold]. In this talk\, we wi ll discuss a relationship between pairs of infinite friezes associated wit h a triangulation of the annulus and explore how one determines the other in an essentially unique way. We will also consider module categories asso ciated with triangulated annuli where infinite friezes may be recovered us ing a homological formula. This is joint work with Karin Baur\, Karin Jaco bsen\, Maitreyee Kulkarni\, and Gordana Todorov.\n LOCATION:https://stable.researchseminars.org/talk/AarHomAlg/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Jorge Vitoria (University of Cagliari) DTSTART:20210426T110000Z DTEND:20210426T120000Z DTSTAMP:20260404T095356Z UID:AarHomAlg/5 DESCRIPTION:Title: Hearts for commutative noetherian rings: derived equivalences and torsion pairs\nby Jorge Vitoria (University of Cagliari) as part of A arhus Homological Algebra Seminar\n\n\nAbstract\nThe structure of the cate gory of modules over a commutative noetherian ring R and of its derived ca tegory 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-structure s in the derived category. We will focus in particular on hearts arising f rom hereditary torsion pairs in Mod(R). These turn out to be Grothendieck categories which are derived equivalent to R and such that part of the la ttice of torsion pairs can be studied using the prime spectrum of R. This talk is based on joint work with Sergio Pavon.\n LOCATION:https://stable.researchseminars.org/talk/AarHomAlg/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Susan J. Sierra (University of Edinburgh) DTSTART:20210505T121500Z DTEND:20210505T131500Z DTSTAMP:20260404T095356Z UID:AarHomAlg/6 DESCRIPTION:Title: The Poisson spectrum of the symmetric algebra of the Virasoro alg ebra\nby Susan J. Sierra (University of Edinburgh) as part of Aarhus H omological Algebra Seminar\n\n\nAbstract\nLet W be the Witt algebra of pol ynomial vector fields on the punctured\ncomplex plane\, and let Vir be the Virasoro algebra\, the unique nontrivial central\nextension of W. We disc uss work in progress with Alexey Petukhov to analyse\nPoisson ideals of th e symmetric algebra of Vir. We focus on understanding\nmaximal Poisson ide als\, which can be given as the Poisson cores of maximal\nideals of Sym(Vi r) and of Sym(W). We give a complete classification of maximal\nideals of Sym(W) which have nontrivial Poisson cores. We then lift this\nclassificat ion to Sym(Vir)\, and use it to show that if $\\lambda \\neq 0$\, then $(z -\n\\lambda)$ is a maximal Poisson ideal of Sym(Vir).\n LOCATION:https://stable.researchseminars.org/talk/AarHomAlg/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Man-Wai Cheung (Harvard University) DTSTART:20210510T110000Z DTEND:20210510T120000Z DTSTAMP:20260404T095356Z UID:AarHomAlg/7 DESCRIPTION:Title: Tropical disks counting\, stability conditions in symplectic geom etry and quiver representations\nby Man-Wai Cheung (Harvard University ) as part of Aarhus Homological Algebra Seminar\n\n\nAbstract\nBridgeland developed stability scattering diagrams relating scattering diagrams with quiver representations. Scattering diagrams were developed as a machinery in mirror symmetry. Together with Travis Mandel\, we associate tropical di sks counting with\nquiver representations by using the stability scatterin g diagrams.\nNext\, together with Yu-Wei Fan and Yu-Shen Lin\, we look at the stable objects for the $A_2$ quiver. It is known that the derived Fuka ya-Seidel category of the rational elliptic surface is the derived categor y of the $A_2$ quiver. We made use of the relation and corresponded the sp ecial Lagrangian with the stable objects in the derived category of cohere nt sheaves.\n LOCATION:https://stable.researchseminars.org/talk/AarHomAlg/7/ END:VEVENT END:VCALENDAR