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:20260422T225717Z 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/ END:VEVENT BEGIN:VEVENT SUMMARY:Rosanna Laking (University of Verona) DTSTART:20210310T131500Z DTEND:20210310T141500Z DTSTAMP:20260422T225717Z 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/ END:VEVENT BEGIN:VEVENT SUMMARY:Karin Baur (University of Leeds) DTSTART:20210317T131500Z DTEND:20210317T141500Z DTSTAMP:20260422T225717Z 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/ END:VEVENT BEGIN:VEVENT SUMMARY:Ilke Canakci (Vrije Universiteit Amsterdam) DTSTART:20210421T121500Z DTEND:20210421T133000Z DTSTAMP:20260422T225717Z 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/ END:VEVENT BEGIN:VEVENT SUMMARY:Jorge Vitoria (University of Cagliari) DTSTART:20210426T110000Z DTEND:20210426T120000Z DTSTAMP:20260422T225717Z 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/ END:VEVENT BEGIN:VEVENT SUMMARY:Susan J. Sierra (University of Edinburgh) DTSTART:20210505T121500Z DTEND:20210505T131500Z DTSTAMP:20260422T225717Z 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 BEGIN:VEVENT SUMMARY:Man-Wai Cheung (Harvard University) DTSTART:20210510T110000Z DTEND:20210510T120000Z DTSTAMP:20260422T225717Z 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/ END:VEVENT END:VCALENDAR