BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Lidia Angeleri Hügel (Università degli Studi di Verona) DTSTART:20210301T140000Z DTEND:20210301T144500Z DTSTAMP:20260421T090249Z UID:cats2021/2 DESCRIPTION:Title: minicourse: Silting and tilting theory I\nby Lidia Angeleri Hügel (U niversità degli Studi di Verona) as part of Additive categories between a lgebra and functional analysis\n\n\nAbstract\nThis mini-course provides an introduction to the notion of a silting object in a triangulated category with coproducts\, introduced independently by Psaroudakis and Vitória\, and by Nicolás\, Saorín and Zvonareva. We will see that silting objects correspond bijectively to certain triples formed by a t-structure and an a djacent co-t-structure. We will also discuss the dual notion of a cosiltin g object and the role of purity in this context. We will then present a no tion of mutation for cosilting objects. Since our objects are not required to be compact\, mutation is not always possible: it is controlled by prop erties of certain torsion pairs in the heart of the associated t-structure . In the case of a two-term cosilting complex in the derived category of a finite dimensional algebra A\, we will explain how these constraints are reflected in the lattice torsA of all torsion pairs in the category modA f ormed by the finite dimensional A-modules.\n\n\n\nThe lectures will be bas ed on joint work with Michal Hrbek\, Rosanna Laking\, Frederik Marks\, Jan Šťovíček and Jorge Vitória.\n LOCATION:https://researchseminars.org/talk/cats2021/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Sven-Ake Wegner (University of Hamburg) DTSTART:20210301T150000Z DTEND:20210301T154500Z DTSTAMP:20260421T090249Z UID:cats2021/3 DESCRIPTION:Title: minicourse: Non-abelian categories in functional analysis I\nby Sven- Ake Wegner (University of Hamburg) as part of Additive categories between algebra and functional analysis\n\n\nAbstract\nIn this mini course we give an introduction to different types of non-abelian categories appearing in functional analysis. Their hierarchy will be discussed and applications o f homological techniques like the existence of extension operators or the parameter dependence of solutions of linear partial differential equations will be sketched. Also\, we will treat examples of exact structures and t he question if they lead to derived equivalences.\n LOCATION:https://researchseminars.org/talk/cats2021/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Yann Palu (UPJV Amiens) DTSTART:20210301T160000Z DTEND:20210301T164500Z DTSTAMP:20260421T090249Z UID:cats2021/4 DESCRIPTION:Title: minicourse: Extriangulated categories I\nby Yann Palu (UPJV Amiens) a s part of Additive categories between algebra and functional analysis\n\n\ nAbstract\nThis minicourse is an introduction to extriangulated categories \, defined in collaboration with Hiroyuki Nakaoka. Extriangulated categori es generalize both exact categories (in the sense of Quillen) and triangul ated categories. \nThe first part of the minicourse will be dedicated to m otivating their definition. Our aim is to present many examples\, and some applications in representation theory.\n LOCATION:https://researchseminars.org/talk/cats2021/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Lidia Angeleri Hügel (Università degli Studi di Verona) DTSTART:20210302T140000Z DTEND:20210302T144500Z DTSTAMP:20260421T090249Z UID:cats2021/5 DESCRIPTION:Title: minicourse: Silting and tilting theory II\nby Lidia Angeleri Hügel ( Università degli Studi di Verona) as part of Additive categories between algebra and functional analysis\n\n\nAbstract\nThis mini-course provides a n introduction to the notion of a silting object in a triangulated categor y with coproducts\, introduced independently by Psaroudakis and Vitória\, and by Nicolás\, Saorín and Zvonareva. We will see that silting objects correspond bijectively to certain triples formed by a t-structure and an adjacent co-t-structure. We will also discuss the dual notion of a cosilti ng object and the role of purity in this context. We will then present a n otion of mutation for cosilting objects. Since our objects are not require d to be compact\, mutation is not always possible: it is controlled by pro per-ties of certain torsion pairs in the heart of the associated t-structu re. In the case of a two-term cosilting complex in the derived category of a finite dimensional algebra A\, we will explain how these con-straints a re reflected in the lattice torsA of all torsion pairs in the category mod A formed by the finite dimensional A-modules.\n\n\n\nThe lectures will be based on joint work with Rosanna Laking\, Frederik Marks\, Jan Šťoví ček and Jorge Vitória.\n LOCATION:https://researchseminars.org/talk/cats2021/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Sven-Ake Wegner (University of Hamburg) DTSTART:20210302T150000Z DTEND:20210302T154500Z DTSTAMP:20260421T090249Z UID:cats2021/6 DESCRIPTION:Title: minicourse: Non-abelian categories in functional analysis II\nby Sven -Ake Wegner (University of Hamburg) as part of Additive categories between algebra and functional analysis\n\n\nAbstract\nIn this mini course we giv e an introduction to different types of non-abelian categories appearing i n functional analysis. Their hierarchy will be discussed and applications of homological techniques like the existence of extension operators or the parameter dependence of solutions of linear partial differential equation s will be sketched. Also\, we will treat examples of exact structures and the question if they lead to derived equivalences.\n LOCATION:https://researchseminars.org/talk/cats2021/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Yann Palu (UPJV Amiens) DTSTART:20210302T160000Z DTEND:20210302T164500Z DTSTAMP:20260421T090249Z UID:cats2021/7 DESCRIPTION:Title: minicourse: Extriangulated categories II\nby Yann Palu (UPJV Amiens) as part of Additive categories between algebra and functional analysis\n\n \nAbstract\nThis minicourse is an introduction to extriangulated categorie s\, defined in collaboration with Hiroyuki Nakaoka. Extriangulated categor ies generalize both exact categories (in the sense of Quillen) and triangu lated categories. \nThe first part of the minicourse will be dedicated to motivating their definition. Our aim is to present many examples\, and som e applications in representation theory.\n LOCATION:https://researchseminars.org/talk/cats2021/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Lidia Angeleri Hügel (Università degli Studi di Verona) DTSTART:20210303T140000Z DTEND:20210303T144500Z DTSTAMP:20260421T090249Z UID:cats2021/8 DESCRIPTION:Title: minicourse: Silting and tilting theory III\nby Lidia Angeleri Hügel (Università degli Studi di Verona) as part of Additive categories between algebra and functional analysis\n\n\nAbstract\nThis mini-course provides an introduction to the notion of a silting object in a triangulated catego ry with coproducts\, introduced independently by Psaroudakis and Vitória\ , and by Nicolás\, Saorín and Zvonareva. We will see that silting object s correspond bijectively to certain triples formed by a t-structure and an adjacent co-t-structure. We will also discuss the dual notion of a cosilt ing object and the role of purity in this context. We will then present a notion of mutation for cosilting objects. Since our objects are not requir ed to be compact\, mutation is not always possible: it is controlled by pr oper-ties of certain torsion pairs in the heart of the associated t-struct ure. In the case of a two-term cosilting complex in the derived category o f a finite dimensional algebra A\, we will explain how these con-straints are reflected in the lattice torsA of all torsion pairs in the category mo dA formed by the finite dimensional A-modules.\n\n\n\nThe lectures will be based on joint work with Rosanna Laking\, Frederik Marks\, Jan Šťovi ́ček and Jorge Vitória.\n LOCATION:https://researchseminars.org/talk/cats2021/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Sven-Ake Wegner (University of Hamburg) DTSTART:20210303T150000Z DTEND:20210303T154500Z DTSTAMP:20260421T090249Z UID:cats2021/9 DESCRIPTION:Title: minicourse: Non-abelian categories in functional analysis III\nby Sve n-Ake Wegner (University of Hamburg) as part of Additive categories betwee n algebra and functional analysis\n\n\nAbstract\nIn this mini course we gi ve an introduction to different types of non-abelian categories appearing in functional analysis. Their hierarchy will be discussed and applications of homological techniques like the existence of extension operators or th e parameter dependence of solutions of linear partial differential equatio ns will be sketched. Also\, we will treat examples of exact structures and the question if they lead to derived equivalences.\n LOCATION:https://researchseminars.org/talk/cats2021/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Yann Palu (UPJV Amiens) DTSTART:20210303T160000Z DTEND:20210303T164500Z DTSTAMP:20260421T090249Z UID:cats2021/10 DESCRIPTION:Title: minicourse: Extriangulated categories III\nby Yann Palu (UPJV Amiens ) as part of Additive categories between algebra and functional analysis\n \n\nAbstract\nLink to the beamer slides on the non-kissing complex:\nhttps ://d28lcup14p4e72.cloudfront.net/261905/5800601/CATS21-Extriangulated-NKC. pdf\n LOCATION:https://researchseminars.org/talk/cats2021/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Bernhard Keller DTSTART:20210301T170000Z DTEND:20210301T174500Z DTSTAMP:20260421T090249Z UID:cats2021/11 DESCRIPTION:Title: minicourse: Derived categories of exact categories I\nby Bernhard Ke ller as part of Additive categories between algebra and functional analysi s\n\n\nAbstract\nIn this minicourse\, we will present the definition of ex act categories (in the sense of Quillen) and the construction of their der ived categories. In the second half of the minicourse\, we will investigat e how to characterize the embedding of an exact category into its (bounded ) derived category by a universal property. We will see how the languages of derivators and\, if time permits\, of infinity-categories\, allow to fo rmulate such properties.\n LOCATION:https://researchseminars.org/talk/cats2021/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Bernhard Keller DTSTART:20210302T170000Z DTEND:20210302T174500Z DTSTAMP:20260421T090249Z UID:cats2021/12 DESCRIPTION:Title: minicourse: Derived categories of exact categories II\nby Bernhard K eller as part of Additive categories between algebra and functional analys is\n\n\nAbstract\nIn this minicourse\, we will present the definition of e xact categories (in the sense of Quillen) and the construction of their de rived categories. In the second half of the minicourse\, we will investiga te how to characterize the embedding of an exact category into its (bounde d) derived category by a universal property. We will see how the languages of derivators and\, if time permits\, of infinity-categories\, allow to f ormulate such properties.\n LOCATION:https://researchseminars.org/talk/cats2021/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Bernhard Keller DTSTART:20210303T170000Z DTEND:20210303T174500Z DTSTAMP:20260421T090249Z UID:cats2021/13 DESCRIPTION:Title: minicourse: Derived categories of exact categories III\nby Bernhard Keller as part of Additive categories between algebra and functional analy sis\n\n\nAbstract\nIn this minicourse\, we will present the definition of exact categories (in the sense of Quillen) and the construction of their d erived categories. In the second half of the minicourse\, we will investig ate how to characterize the embedding of an exact category into its (bound ed) derived category by a universal property. We will see how the language s of derivators and\, if time permits\, of infinity-categories\, allow to formulate such properties.\n LOCATION:https://researchseminars.org/talk/cats2021/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexei Pirkovskii (HSE University\, Moscow) DTSTART:20210304T140000Z DTEND:20210304T143000Z DTSTAMP:20260421T090249Z UID:cats2021/14 DESCRIPTION:Title: Flat locally convex modules beyond the metrizable case\nby Alexei Pi rkovskii (HSE University\, Moscow) as part of Additive categories between algebra and functional analysis\n\n\nAbstract\nWe begin by surveying class ical results (due to Johnson\, Helemskii\, and Sheinberg) on amenable Bana ch algebras and flat Banach modules. In particular\, we discuss Helemskii- Sheinberg's theorem which states that a Banach algebra A is Johnson amenab le if and only if its unitization is a flat Banach A-bimodule. Next we loo k at some possible extensions of these concepts to more general locally co nvex algebras and modules. The "naive" generalization of the notion of a f lat Banach module to the nonmetrizable setting turns out to be not very us eful. We suggest a modified definition\, and we show how it works in concr ete situations. As an application\, we give a characterization of amenable co-echelon algebras obtained in our recent perprint with Krzysztof Piszcz ek. Curiously\, the nonmetrizable case requires some essentially new tools (as compared to the Banach case)\, not only from analysis\, but also from homological algebra (t-structures and their hearts).\n LOCATION:https://researchseminars.org/talk/cats2021/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Sergei Akbarov (Higher School of Economics) DTSTART:20210304T144500Z DTEND:20210304T151500Z DTSTAMP:20260421T090249Z UID:cats2021/15 DESCRIPTION:Title: Category of stereotype spaces\nby Sergei Akbarov (Higher School of E conomics) as part of Additive categories between algebra and functional an alysis\n\n\nAbstract\nIn this talk I'll present some standard facts about the category $\\operatorname{Ste}$ of stereotype spaces. These are locally convex spaces reflexive under the assumption that the dual space $X'$ is endowed with the topology of uniform convergence on totally bounded sets i n $X$. It is known that this category is extremely wide\, since it contain s all quasicomplete barreled spaces (in particular\, all Fréchet spaces). At the same time $\\operatorname{Ste}$ is pre-abelian\, bicomplete and a *-autonomous category. This\, in a sense\, makes $\\operatorname{Ste}$ uni que today among the categories of Functional Analysis in terms of its feat ure set and opens new unexpected connections between Functional Analysis a nd other areas of mathematics\, such as Algebra and Geometry.\n LOCATION:https://researchseminars.org/talk/cats2021/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Jochen Wengenroth (University of Trier) DTSTART:20210304T153000Z DTEND:20210304T160000Z DTSTAMP:20260421T090249Z UID:cats2021/16 DESCRIPTION:Title: The Mittag-Leffler condition in analysis\nby Jochen Wengenroth (Univ ersity of Trier) as part of Additive categories between algebra and functi onal analysis\n\n\nAbstract\nHomological algebraists have stolen the Mitta g-Leffler condition for projective systems as a tool to calculate\, e.g.\, cohomologies or derived functors. \n\nOn the occasion of Gösta Mittag-Le ffler's 175th birthday in two weeks\, we try to explain the origin and som e applications of his condition in functional analysis.\n LOCATION:https://researchseminars.org/talk/cats2021/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Simone Virili (Università degli studi di Udine) DTSTART:20210304T170000Z DTEND:20210304T173000Z DTSTAMP:20260421T090249Z UID:cats2021/17 DESCRIPTION:Title: Abelian recollements of categories of modules over preadditive categorie s\nby Simone Virili (Università degli studi di Udine) as part of Addi tive categories between algebra and functional analysis\n\n\nAbstract\nPsa roudakis and Vitoria have established that\, for a category of modules ove r a unitary ring\, there is a correspondence between Abelian recollements by categories of modules and idempotent elements in the ring. In this talk we show how to extend this results to modules over preadditive categories (i.e.\, rings with several objects). In this more general setting\, some of the proofs actually get simplified and the result can be probably bette r understood. \nFinally\, we apply the same methods to construct an exampl e of a locally finitely presented Grothendieck (Ab.4*) category that does not have enough projectives.\n LOCATION:https://researchseminars.org/talk/cats2021/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Francesca Mantese (University of Verona) DTSTART:20210304T174500Z DTEND:20210304T181500Z DTSTAMP:20260421T090249Z UID:cats2021/18 DESCRIPTION:Title: On the module category of Leavitt path algebras\nby Francesca Mantes e (University of Verona) as part of Additive categories between algebra an d functional analysis\n\n\nAbstract\nLeavitt path algebras were introduced in [1] as algebraic analogues of graph $C^{\\*}$-algebras and as natural generalizations of Leavitt algebras of type $(1\,n)$ built in [2]. Moreove r\, they turn out to be perfect localizations of path algebras [3]. The va rious ring-theoretical properties of these algebras have been actively inv estigated. In contrast\, the investigation of their module category is sti ll at an early stage.\nIn this talk we focus on the structure of the simpl e\, projective and injective modules over certain classes of Leavitt path algebras\, presenting results which are part of a joint project with Gene Abrams and Alberto Tonolo.\n\n\n\n[1] G. Abrams\, G. Aranda Pino\, The Lea vitt path algebra of a graph\, J. Algebra 293 (2005)\, 319 - 334.\n\n[2] W .G. Leavitt\, The module type of a ring\, Trans. Amer. Math. Soc. 103 (196 2)\, 113 - 130.\n\n[3] P.Ara\, M. Brustenga\, Module theory over Leavitt p ath algebras and K -theory\, J. Pure Appl. Algebra 214 (2010) 1131–1151 \n LOCATION:https://researchseminars.org/talk/cats2021/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Septimiu Crivei (Babes-Bolyai University) DTSTART:20210305T140000Z DTEND:20210305T143000Z DTSTAMP:20260421T090249Z UID:cats2021/19 DESCRIPTION:Title: Uniqueness of uniform decompositions in exact categories\nby Septimi u Crivei (Babes-Bolyai University) as part of Additive categories between algebra and functional analysis\n\n\nAbstract\nTwo uniqueness theorems on uniform decompositions due to Krause\, Diracca and Facchini are extended f rom abelian categories to weakly idempotent complete exact categories. We give applications to (quasi-)abelian categories\, finitely accessible addi tive categories and exactly definable additive categories. \n\nThis is joi nt work with Mustafa Kemal Berktas\, Fatma Kaynarca and Derya Keskin Tutun cu.\n LOCATION:https://researchseminars.org/talk/cats2021/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Aran Tattar DTSTART:20210305T144500Z DTEND:20210305T151500Z DTSTAMP:20260421T090249Z UID:cats2021/20 DESCRIPTION:Title: Intersections and sums in exact categories\nby Aran Tattar as part o f Additive categories between algebra and functional analysis\n\n\nAbstrac t\nWe discuss ways to generalise the intersections and sums of subobjects to exact categories (from abelian categories). One way leads to new charac terisations of quasi-abelian and abelian categories\; another allows us to study the Jordan-Hoelder property for exact categories and describe cases when this property is satisfied. \n\nBased on joint work with T. Brüstle and S. Hassoun\n LOCATION:https://researchseminars.org/talk/cats2021/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Luisa Fiorot DTSTART:20210305T153000Z DTEND:20210305T160000Z DTSTAMP:20260421T090249Z UID:cats2021/21 DESCRIPTION:Title: n-quasi-abelian categories\nby Luisa Fiorot as part of Additive cate gories between algebra and functional analysis\n\n\nAbstract\nGiven an abe lian category A its derived category D(A) admits a natural t-structure who se heart is A. Moreover by the Auslander’s Formula A is equivalent to th e quotient category of coherent functors by the Serre subcategory of effec able functors.\n\nWe can associate to an exact category E its derived cat egory D(E)\, does D(E) admit a canonical t-structure? If such a t-structur e exists\, is it possible to describe its heart in terms of coherent funct ors?\n\nTesting this problem on a quasi-abelian category E we get:\nits de rived category D(E) admits two canonical t-structures (left and right) who se hearts L and R are derived equivalent and their intersection in D(E) is E.\nIf E is quasi-abelian but not abelian the "distance" between these tw o t-structures is 1\, while in the abelian\ncase these two t-structures co incides and their "distance" is 0.\nMoreover L (resp. R) can be described by the Auslander’s Formula as the quotient category of contravariant (re sp. covariant) coherent functors by the Serre subcategory of effecable fun ctors.\n\nWe extend this picture into a hierarchy of n-quasi-abelian categ ories: n=0 are abelian categories\, n=1 are quasi-abelian categories\, n=2 are pre-abelian categories....\n\n\nThis talk is based on the paper\nhttp s://arxiv.org/abs/1602.08253v3\n LOCATION:https://researchseminars.org/talk/cats2021/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Gustavo Jasso DTSTART:20210305T170000Z DTEND:20210305T173000Z DTSTAMP:20260421T090249Z UID:cats2021/22 DESCRIPTION:Title: A quick introduction to n-exact categories\nby Gustavo Jasso as part of Additive categories between algebra and functional analysis\n\n\nAbstr act\nn-exact categories are a class of additive categories which can be re garded as analogues of exact categories from the point of view of Iyama's higher Auslander-Reiten theory and of higher homological algebra. In this 30 min talk I will give quick introduction to the theory of n-exact catego ries\, highlighting some of the main ideas and motivating examples.\n LOCATION:https://researchseminars.org/talk/cats2021/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Johanne Haugland (NTNU) DTSTART:20210305T174500Z DTEND:20210305T181500Z DTSTAMP:20260421T090249Z UID:cats2021/23 DESCRIPTION:Title: Functors and subcategories of n-exangulated categories\nby Johanne H augland (NTNU) as part of Additive categories between algebra and function al analysis\n\n\nAbstract\nHerschend\, Liu and Nakaoka introduced $n$-exan gulated categories as a higher dimensional analogue of extriangulated cate gories. Natural examples are given by $n$-exact and $(n+2)$-angulated cate gories in the sense of Jasso and Geiss–Keller–Oppermann. In this talk\ , we give a brief introduction to $n$-exangulated categories and explain h ow we can understand their subcategories in terms of subgroups of the asso ciated Grothendieck group. We also discuss functors between such categorie s. This is based on joint work in progress with R. Bennett-Tennenhaus\, M. H. Sandøy and A. Shah.\n LOCATION:https://researchseminars.org/talk/cats2021/23/ END:VEVENT END:VCALENDAR