\ n* Higher Auslander-Reiten theory in the sense of Iyama

\n* Waldhausen K-theory of differential graded categories\n\nIf time permits\, as a first application of the above relationship\, I\nwill outline a symplecto-geome tric proof of a recent result of Beckert\nconcerning the derived equivalen ce between higher Auslander algebras of\ndifferent dimensions. This is a r eport on joint work with Tobias\nDyckerhoff and Yankı Lekili.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Baptiste Rognerud (University of Paris) DTSTART;VALUE=DATE-TIME:20200608T120000Z DTEND;VALUE=DATE-TIME:20200608T123000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/8 DESCRIPTION:Title: Combinatorics of quasi-hereditary structures\, I\nby Bap tiste Rognerud (University of Paris) as part of Paris algebra seminar\n\n\ nAbstract\nQuasi-hereditary algebras were introduced by Cline\, Parshall a nd Scott as a tool to study highest weight theories which arise in the rep resentation theories of semi-simple complex Lie algebras and reductive gro ups. Surprisingly\, there are now many examples of such algebras\, such as Schur algebras\, algebras of global dimension at most two\, incidence alg ebras and many more.\n\nA quasi-hereditary algebra is an Artin algebra tog ether with a partial order on its set of isomorphism classes of simple mod ules which satisfies certain conditions. In the early examples the partial order predated (and motivated) the theory\, so the choice was clear. Howe ver\, there are instances of quasi-hereditary algebras where there is no n atural choice for the partial ordering and even if there is such a natural choice\, one may wonder about all the possible orderings.\nIn this talk w e will explain that all these choices for an algebra $A$ can be organized in a finite partial order which is in relation with the tilting theory of $A$. In a second part of the talk we will focus on the case where $A$ is t he path algebra of a Dynkin quiver.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Yuta Kimura (Bielefeld) DTSTART;VALUE=DATE-TIME:20200608T123000Z DTEND;VALUE=DATE-TIME:20200608T130000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/9 DESCRIPTION:Title: Combinatorics of quasi-hereditary structures\, II\nby Yu ta Kimura (Bielefeld) as part of Paris algebra seminar\n\n\nAbstract\nQuas i-hereditary algebras were introduced by Cline\, Parshall and Scott as a t ool to study highest weight theories which arise in the representation the ories of semi-simple complex Lie algebras and reductive groups. Surprising ly\, there are now many examples of such algebras\, such as Schur algebras \, algebras of global dimension at most two\, incidence algebras and many more.\n\nA quasi-hereditary algebra is an Artin algebra together with a pa rtial order on its set of isomorphism classes of simple modules which sati sfies certain conditions. In the early examples the partial order predated (and motivated) the theory\, so the choice was clear. However\, there are instances of quasi-hereditary algebras where there is no natural choice f or the partial ordering and even if there is such a natural choice\, one m ay wonder about all the possible orderings.\nIn this talk we will explain that all these choices for an algebra $A$ can be organized in a finite par tial order which is in relation with the tilting theory of $A$. In a secon d part of the talk we will focus on the case where $A$ is the path algebra of a Dynkin quiver.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Christof Geiss (UNAM) DTSTART;VALUE=DATE-TIME:20200615T120000Z DTEND;VALUE=DATE-TIME:20200615T130000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/10 DESCRIPTION:Title: Generic bases for surface cluster algebras\nby Christof Geiss (UNAM) as part of Paris algebra seminar\n\n\nAbstract\nThis is a re port on joint work with D. Labardini-Fragoso and J. Schröer. We show that for most marked surfaces with non-empty boundary\, possibly with puncture s\, the generic Caldero-Chapoton functions form a basis of the correspondi ng cluster algebras for any choice of geometric coefficients. For surfaces without punctures the $\\tau$-reduced components of the corresponding gen tle Jacobian algebra are naturally parametrized by X-laminations of the su rface\, and it is easy to see that for principal coefficients\, the generi c basis coincides with the bangle basis introduced by Musiker-Schiffler-Wi lliams.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Myungho Kim (Kyung Hee University\, Seoul) DTSTART;VALUE=DATE-TIME:20200622T120000Z DTEND;VALUE=DATE-TIME:20200622T130000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/11 DESCRIPTION:Title: Braid group action on the module category of quantum affine algebras\nby Myungho Kim (Kyung Hee University\, Seoul) as part of Pa ris algebra seminar\n\n\nAbstract\nLet $g_0$ be a simple Lie algebra of ty pe $ADE$ and let $U′_q(g)$ be the corresponding untwisted quantum affine algebra. We found an action of the braid group $B(g_0)$ on the quantum Gr othendieck ring $K_t(g)$ of Hernandez-Leclerc's category $C^0_g$. In the c ase of $g_0=A_{N−1}$\, we construct a monoidal autofunctor $S_i$ for eac h integer $i$ on a category $T_N$ arising from the quiver Hecke algebra o f type $A_\\infty$. \nSince there is an isomorphism between the Grothendie ck ring $K(T_N)$ of $T_N$ and the quantum Grothendieck ring $K_t(A^(1)_{N −1})$\, the functors $S_i$\, $(i=1\, ...\, N-1)$\, recover the action of the braid group $B(A_{N−1})$. \nThis is a joint work with Masaki Kashiw ara\, Euiyong Park and Se-jin Oh.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Osamu Iyama (Nagoya) DTSTART;VALUE=DATE-TIME:20200713T120000Z DTEND;VALUE=DATE-TIME:20200713T130000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/13 DESCRIPTION:Title: Tilting theory of contracted preprojective algebras and cDV singularities\nby Osamu Iyama (Nagoya) as part of Paris algebra semin ar\n\n\nAbstract\nA preprojective algebra of non-Dynkin type has a family of tilting modules associated with the elements in the corresponding Coxet er group W. This family is useful to study the representation theory of th e preprojective algebra and also to categorify cluster algebras.\nIn this talk\, I will discuss tilting theory of a contracted preprojective algebra \, which is a subalgebra eAe of a preprojective algebra A given by an idem potent e of A. It has a family of tilting modules associated with the cham bers in the contracted Tits cone. They correspond bijectively with certain double cosets in W modulo parabolic subgroups. \nI will apply these resul ts to classify a certain family of reflexive modules over a cDV singularit ies R\, called maximal modifying (=MM) modules. We construct an injective map from MM R-modules to tilting modules over a contracted preprojective a lgebra of extended Dynkin type. This is bijective if R has at worst an iso lated singularity. We can recover previous results (Burban-I-Keller-Reiten \, I-Wemyss) as a very special case.\nThis is joint work with Michael Wemy ss.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Linyuan Liu (刘琳媛) (Sydney) DTSTART;VALUE=DATE-TIME:20200629T120000Z DTEND;VALUE=DATE-TIME:20200629T130000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/14 DESCRIPTION:Title: Modular Brylinski-Kostant filtration of tilting modules \nby Linyuan Liu (刘琳媛) (Sydney) as part of Paris algebra seminar\n\n \nAbstract\nLet $G$ be a reductive algebraic group over a field $k$. When $k=\\mathbb{C}$\, R. K. Brylinski constructed a filtration of weight space s of a $G$-module\, using the action of a principal nilpotent element of t he Lie algebra\, and proved that this filtration corresponds to Lusztig's $q$-analogue of the weight multiplicity. Later\, Ginzburg discovered that this filtration has an interesting geometric interpretation via the geomet ric Satake correspondence. Recently\, we managed to generalise this result to the case where $k$ is a field of good positive characteristics. I will give a brief introduction to both historical results and our new result i n the talk.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Xin Fang (房欣) (Cologne) DTSTART;VALUE=DATE-TIME:20200706T120000Z DTEND;VALUE=DATE-TIME:20200706T123000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/15 DESCRIPTION:Title: Exact structures and degenerations of Hall algebras\, I \nby Xin Fang (房欣) (Cologne) as part of Paris algebra seminar\n\n\nAbs tract\nIn this talk\, we will explain relations between exact structures o n an additively finite additive category and degenerations of the associat ed Hall algebras. The first part of the talk will be devoted to the main m otivation provided by concrete examples of degenerations of negative parts of quantum groups arising as Hall algebras of quiver representations. We will then turn to Lie theory in order to establish a link from these examp les to tropical flag varieties and certain quiver Grassmannians. In the se cond part of the talk we will present results in the general case and sket ch their proofs based on Auslander-Reiten theory. If time permits\, we wil l briefly discuss further conjectural examples and generalizations.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Mikhail Gorsky (Stuttgart) DTSTART;VALUE=DATE-TIME:20200706T123000Z DTEND;VALUE=DATE-TIME:20200706T130000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/16 DESCRIPTION:Title: Exact structures and degenerations of Hall algebras\, II\nby Mikhail Gorsky (Stuttgart) as part of Paris algebra seminar\n\n\nAbs tract\nIn this talk\, we will explain relations between exact structures o n an additively finite additive category and degenerations of the associat ed Hall algebras. The first part of the talk will be devoted to the main m otivation provided by concrete examples of degenerations of negative parts of quantum groups arising as Hall algebras of quiver representations. We will then turn to Lie theory in order to establish a link from these examp les to tropical flag varieties and certain quiver Grassmannians. In the se cond part of the talk we will present results in the general case and sket ch their proofs based on Auslander-Reiten theory. If time permits\, we wil l briefly discuss further conjectural examples and generalizations.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Liran Shaul (Prague) DTSTART;VALUE=DATE-TIME:20200914T120000Z DTEND;VALUE=DATE-TIME:20200914T130000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/17 DESCRIPTION:Title: The Cohen–Macaulay property in derived algebraic geometry \nby Liran Shaul (Prague) as part of Paris algebra seminar\n\n\nAbstra ct\nIn this talk\, we explain how to extend the theory of Cohen-Macaulay\n rings to the setting of commutative non-positive DG-rings. By studying\nlo cal cohomology in the DG-setting\, one obtains certain amplitude\ninequali ties about certain DG-modules of finite injective dimension.\nWhen these i nequalities are equalities\, we arrive at the notion of a\nCohen-Macaulay DG-ring.\n\nWe then show that these arise naturally in many situations\, a nd\nexplain their basic theory. We explain that any derived quotient of a \nCohen-Macaulay ring is Cohen-Macaulay\,\nand show that Cohen-Macaulaynes s is the generic local situation in\nderived algebraic geometry: under mil d hypothesis\, every eventually\ncoconnective locally noetherian derived s cheme is Cohen-Macaulay on a\ndense open set.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Zhengfang Wang (Stuttgart) DTSTART;VALUE=DATE-TIME:20200928T120000Z DTEND;VALUE=DATE-TIME:20200928T130000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/18 DESCRIPTION:Title: $B_\\infty$-algebras and Keller’s conjecture for singular Hochschild cohomology\nby Zhengfang Wang (Stuttgart) as part of Paris algebra seminar\n\n\nAbstract\nWe first give a basic introduction to $B_\ \infty$-algebras. Then from a $B_\\infty$-algebra A\, we contruct two new $B_\\infty$-algebras by using two different swapping maps: the opposite $ B_\\infty$-algebra and the transpose $B_\\infty$-algebra. Quite surprising ly\, we show that under a certain condition on A (satisfied\, for instance \, by brace $B_\\infty$-algebras or Gerstenhaber-Voronov algebras) these t wo $B_\\infty$-algebras are naturally isomorphic\, which is motivated from Kontsevich-Soibelman's minimal operad. \n\nWe also explain the role of th e above result in the proof of Keller's conjecture for singular Hochschild cohomology in the case of radical square zero algebras. This is joint wor k with Xiaowu Chen and Huanhuan Li.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Maria Julia Redondo (Bahia Blanca) DTSTART;VALUE=DATE-TIME:20200921T120000Z DTEND;VALUE=DATE-TIME:20200921T130000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/19 DESCRIPTION:Title: $L_\\infty$-structure on Barzdell's complex for monomial al gebras\nby Maria Julia Redondo (Bahia Blanca) as part of Paris algebra seminar\n\n\nAbstract\nWhen dealing with a monomial algebra $A$\, Bardzel l’s complex $B(A)$ has shown to be more efficient for computing Hochschi ld cohomology groups of $A$ than the Hochschild complex $C(A)$.\nSince $C( A)[1]$ is a dg Lie algebra\, it is natural to ask if the comparison morphi sms between these complexes allows us to transfer the dg Lie structure to $B(A)[1]$. This is true for radical square zero algebras\, but it is not true in general for monomial algebras.\nIn this talk\, I will describe an explicit $L_\\infty$-structure on $B(A)$ that induces a weak equivalence o f $L_\\infty$-algebras between $B(A)$ and $C(A)$. This allows us to descr ibe the Maurer-Cartan equation in terms of elements of degree 2 in $B(A)$ and make concrete computations when $A$ is a truncated monomial algebra.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Dylan Allegretti (UBC Vancouver) DTSTART;VALUE=DATE-TIME:20201005T120000Z DTEND;VALUE=DATE-TIME:20201005T130000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/20 DESCRIPTION:Title: Wall-crossing and differential equations\nby Dylan Alle gretti (UBC Vancouver) as part of Paris algebra seminar\n\n\nAbstract\nThe Kontsevich-Soibelman wall-crossing formula describes the wall-crossing be havior of BPS invariants in Donaldson-Thomas theory. It can be formulated as an identity between (possibly infinite) products of automorphisms of a formal power series ring. In this talk\, I will explain how these same pro ducts also appear in the exact WKB analysis of Schrödinger's equation. In this context\, they describe the Stokes phenomenon for objects known as V oros symbols.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Ryo Fujita (Paris\, IMJ-PRG) DTSTART;VALUE=DATE-TIME:20201012T120000Z DTEND;VALUE=DATE-TIME:20201012T130000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/22 DESCRIPTION:Title: Twisted Auslander-Reiten quivers\, quantum Cartan matrix an d representation theory of quantum affine algebras\nby Ryo Fujita (Par is\, IMJ-PRG) as part of Paris algebra seminar\n\n\nAbstract\nFor a comple x simple Lie algebra $g$\, its quantum Cartan matrix plays an important ro le in the representation theory of the quantum affine algebra of $g$. When $g$ is of type ADE\, Hernandez-Leclerc (2015) related its quantum Cartan matrix with the representation theory of Dynkin quivers and hence with the combinatorics of adapted words in the Weyl group of the corresponding ADE type. In this talk\, we introduce the notion of Q-data\, which can be reg arded as a combinatorial generalization of a Dynkin quiver with height fun ction\, and its twisted Auslander-Reiten quiver. Using them\, we relate th e quantum Cartan matrix of type BCFG with the combinatorics of twisted ada pted words in the Weyl group of the corresponding unfolded ADE type introd uced by Oh-Suh (2019). Also\, we see their relation to the representation theory of quantum affine algebras. For example\, we present a (partially c onjectural) unified expression of the denominators of R-matrices between t he Kirillov-Reshetikhin modules in terms of the quantum Cartan matrices. T his is a joint work with Se-jin Oh.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Norihiro Hanihara (Nagoya) DTSTART;VALUE=DATE-TIME:20201019T120000Z DTEND;VALUE=DATE-TIME:20201019T130000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/23 DESCRIPTION:Title: Cluster categories of formal dg algebras\nby Norihiro H anihara (Nagoya) as part of Paris algebra seminar\n\n\nAbstract\nCluster c ategories are Calabi-Yau triangulated categories endowed with cluster tilt ing objects. They have played an important role in the (additive) categori fication of cluster algebras. We study the version developed by Amiot-Guo- Keller\, which is defined in terms of CY dg algebras. Given a negatively g raded (non-dg) CY algebra\, we view it as a dg algebra with trivial differ ential. We give a description of the cluster category of such a formal dg algebra as the triangulated hull of an orbit category of a derived categor y\, and also as the singularity category of a finite dimensional algebra. Furthermore\, if time permits\, we will talk about a certain converse of t his construction\, giving a \nMorita-type theorem for CY triangulated cate gories arising from hereditary algebras\, partially generalizing that of K eller-Reiten.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Stéphane Launois (Kent) DTSTART;VALUE=DATE-TIME:20201109T130000Z DTEND;VALUE=DATE-TIME:20201109T140000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/24 DESCRIPTION:Title: Catenarity and Tauvel’s height formula for quantum nilpot ent algebras\nby Stéphane Launois (Kent) as part of Paris algebra sem inar\n\n\nAbstract\nThis talk is based on joint work with Ken Goodearl and Tom Lenagan. \nI will explain why quantum nilpotent algebras are catenar y\, that is\, why all saturated chains of inclusions of prime ideals in a quantum nilpotent algebra have the same length. As a corollary\, we obtain that Tauvel’s height formula holds for quantum nilpotent algebras. Time permitting\, \nI will present a different strategy to prove the latter re sult.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Wai-kit Yeung (Tokyo\, IPMU) DTSTART;VALUE=DATE-TIME:20201026T130000Z DTEND;VALUE=DATE-TIME:20201026T140000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/25 DESCRIPTION:Title: Pre-Calabi-Yau algebras\nby Wai-kit Yeung (Tokyo\, IPMU ) as part of Paris algebra seminar\n\n\nAbstract\nPre-Calabi-Yau categorie s are algebraic structures first studied by Kontsevich and Vlassopoulos. T hey can be viewed as a noncommutative analogue of Poisson structures\, jus t like Calabi-Yau structures can be viewed as a noncommutative analogue of symplectic structures. In this talk\, we discuss several aspects of this notion.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/25/ END:VEVENT BEGIN:VEVENT SUMMARY:Eleonore Faber (Leeds) DTSTART;VALUE=DATE-TIME:20201116T130000Z DTEND;VALUE=DATE-TIME:20201116T140000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/26 DESCRIPTION:Title: McKay quivers of complex reflection groups and the McKay co rrespondence\nby Eleonore Faber (Leeds) as part of Paris algebra semin ar\n\n\nAbstract\nFinite complex reflection groups were classified by Shep herd\nand Todd: up to finitely many exceptions they are the groups G(r\,p\ ,n).\nIn this talk we give a combinatorial description of the McKay quiver s of\nthese groups. Further we will comment on a McKay correspondence for\ ncomplex reflection groups. This is joint work with R.-O. Buchweitz\, C.\n Ingalls\, and M. Lewis.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/26/ END:VEVENT BEGIN:VEVENT SUMMARY:Sarah Scherotzke (Luxembourg) DTSTART;VALUE=DATE-TIME:20201123T130000Z DTEND;VALUE=DATE-TIME:20201123T140000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/27 DESCRIPTION:Title: Cotangent complexes of moduli spaces and Ginzburg dg algebr as\nby Sarah Scherotzke (Luxembourg) as part of Paris algebra seminar\ n\n\nAbstract\nWe start by giving an introduction to the notion of moduli stack of a dg category. Then we will explain what shifted symplectic struc tures are and how they are connected to Calabi-Yau structures on dg catego ries. More concretely\, we will show that the cotangent complex of the mod uli stack of a dg category A is isomorphic to the moduli stack of the *Cal abi-Yau completion* of A. This answers a conjecture of Keller-Yeung. This is joint work with Damien Calaque and Tristan Bozec available on the arXiv.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/27/ END:VEVENT BEGIN:VEVENT SUMMARY:Elie Casbi (MPI Bonn) DTSTART;VALUE=DATE-TIME:20201102T130000Z DTEND;VALUE=DATE-TIME:20201102T140000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/28 DESCRIPTION:Title: Equivariant multiplicities of simply-laced type flag minors \nby Elie Casbi (MPI Bonn) as part of Paris algebra seminar\n\n\nAbstr act\nThe study of remarkable bases of (quantum) coordinate rings has been an area of\nintensive research since the early 90's. For instance\, the mu ltiplicative properties of \nthese bases (in particular the dual canonical basis) was one of the main motivations for\nthe introduction of cluster a lgebras by Fomin and Zelevinsky around 2000. \nIn recent work\, Baumann-Ka mnitzer-Knutson introduced an algebra morphism \n$\\overline{D}$ from the coordinate algebra $\\mathbb{C}[N]$ of a maximal unipotent subgroup $N$\n to the function field of a maximal torus. It is related to the geometry of \nMirkovic-Vilonen cycles via the notion of equivariant multiplicity. Thi s morphism \nturns out to be useful for comparing good bases of the coordi nate algebra \n$\\mathbb{C}[N]$. We will focus on comparing the values ta ken by $\\overline{D}$ on several distinguished elements of the Mirkovic-V ilonen basis and the dual canonical basis. For the latter one\,\nwe will u se Kang-Kashiwara-Kim-Oh's monoidal categorification of the cluster\nstruc ture of the cluster structure of $\\mathbb{C}[N]$ via quiver Hecke algebra s as well as\nrecent results by Kashiwara-Kim. This will lead us to an exp licit description of\nthe images under $\\overline{D}$ of the flag minors of $\\mathbb{C}[N]$ as well as remarkable\nidentities between them.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/28/ END:VEVENT BEGIN:VEVENT SUMMARY:Markus Reineke (Bochum) DTSTART;VALUE=DATE-TIME:20201130T130000Z DTEND;VALUE=DATE-TIME:20201130T140000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/29 DESCRIPTION:Title: Wild quantum dilogarithm identities\nby Markus Reineke (Bochum) as part of Paris algebra seminar\n\n\nAbstract\nWe formulate and discuss "wild" analogues of the Fadeev-Kashaev identity for quantum diloga rithms. We review a general quiver setup\nfor such identities\, resulting from wall-crossing formulas\, motivic Donaldson-Thomas invariants\, and th e geometry of quiver moduli spaces. The quantum dilogarithm identities are then derived from special properties of representations of generalized Kr onecker quivers.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/29/ END:VEVENT BEGIN:VEVENT SUMMARY:Manon Defosseux (Université de Paris) DTSTART;VALUE=DATE-TIME:20210111T130000Z DTEND;VALUE=DATE-TIME:20210111T140000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/30 DESCRIPTION:Title: Brownian motion in the unit interval and the Littelmann pat h model\nby Manon Defosseux (Université de Paris) as part of Paris al gebra seminar\n\n\nAbstract\nWe will present for a Brownian motion in the unit interval a Pitman type\ntheorem obtained recently in joint work with Philippe Bougerol. We will focus\non algebraic aspects and will explain ho w it is related to the Littelmann path\nmodel for an affine Kac–Moody al gebra of extended type $A_1$.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/30/ END:VEVENT BEGIN:VEVENT SUMMARY:Estanislao Herscovich (Grenoble) DTSTART;VALUE=DATE-TIME:20210118T130000Z DTEND;VALUE=DATE-TIME:20210118T140000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/31 DESCRIPTION:Title: Double quasi-Poisson algebras are pre-Calabi-Yau\nby Es tanislao Herscovich (Grenoble) as part of Paris algebra seminar\n\n\nAbstr act\nDouble Poisson and double quasi-Poisson algebras were introduced by M . Van den Bergh in his study of noncommutative quasi-Poisson geometry. Nam ely\, they satisfy the so-called Kontsevich-Rosenberg principle\, since th e representation scheme of a double (quasi-)Poisson algebra has a natural (quasi-)Poisson structure. On the other hand\, N. Iyudu and M. Kontsevich found a link between double Poisson algebras and pre-Calabi-Yau algebras\, a notion introduced by Kontsevich and Y. Vlassopoulos. The aim of this ta lk will be to explain how such a connection can be extended to double quas i-Poisson algebras\, which thus give rise to pre-Calabi-Yau algebras. This pre-Calabi-Yau structure is however more involved in the case of double q uasi-Poisson algebras since\, in particular\, we get an infinite number of nonvanishing higher multiplications for the associated pre-Calabi-Yau alg ebra\, which involve the Bernoulli numbers. \n\nThis is joint work with D. Fernández from the Universität Bielefeld.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/31/ END:VEVENT BEGIN:VEVENT SUMMARY:Emmanuel Letellier (Université de Paris) DTSTART;VALUE=DATE-TIME:20201214T130000Z DTEND;VALUE=DATE-TIME:20201214T140000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/32 DESCRIPTION:Title: E-series of character varieties associated with non orienta ble surfaces\nby Emmanuel Letellier (Université de Paris) as part of Paris algebra seminar\n\n\nAbstract\nIn this talk we will be interested in two kinds of character varieties associated to a compact non-orientable s urface S. The first one is just the quotient stack of all representations of the fundamental group of S in GL(n\,C). For the second one\, we conside r k punctures of S as well as k semisimple conjugacy classes of GL(n\,C). We then consider the stack of anti-invariant local systems on the orienta tion covering of S with local monodromies around the punctures in the pres cribed conjugacy classes. We compute the number of points of these spaces over finite fields and we give a cohomological interpretation of our count ing formulas. For the second kind of character varieties\, we give a conje ctural formula for the mixed Poincaré series in terms of Macdonald symmet ric functions.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/32/ END:VEVENT BEGIN:VEVENT SUMMARY:Ruslan Maksimau (Montpellier) DTSTART;VALUE=DATE-TIME:20201207T130000Z DTEND;VALUE=DATE-TIME:20201207T140000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/33 DESCRIPTION:Title: KLR algebras for curves and semi-cuspidal representations\nby Ruslan Maksimau (Montpellier) as part of Paris algebra seminar\n\n\ nAbstract\nThe talk is based on the preprint arXiv:2010.01419. This is joi nt work with Alexandre Minets.\n\nThe KLR algebras (also called quiver Hec ke algebras) are known to have the following geometric construction: they are isomorphic to the (equivariant) Borel-Moore homology of the Steinberg variety. A point of this variety is given by a representation of a quiver and two full flags of subrepresentations.\n\nWe define and study analogues of KLR algebras for curves (curve Hecke algebras). We define these algebr as geometrically\, similarly to usual KLR algebras. But we replace represe ntations of a quiver by torsion sheaves on a smooth curve C. In particular \, for C=P1\, we get a geometric realization of the affine zigzag algebra of type A1. The case C=P1 is particularly interesting because it allows us to describe the imaginary semi-cuspidal category for the KLR algebra for affine sl2.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/33/ END:VEVENT BEGIN:VEVENT SUMMARY:Victoria Lebed (Caen) DTSTART;VALUE=DATE-TIME:20210125T130000Z DTEND;VALUE=DATE-TIME:20210125T140000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/34 DESCRIPTION:Title: Homotopical tools for computing rack homology\nby Victo ria Lebed (Caen) as part of Paris algebra seminar\n\n\nAbstract\nRacks are certain algebraic structures yielding powerful tools for knot theory\, Ho pf algebra classification and other areas. Rack homology plays a crucial r ole in these applications. The homology of a rack is very easy to define ( via an explicit chain complex)\, but extremely difficult to compute. Until recently\, the full homology was known only for three families of racks. Together with Markus Szymik\, we added a forth family to this list\, the f amily of permutation racks. More importantly\, our work unexpectedly broug ht homotopical methods into the area\, and showed that in spite of their a bstract flavour they can yield concrete computations. The necessary backgr ound on racks and their homology\, as well as an overview of the tools pre viously used for its computation\, will be given.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/34/ END:VEVENT BEGIN:VEVENT SUMMARY:Amnon Yekutieli (Ben Gurion University) DTSTART;VALUE=DATE-TIME:20210301T130000Z DTEND;VALUE=DATE-TIME:20210301T140000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/35 DESCRIPTION:Title: Rigidity\, Residues and Duality: Overview and Recent Progre ss\nby Amnon Yekutieli (Ben Gurion University) as part of Paris algebr a seminar\n\n\nAbstract\nIn this lecture\, we explain the theory of rigid residue complexes in commutative algebra and algebraic geometry. Unlike al l previous approaches to Grothendieck Duality\, the rigid approach concent rates on rigid residue complexes over rings\, and their intricate yet robu st properties. Most of the lecture will about the results for rings. The g eometrization\, i.e. the passage to rigid residue complexes on schemes and Deligne-Mumford (DM) stacks\, by gluing\, is fairly easy. In the geometri c part of the theory\, the main results are the Rigid Residue Theorem and the Rigid Duality Theorem for proper maps between schemes\, and for tame p roper maps between DM stacks. These results will only be outlined briefly. \n\nMore details are available in the eprint with the same title at\nhttp s://arxiv.org/abs/2102.00255\n\nThe lecture notes can be downloaded from \nhttp://www.math.bgu.ac.il/~amyekut/lectures/RRD-2021/notes.pdf\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/35/ END:VEVENT BEGIN:VEVENT SUMMARY:Pedro Tamaroff (Dublin) DTSTART;VALUE=DATE-TIME:20210201T130000Z DTEND;VALUE=DATE-TIME:20210201T140000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/36 DESCRIPTION:Title: Poincaré--Birkhoff--Witt theorems: homotopical and effecti ve computational methods for universal envelopes\nby Pedro Tamaroff (D ublin) as part of Paris algebra seminar\n\n\nAbstract\nIn joint work with V. Dotsenko\, we developed a categorical framework for Poincaré-Birkhoff- Witt type theorems about universal enveloping algebras of various algebrai c structures\, and used methods of term rewriting for operads to obtain ne w PBW theorems\, in particular answering an open question of J.-L. Loday. Later\, in joint work with A. Khoroshkin\, we developed a formalism to stu dy Poincaré–Birkhoff–Witt type theorems for universal envelopes of al gebras over differential graded operads\, motivated by the problem of comp uting the universal enveloping algebra functor on dg Lie algebras in the h omotopy category. Our formalism allows us\, among other things\, to obtain a homotopy invariant version of the classical Poincaré–Birkhoff–Witt theorem for universal envelopes of Lie algebras\, and extend Quillen's qu asi-isomorphism C(g) ---> BU(g) to homotopy Lie algebras. I will survey an d explain the role homological algebra\, homotopical algebra\, and effecti ve computational methods play in the main results obtained with both V. Do tsenko (1804.06485) and A. Khoroshikin (2003.06055) and\, if time allows\, explain a new direction in which these methods can be used to study certa in operads as universal envelopes of pre-Lie algebras.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/36/ END:VEVENT BEGIN:VEVENT SUMMARY:Deniz Kus (Bochum) DTSTART;VALUE=DATE-TIME:20210315T130000Z DTEND;VALUE=DATE-TIME:20210315T140000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/37 DESCRIPTION:Title: Prime representations in the Hernandez-Leclerc category \nby Deniz Kus (Bochum) as part of Paris algebra seminar\n\n\nAbstract\nGe nerators and relations of graded limits of certain finite dimensional irre ducible representations of quantum affine algebras have been determined in recent years. For example\, the representations in the Hernandez-Leclerc category corresponding to cluster variables appear to be certain truncatio ns of representations for current algebras and tensor products are related to the notion of fusion products. In this talk we will discuss some known results on this topic and study the classical and graded characters of pr ime representations in the HL category.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/37/ END:VEVENT BEGIN:VEVENT SUMMARY:Milen Yakimov (Northeastern) DTSTART;VALUE=DATE-TIME:20210215T130000Z DTEND;VALUE=DATE-TIME:20210215T140000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/38 DESCRIPTION:Title: Root of unity quantum cluster algebras\nby Milen Yakimo v (Northeastern) as part of Paris algebra seminar\n\n\nAbstract\nWe will d escribe a theory of root of unity quantum cluster algebras\, which are not necessarily specializations of quantum cluster algebras. All such algebra s are shown to be polynomial identity (PI) algebras. Inside each of them\, we construct a canonical central subalgebra which is proved to be isomorp hic to the underlying cluster algebra. (In turn\, this is used to show tha t two exchange graphs are canonically isomorphic). This setting generalize s the De Concini-Kac-Procesi central subalgebras in big quantum groups and presents a general framework for studying the representation theory of qu antum algebras at roots of unity by means of cluster algebras as the relev ant data becomes (PI algebra\, canonical central subalgebra)=(root of unit y quantum cluster algebra\, underlying cluster algebra). We also obtain a formula for the corresponding discriminant in this general setting that ca n be applied in many concrete situations of interest\, such as the discrim inants of all root of unity quantum unipotent cells for symmetrizable Kac- Moody algebras\, defined integrally over Z[root of unity]. This is a joint work with Bach Nguyen (Xavier Univ) and Kurt Trampel (Notre Dame Univ).\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/38/ END:VEVENT BEGIN:VEVENT SUMMARY:Sondre Kvamme (Uppsala) DTSTART;VALUE=DATE-TIME:20210208T130000Z DTEND;VALUE=DATE-TIME:20210208T140000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/39 DESCRIPTION:Title: Admissibly finitely presented functors for exact categories \nby Sondre Kvamme (Uppsala) as part of Paris algebra seminar\n\n\nAbs tract\nIn this talk we introduce the category of admissibly finitely prese nted functors mod_{adm}(E) for an exact category E. In particular\, we ch aracterize exact categories of the form mod_{adm}(E)\, and show that they have properties similar to module categories of Auslander algebras. For a fixed idempotent complete category C\, we also use this construction to sh ow that exact structures on C correspond to certain resolving subcategorie s in mod(C). This is joint work with Ruben Henrard and Adam-Christiaan van Roosmalen.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/39/ END:VEVENT BEGIN:VEVENT SUMMARY:Ryo Fujita (University of Paris) DTSTART;VALUE=DATE-TIME:20210308T130000Z DTEND;VALUE=DATE-TIME:20210308T140000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/40 DESCRIPTION:Title: Isomorphisms among quantum Grothendieck rings and propagati on of positivity\nby Ryo Fujita (University of Paris) as part of Paris algebra seminar\n\n\nAbstract\nFor a complex simple Lie algebra $\\mathfr ak{g}$\, finite-dimensional representations of its quantum loop algebra fo rm an interesting monoidal abelian category\, which has been studied from various perspectives. Related to the fundamental problem of determining th e characters of irreducible representations\, we consider its quantum Grot hendieck ring\, a 1-parameter deformation of the usual Grothendieck ring. When $\\mathfrak{g}$ is of simply-laced type\, Nakajima and Varagnolo-Vass erot proved that it enjoys some positivity properties based on the geometr y of quiver varieties. In this talk\, we show that the same positivities h old also for non-simply-laced type by establishing an isomorphism between the quantum Grothendieck ring of non-simply-laced type and that of ''unfol ded'' simply-laced type. In addition\, we find that an analog of Kazhdan-L usztig conjecture holds for several new cases in non-simply-laced type. Th is is a joint work with David Hernandez\, Se-jin Oh\, and Hironori Oya.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/40/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexander P. Veselov (Loughborough (UK) and Moscow (Russia)) DTSTART;VALUE=DATE-TIME:20210322T130000Z DTEND;VALUE=DATE-TIME:20210322T140000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/42 DESCRIPTION:Title: Automorphic Lie algebras and modular forms\nby Alexande r P. Veselov (Loughborough (UK) and Moscow (Russia)) as part of Paris alge bra seminar\n\n\nAbstract\nThe automorphic Lie algebras can be viewed as g eneralisations of twisted loop Lie algebras\, when a group $G$ acts holomo rphically and discretely on a Riemann surface and by automorphisms on the chosen Lie algebra. \n \nIn the talk we will discuss the automorphic Lie a lgebras of modular type\, when $G$ is a finite index subgroup of the modul ar group $\\Gamma=SL(2\, \\mathbb Z)$ acting on the upper half plane. In the case when the action of $G$ can be extended to $SL(2\,\\mathbb C)$ we prove analogues of Kac’s isomorphism theorem for the twisted loop Lie al gebras.\nFor the modular group and some of its principal congruence subgro ups we provide an explicit description of such isomorphisms using the clas sical theory of modular forms.\n \nThe talk is based on the ongoing joint work with Vincent Knibbeler and Sara Lombardo.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/42/ END:VEVENT BEGIN:VEVENT SUMMARY:Valentin Ovsienko (Reims) DTSTART;VALUE=DATE-TIME:20210222T130000Z DTEND;VALUE=DATE-TIME:20210222T140000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/43 DESCRIPTION:Title: Combinatorial and analytic properties of q-deformed real n umbers\nby Valentin Ovsienko (Reims) as part of Paris algebra seminar\ n\n\nAbstract\nI will explain a recent notion of \nq-deformed real numbers \, and discuss its various combinatorial and analytic properties. A "\nq-d eformed real" is a Laurent series in one variable\, \nq\, with integer coe fficients. The subject is connected to different theories\, such as knot i nvariants\, continued fractions\, and cluster algebras. I will formulate a challenging conjecture about the convergence of the series arising as \nq -deformed real numbers. (Here we understand \nq as a complex variable.) Th e conjecture is proved in particular cases and concrete examples. In the m ost simple examples of q-Fibonacci and q-Pell numbers\, the explicit formu las for the radius of convergence are very similar to certain formulas of Ramanujan. \nThe talk is based on a joint work with Ludivine Leclere\, Sop hie Morier-Genoud and Alexander Veselov.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/43/ END:VEVENT BEGIN:VEVENT SUMMARY:Oleksandr Tsymbaliuk (Purdue) DTSTART;VALUE=DATE-TIME:20210503T120000Z DTEND;VALUE=DATE-TIME:20210503T130000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/44 DESCRIPTION:Title: Quantum loop groups and shuffle algebras via Lyndon words\nby Oleksandr Tsymbaliuk (Purdue) as part of Paris algebra seminar\n\n\ nAbstract\nClassical q-shuffle algebras provide combinatorial models for t he positive half U_q(n) of a finite quantum group. We define a loop versio n of this construction\, yielding a combinatorial model for the positive h alf U_q(Ln) of a quantum loop group. In particular\, we construct a PBW ba sis of U_q(Ln) indexed by standard Lyndon words\, generalizing the work of Lalonde-Ram\, Leclerc and Rosso in the U_q(n) case. We also connect this to Enriquez' degeneration A of the elliptic algebras of Feigin-Odesskii\, proving a conjecture that describes the image of the embedding U_q(Ln) --- > A in terms of pole and wheel conditions. Joint work with Andrei Negut.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/44/ END:VEVENT BEGIN:VEVENT SUMMARY:Gregg Musiker (Minnesota) DTSTART;VALUE=DATE-TIME:20210426T120000Z DTEND;VALUE=DATE-TIME:20210426T130000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/45 DESCRIPTION:Title: Combinatorial Expansion Formulas for Decorated Super-Teichm üller Spaces\nby Gregg Musiker (Minnesota) as part of Paris algebra s eminar\n\n\nAbstract\nMotivated by the definition of super Teichmuller spa ces\, and Penner-Zeitlin's recent extension of this definition to decorate d super Teichmuller space\, as examples of super Riemann surfaces\, we use the super Ptolemy relations to obtain formulas for super lambda-lengths a ssociated to arcs in a bordered surface. In the special case of a disk\, w e are able to give combinatorial expansion formulas for the super lambda-l engths associated to diagonals of a polygon in the spirit of Ralf Schiffle r's T-path formulas for type A cluster algebras. We further connect our fo rmulas to the super-friezes of Morier-Genoud\, Ovsienko\, and Tabachnikov\ , and obtain partial progress towards defining super cluster algebras of t ype A. In particular\, following Penner-Zeitlin\, we are able to get formu las (up to signs) for the mu-invariants associated to triangles in a trian gulated polygon\, and explain how these provide a step towards understandi ng odd variables of a super cluster algebra. This is joint work with Nich olas Ovenhouse and Sylvester Zhang.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/45/ END:VEVENT BEGIN:VEVENT SUMMARY:Sergey Mozgovoy (Trinity College Dublin) DTSTART;VALUE=DATE-TIME:20210329T120000Z DTEND;VALUE=DATE-TIME:20210329T130000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/47 DESCRIPTION:Title: Operadic approach to wall-crossing and attractor invariants \nby Sergey Mozgovoy (Trinity College Dublin) as part of Paris algebra seminar\n\n\nAbstract\nWall-crossing describes how various invariants in algebraic geometry and theoretical physics transform under the variation o f parameters. In this talk I will discuss a framework\, reminiscent of col lections and plethysms in the theory of operads\, that concenptualizes tho se transformation rules. I will describe how some new and existing wall-cr ossing formulas can be proved using this approach. In particular\, I will discuss applications to attractor invariants (also called initial data in the theory of scattering diagrams).\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/47/ END:VEVENT BEGIN:VEVENT SUMMARY:Erik Darpoe (Nagoya) DTSTART;VALUE=DATE-TIME:20210412T120000Z DTEND;VALUE=DATE-TIME:20210412T130000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/48 DESCRIPTION:Title: Periodic trivial extension algebras and fractionally Calabi –Yau algebras\nby Erik Darpoe (Nagoya) as part of Paris algebra semi nar\n\n\nAbstract\nAn important open problem in the homological algebra of self-injective algebras is to characterise periodic algebras. An algebra B is said to be periodic if if has a periodic projective resolution as a B -B-bimodule.\n\nIn this talk\, I will present a solution to this problem f or trivial extension algebras: the trivial extension algebra T(A) of a fin ite-dimensional algebra A is periodic if and only if A has finite global d imension and is fractionally Calabi-Yau.\n\nThis is based on joint work wi th Chan\, Iyama and Marczinzik.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/48/ END:VEVENT BEGIN:VEVENT SUMMARY:Pierre Baumann (Strasbourg) DTSTART;VALUE=DATE-TIME:20210510T120000Z DTEND;VALUE=DATE-TIME:20210510T130000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/49 DESCRIPTION:Title: Explicit calculations in the geometric Satake equivalence\nby Pierre Baumann (Strasbourg) as part of Paris algebra seminar\n\n\nA bstract\nLet $G$ be a complex connected reductive group. As shown by Mirko vić and Vilonen\, the geometric Satake equivalence yields a basis in each irreducible rational representation of $G$\, defined out of algebraic cyc les in the affine Grassmannian of the Langlands dual of $G$. Goncharov and Shen extended this construction to each tensor product of irreducible rep resentations. We will investigate the properties of all these bases and ex plain a method to compute them. Based on a joint work with Peter Littelman n and Stéphane Gaussent.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/49/ END:VEVENT BEGIN:VEVENT SUMMARY:Damien Calaque (Montpellier) DTSTART;VALUE=DATE-TIME:20210531T120000Z DTEND;VALUE=DATE-TIME:20210531T130000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/50 DESCRIPTION:Title: Calabi-Yau structures for multiplicative preprojective alge bras\nby Damien Calaque (Montpellier) as part of Paris algebra seminar \n\n\nAbstract\nI will start by motivating and recalling Calabi-Yau struct ures and relative versions thereof. \nI will then provide several examples of Calabi-Yau structures occurring in the context of (dg-versions of) mul tiplicative preprojective algebras. The A_2 case\, that we will describe i n detail\, will be used as a building block for general quivers. At the en d of the talk\, I will describe a strategy for a comparison with other con structions\, for instance Van den Bergh's quasi-bi-hamiltonian structures. \nThis is a report on joint work with Tristan Bozec and Sarah Scherotzke. \n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/50/ END:VEVENT BEGIN:VEVENT SUMMARY:Nicholas Williams (Leicester) DTSTART;VALUE=DATE-TIME:20210419T120000Z DTEND;VALUE=DATE-TIME:20210419T130000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/51 DESCRIPTION:Title: The higher Stasheff–Tamari orders in representation theor y\nby Nicholas Williams (Leicester) as part of Paris algebra seminar\n \n\nAbstract\nOppermann and Thomas show that tilting modules over Iyama's higher Auslander algebras of type A are in bijection with triangulations o f even-dimensional cyclic polytopes. Triangulations of cyclic polytopes ar e partially ordered in two natural ways known as the higher Stasheff–Tam ari orders\, which were introduced in the 1990s by Kapranov\, Voevodsky\, Edelman\, and Reiner as higher-dimensional generalisations of the Tamari l attice. These two partial orders were conjectured to be equal in 1996 by E delman and Reiner\, but this is still an open problem. We show how the hig her Stasheff–Tamari orders correspond in even dimensions to natural orde rs on tilting modules which were studied by Riedtmann\, Schofield\, Happel \, and Unger. This then allows us to complete the picture of Oppermann and Thomas by showing that triangulations of odd-dimensional cyclic polytopes correspond to equivalence classes of d-maximal green sequences\, which we introduce as higher-dimensional analogues of Keller’s maximal green seq uences. We show that the higher Stasheff–Tamari orders correspond to nat ural orders on equivalence classes of d-maximal green sequences\, which re late to the no-gap conjecture of Brüstle\, Dupont\, and Perotin. If time permits\, we will also briefly discuss more recent work concerning the rel ation between the first higher Stasheff–Tamari orders and the higher Bru hat orders\, which are higher-dimensional analogues of the weak Bruhat ord er on the symmetric group.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/51/ END:VEVENT BEGIN:VEVENT SUMMARY:Sachin Gautam (Ohio State) DTSTART;VALUE=DATE-TIME:20210517T120000Z DTEND;VALUE=DATE-TIME:20210517T130000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/52 DESCRIPTION:Title: Poles of finite-dimensional representations of Yangians \nby Sachin Gautam (Ohio State) as part of Paris algebra seminar\n\n\nAbst ract\nThe Yangian associated to a simple Lie algebra g is a Hopf algebra w hich quantizes the Lie algebra of polynomials g[t]. Its finite-dimensional representation theory has remarkable connections with equivariant cohomol ogy\, combinatorics\, integrable systems and mathematical physics. Concret ely\, a finite-dimensional representation of the Yangian is prescribed by a finite collection of operators whose coefficients are rational functions \, satisfying a list of commutation relations.\n\nIn this talk I will give an explicit combinatorial description of the sets of poles of the rationa l currents of the Yangian\, acting on an irreducible finite-dimensional re presentation. This result uses the generalization of Baxter's Q-operators obtained by Frenkel-Hernandez. Based on a joint work with Curtis Wendlandt (arxiv:2009.06427).\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/52/ END:VEVENT BEGIN:VEVENT SUMMARY:Justine Fasquel (Lille) DTSTART;VALUE=DATE-TIME:20210614T120000Z DTEND;VALUE=DATE-TIME:20210614T130000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/53 DESCRIPTION:Title: Rationality at admissible levels of the simple W-algebras a ssociated with subregular nilpotent elements in sp_4\nby Justine Fasqu el (Lille) as part of Paris algebra seminar\n\n\nAbstract\nW-algebras are certain vertex algebras obtained from the quantized Drinfeld-Sokolov reduc tion of universal affine vertex algebras associated with a complex paramet er k and a simple complex Lie algebra g. Their simple quotients are believ ed to be rational for specific values of k\, called admissible\, which dep end on the choice of a nilpotent orbit in g. Here\, by rationality\, one m eans the complete reducibility of their positively graded modules.\n\nThis conjecture was partially proved by Arakawa-van Ekeren and Creutzig-Linsha w. In this talk\, I will discuss some consequences of the rationality for a very concrete example\, namely the W-algebra associated with a subregula r nilpotent element of the symplectic Lie algebra sp_4. In particular\, we will be interested in certain actions on the W-algebra and the set of its simple modules.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/53/ END:VEVENT BEGIN:VEVENT SUMMARY:Dan Kaplan (Birmingham) DTSTART;VALUE=DATE-TIME:20210524T120000Z DTEND;VALUE=DATE-TIME:20210524T130000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/54 DESCRIPTION:Title: Multiplicative preprojective algebras for Dynkin quivers\nby Dan Kaplan (Birmingham) as part of Paris algebra seminar\n\n\nAbstra ct\nCrawley-Boevey and Shaw defined the multiplicative preprojective algeb ra to understand Kac’s middle convolution and to solve the Deligne-Simps on problem. In Shaw’s thesis he noticed a curious phenomenon: for the D_ 4 quiver the multiplicative preprojective algebra (with parameter q=1) is isomorphic to the (additive) preprojective algebra if and only if the unde rlying field has characteristic not two. Later\, Crawley-Boevey proved the multiplicative and additive preprojective algebras are isomorphic for all Dynkin quivers over the complex numbers. Recent work of Etgü-Lekili and Lekili-Ueda\, in the dg-setting\, sharpens the result to hold over fields of good characteristic\, meaning characteristic not 2 in type D\, not 2 or 3 in type E and not 2\, 3\, or 5 for E_8. Neither work produces an isomor phism. \n\nIn this talk\, I will explain how to construct these isomorphis ms and prove their non-existence in the bad (i.e.\, not good) characterist ics. For each bad characteristic\, a single class in zeroth Hochschild hom ology obstructs the existence of an isomorphism. Time permitting\, I’ll explain how to interpret these results in the dg-setting where the 2-Calab i-Yau property allows us to recast these obstructions as non-trivial defor mations\, using Van den Bergh duality.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/54/ END:VEVENT BEGIN:VEVENT SUMMARY:Pierrick Bousseau (Orsay) DTSTART;VALUE=DATE-TIME:20210607T120000Z DTEND;VALUE=DATE-TIME:20210607T130000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/55 DESCRIPTION:Title: The flow tree formula for Donaldson-Thomas invariants of qu ivers with potentials\nby Pierrick Bousseau (Orsay) as part of Paris a lgebra seminar\n\n\nAbstract\nVery generally\, Donaldson-Thomas invariants are counts of stable objects in Calabi-Yau triangulated categories of dim ension 3. A natural source of examples is provided by the representation t heory of quivers with potentials. I will present a proof of a formula\, co njectured by Alexandrov-Pioline from string-theory arguments\, which compu tes Donaldson-Thomas invariants of a quiver with potential in terms of a m uch smaller set of "attractor invariants". The proof uses the framework of scattering diagrams to reorganize sequences of iterated applications of t he Kontsevich-Soibelman wall-crossing formula. This is joint work with Hü lya Argüz.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/55/ END:VEVENT BEGIN:VEVENT SUMMARY:Shunsuke Kano (Tōhoku) DTSTART;VALUE=DATE-TIME:20210621T120000Z DTEND;VALUE=DATE-TIME:20210621T130000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/56 DESCRIPTION:Title: Categorical dynamical systems arising from sign-stable muta tion loops\nby Shunsuke Kano (Tōhoku) as part of Paris algebra semina r\n\n\nAbstract\nA pair formed by a triangulated category and an autoequiv alence is called a \ncategorical dynamical system. Its complexity is measu red by the so-called categorical entropy. \nIn this talk\, I will present a computation of the categorical entropies of categorical dynamical system s obtained by lifting a sign-stable mutation loop of a quiver to an autoeq uivalence of the derived category of the corresponding Ginzburg dg algebra .\nThe notion of sign-stability is introduced as a generalization of the p seudo-Anosov property of mapping classes of surfaces. If time permits\, we will discuss the pseudo-Anosovness of the autoequivalences constructed.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/56/ END:VEVENT BEGIN:VEVENT SUMMARY:Mikhail Gorsky (Amiens) DTSTART;VALUE=DATE-TIME:20210628T120000Z DTEND;VALUE=DATE-TIME:20210628T130000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/57 DESCRIPTION:Title: Braid varieties\, positroids\, and Legendrian links\nby Mikhail Gorsky (Amiens) as part of Paris algebra seminar\n\n\nAbstract\nI will discuss a class of affine algebraic varieties associated with positi ve braids\, their cluster structures and their relation to open Bott-Samel son varieties. First\, I will explain our motivation which comes both from symplectic topology and from the study of HOMFLY-PT polynomials. Then we will discuss how the study of DG algebras associated with certain Legendri an links may help us to better understand the algebraic geometry of Richar dson varieties in type A. I will illustrate our results and conjectures co ncerning this interplay between topology and algebraic geometry with the e xample of open positroid varieties in Grassmannians. If time permits\, I w ill briefly explain conjectural relations between certain stratifications of braid varieties and cluster structures on their coordinate rings. This is joint work with Roger Casals\, Eugene Gorsky\, and José Simental.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/57/ END:VEVENT BEGIN:VEVENT SUMMARY:Ehud Meir (Aberdeen) DTSTART;VALUE=DATE-TIME:20210705T120000Z DTEND;VALUE=DATE-TIME:20210705T130000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/58 DESCRIPTION:Title: Interpolations of monoidal categories by invariant theory\nby Ehud Meir (Aberdeen) as part of Paris algebra seminar\n\n\nAbstract \nIn this talk\, I will present a recent construction that enables one to\ ninterpolate symmetric monoidal categories by interpolating algebraic\nstr uctures and their automorphism groups.\nI will explain how one can recover the constructions of Deligne for\ncategories such as Rep(S_t)\, Rep(O_t) and Rep(Sp_t)\, the constructions\nof Knop for wreath products with S_t an d GL_t(O_r)\, where O_r is a\nfinite quotient of a discrete valuation ring \, and also the TQFT\ncategories recently constructed from a rational func tion by Khovanov\, Ostrik\, and Kononov.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/58/ END:VEVENT BEGIN:VEVENT SUMMARY:Giovanni Cerulli Irelli (Rome La Sapienza) DTSTART;VALUE=DATE-TIME:20211004T120000Z DTEND;VALUE=DATE-TIME:20211004T130000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/59 DESCRIPTION:Title: On degeneration and extensions of symplectic and orthogonal quiver representations\nby Giovanni Cerulli Irelli (Rome La Sapienza) as part of Paris algebra seminar\n\n\nAbstract\nMotivated by linear degen erations of flag varieties\, and the study of 2-nilpotent B-orbits for cla ssical groups\, I will review the representation theory of symmetric quive rs\, initiated by Derksen and Weyman in 2002. I will then focus on the pro blem of describing the orbit closures in this context and how to relate it to the orbit closures for the underlying quivers. In collaboration with M . Boos we have recently given an answer to this problem for symmetric quiv ers of finite type. I believe that this result is a very special case of a much deeper and general result that I will mention in the form of conject ures and open problems. The talk is based on the preprint version of my pa per with Boos available on the arXiv as 2106.08666.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/59/ END:VEVENT BEGIN:VEVENT SUMMARY:Maxim Gurevich (Technion\, Haifa) DTSTART;VALUE=DATE-TIME:20211011T120000Z DTEND;VALUE=DATE-TIME:20211011T130000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/60 DESCRIPTION:Title: RSK-transform for L-parameters\nby Maxim Gurevich (Tech nion\, Haifa) as part of Paris algebra seminar\n\nAbstract: TBA\n\nWhat is common between the Specht construction for modules over\npermutation grou ps\, normal sequences of quiver Hecke algebra modules à\nla Kashiwara-Kim \, and the local Langlands classification for GL_n ?\nI would like to show how these themes fit well together under a\nframework of a representation -theoretic Robinson-Schensted-Knuth\ntransform\, devised recently in my wo rk with Erez Lapid on\nrepresentations of p-adic groups.\n\nOn one hand\, RSK-standard modules are curious models for all smooth\nirreducible GL_n-r epresentations. Yet\, going through Bernstein-Rouquier\ncategorical equiva lences this notion is quantized into its natural\nexistence in the realm o f type A quiver Hecke algebras. A convenient\nbridge is thus portrayed bet ween the cyclotomic approach of classifying\nsimple modules through a gene ralized Specht construction\, and the\nPBW-basis approach from Lusztig's w ork on quantum groups.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/60/ END:VEVENT BEGIN:VEVENT SUMMARY:Matthew Pressland (Leeds) DTSTART;VALUE=DATE-TIME:20211018T120000Z DTEND;VALUE=DATE-TIME:20211018T130000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/63 DESCRIPTION:Title: A cluster character for y-variables\nby Matthew Pressla nd (Leeds) as part of Paris algebra seminar\n\n\nAbstract\nGiven a (Froben ius or triangulated) cluster category\, I will explain how to categorify v arious cluster algebraic identities via lattice maps associated to pairs o f cluster-tilting objects. For example\, one such map is the index\, well- known to categorify g-vectors. Using this formalism\, I will recall the cl uster character for x-variables developed by Caldero–Chapoton\, Palu\, F u–Keller and others\, and give a similar categorical expression for y-va riables. This is joint work with Jan E. Grabowski.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/63/ END:VEVENT BEGIN:VEVENT SUMMARY:Haicheng Zhang (Nanjing Normal University) DTSTART;VALUE=DATE-TIME:20211108T130000Z DTEND;VALUE=DATE-TIME:20211108T140000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/66 DESCRIPTION:Title: Hall algebras of extriangulated categories and quantum clus ter algebras\nby Haicheng Zhang (Nanjing Normal University) as part of Paris algebra seminar\n\n\nAbstract\nFirstly\, we define the Hall algebra of an extriangulated category\, a notion introduced by Nakaoka and Palu. Then for a finite acyclic valued quiver Q\, we consider the Hall algebras of certain subcategories of the bounded derived category of the represent ation category of Q over a finite field\, which are extriangulated categor ies. We recover the quantum Caldero-Chapoton formula via the Hall algebra approach and give the higher-dimensional (cluster) multiplication formulas in the quantum cluster algebra of Q with arbitrary coefficients\, which c an be viewed as the quantum version of the Caldero-Keller multiplication f ormula in the cluster algebra. This talk is based on the joint preprints a rXiv:2005.10617\, 2107.05883 and 2108.03558.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/66/ END:VEVENT BEGIN:VEVENT SUMMARY:Ryo Fujita (University of Paris) DTSTART;VALUE=DATE-TIME:20211122T130000Z DTEND;VALUE=DATE-TIME:20211122T140000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/67 DESCRIPTION:Title: Deformed Cartan matrices and generalized preprojective alge bras\, II\nby Ryo Fujita (University of Paris) as part of Paris algebr a seminar\n\n\nAbstract\nIn their study of deformed W-algebras associated with complex simple Lie algebras\, E. Frenkel-Reshetikhin (1998) introduce d certain two parameter deformations of the Cartan matrices. They play an important role in the representation theory of quantum affine algebras. In the former half of this talk\, we explain a representation-theoretic inte rpretation of these deformed Cartan matrices and their inverses in terms o f the generalized preprojective algebras recently introduced by Geiss-Lecl erc-Schröer (2017). In the latter half of the talk\, we discuss its appli cation to the representation theory of quantum affine algebras in connecti on with the theory of cluster algebras.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/67/ END:VEVENT BEGIN:VEVENT SUMMARY:Kota Murakami (Kyoto) DTSTART;VALUE=DATE-TIME:20211122T130000Z DTEND;VALUE=DATE-TIME:20211122T140000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/68 DESCRIPTION:Title: Deformed Cartan matrices and generalized preprojective alge bras\, I\nby Kota Murakami (Kyoto) as part of Paris algebra seminar\n\ n\nAbstract\nIn their study of deformed W-algebras associated with complex simple Lie algebras\, E. Frenkel-Reshetikhin (1998) introduced certain tw o parameter deformations of the Cartan matrices. They play an important ro le in the representation theory of quantum affine algebras. In the former half of this talk\, we explain a representation-theoretic interpretation o f these deformed Cartan matrices and their inverses in terms of the genera lized preprojective algebras recently introduced by Geiss-Leclerc-Schröer (2017). In the latter half of the talk\, we discuss its application to th e representation theory of quantum affine algebras in connection with the theory of cluster algebras.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/68/ END:VEVENT BEGIN:VEVENT SUMMARY:Lucien Hennecart (Edinburgh) DTSTART;VALUE=DATE-TIME:20211025T120000Z DTEND;VALUE=DATE-TIME:20211025T130000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/69 DESCRIPTION:Title: (Canonical) bases of the elliptic Hall algebra\nby Luci en Hennecart (Edinburgh) as part of Paris algebra seminar\n\n\nAbstract\nT he global nilpotent cone is a closed substack of the stack of Higgs sheave s on a smooth projective curve whose geometry has been studied in depth an d is also an essential object in the geometric Langlands program. It is a highly singular stack and in particular it has several irreducible compone nts which were rather recently explicitly described by Bozec. In this talk \, we will concentrate on elliptic curves. We will recall Bozec's parametr ization of the set of irreducible components of the global nilpotent cone and present another parametrization of the same set using (a refinement of ) the Harder-Narasimhan stratification of the stack of coherent sheaves on the elliptic curve. Then\, we raise the question of the comparison of the se two bases\, showing the emergence piecewise linear structures. We will also see how the second description can be useful to understand a part of the cohomological Hall algebra of an elliptic curve.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/69/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Wemyss (Edinburgh) DTSTART;VALUE=DATE-TIME:20220131T130000Z DTEND;VALUE=DATE-TIME:20220131T140000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/70 DESCRIPTION:Title: Local Normal Forms of Noncommutative Functions\nby Mich ael Wemyss (Edinburgh) as part of Paris algebra seminar\n\n\nAbstract\nThi s talk will explain how to generalise Arnold's results classifying commuta tive singularities into the noncommutative setting\, and will classify fin ite dimensional Jacobi algebras arising on the d-loop quiver. The surpris ing thing is that a classification should exist at all\, and it is even mo re surprising that ADE enters. I will spend most of my time explaining wh at the algebras are\, why they classify\, and how to intrinsically extract ADE information from them. At the end\, I'll briefly explain why I'm real ly interested in this problem\, the connection with different quivers\, an d the applications of the above classification to curve counting and birat ional geometry. This is all joint work with Gavin Brown.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/70/ END:VEVENT BEGIN:VEVENT SUMMARY:Lang Mou (Cambridge) DTSTART;VALUE=DATE-TIME:20211115T130000Z DTEND;VALUE=DATE-TIME:20211115T140000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/71 DESCRIPTION:Title: Generalized cluster dualities\nby Lang Mou (Cambridge) as part of Paris algebra seminar\n\n\nAbstract\nFock and Goncharov introdu ced dualities between cluster varieties. I will explain how this duality u nder the framework of Gross-Hacking-Keel-Kontsevich can be naturally exten ded to generalized cluster varieties in the sense of Chekhov-Shapiro. In p articular\, I will construct generalized cluster scattering diagrams which are used to construct bases of functions on the dual varieties. As a gene ralized A-cluster variety yields a generalized cluster algebra\, certain p ositivity property of the cluster monomials will be derived as a result of the positivity of the corresponding scattering diagram. This talk is main ly based on arXiv: 2110.02416.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/71/ END:VEVENT BEGIN:VEVENT SUMMARY:Chris Fraser (Minnesota) DTSTART;VALUE=DATE-TIME:20211129T130000Z DTEND;VALUE=DATE-TIME:20211129T140000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/72 DESCRIPTION:Title: Automorphisms of open positroid varieties from braids\n by Chris Fraser (Minnesota) as part of Paris algebra seminar\n\n\nAbstract \nPositroid varieties are distinguished subvarieties of Grassmannians whic h have cluster structure(s). I will give some reminders on the combinatori cs underlying these cluster structures\, partially based on a joint work w ith Melissa Sherman-Bennett. In a previous work\, I described an action of a certain braid group on the top-dimensional positroid subvariety by "qua si" cluster automorphisms. I will explain how a similar statement can be e xtended to arbitrary open positroid varieties. This is joint with Bernhard Keller.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/72/ END:VEVENT BEGIN:VEVENT SUMMARY:Abel Lacabanne (Clermont-Ferrand) DTSTART;VALUE=DATE-TIME:20211213T130000Z DTEND;VALUE=DATE-TIME:20211213T140000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/73 DESCRIPTION:Title: Higher rank Askey-Wilson algebras as skein algebras\nby Abel Lacabanne (Clermont-Ferrand) as part of Paris algebra seminar\n\n\nA bstract\nThe skein algebra of a surface is built from the framed unoriente d links in the thickened surface\, modulo the Kauffman bracket relations. If the surface is the $4$-punctured sphere\, it turns out that the skein a lgebra is a central extension of the universal Askey-Wilson algebra. De Bi e\, De Clercq and Van de Vijver proposed a definition of higher rank Askey -Wilson algebras\, as a subalgebra of an $n$-fold tensor product of $U_q(\ \mathfrak{sl}_2)$. The aim of this talk is to explain an isomorphism betwe en these higher rank Askey-Wilson algebras\, and the skein algebras of pun ctured spheres. The diagrammatic flavour of the skein algebra provides the n an efficient way to compute some relations between some elements of the Askey-Wilson algebra\, notably the $q$-commutation relations discovered by De Clercq. This is joint work with J. Cooke.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/73/ END:VEVENT BEGIN:VEVENT SUMMARY:Nicholas Ovenhouse (Minnesota) DTSTART;VALUE=DATE-TIME:20211206T130000Z DTEND;VALUE=DATE-TIME:20211206T140000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/74 DESCRIPTION:Title: q-Rational Numbers and Finite Schubert Varieties\nby Ni cholas Ovenhouse (Minnesota) as part of Paris algebra seminar\n\n\nAbstrac t\nRecently\, Morier-Genoud and Ovsienko generalized the notion of q-integ ers to include rational numbers. The q-analogue of a rational number is so me rational function with integer coefficients. There are some known combi natorial interpretations of the numerators as rank generating functions of certain posets. I will review this interpretation\, and re-phrase it in t erms of lattice paths on "snake graphs". Using this snake graph interpreta tion\, I will explain how the numerators count the number of points in som e variety over a finite field. This variety is a union of Schubert cells i n some Grassmannian.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/74/ END:VEVENT BEGIN:VEVENT SUMMARY:Alfredo Nájera Chávez (Oaxaca) DTSTART;VALUE=DATE-TIME:20220117T130000Z DTEND;VALUE=DATE-TIME:20220117T140000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/75 DESCRIPTION:Title: Deformation theory for finite cluster complexes\nby Alf redo Nájera Chávez (Oaxaca) as part of Paris algebra seminar\n\n\nAbstra ct\nCluster complexes are a certain class of simplicial complexes that nat urally arise in the theory of cluster algebras. They codify a wealth of fu ndamental information about cluster algebras. The purpose of this talk is to elaborate on a geometric relationship between cluster algebras and clus ter complexes. In vague words\, this relationship is the following: cluste r algebras of finite cluster type with universal coefficients may be obtai ned via a torus action on a Hilbert scheme. In particular\, we will discus s the deformation theory of the Stanley-Reisner ring associated to a finit e cluster complex and present some applications related to the Gröbner th eory of the ideal of relations among cluster and frozen variables of a clu ster algebra of finite cluster type. Time permitting I will elaborate on h ow to generalize this approach to the context of tau-tilting finite algebr as.\n\nThis is based on a joint project with Nathan Ilten and Hipolito Tre ffinger whose first outcome is the preprint arXiv:2111.02566.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/75/ END:VEVENT BEGIN:VEVENT SUMMARY:Merlin Christ (Hamburg) DTSTART;VALUE=DATE-TIME:20220124T130000Z DTEND;VALUE=DATE-TIME:20220124T140000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/76 DESCRIPTION:Title: Gluing constructions of Ginzburg algebras and cluster categ ories\nby Merlin Christ (Hamburg) as part of Paris algebra seminar\n\n \nAbstract\nGinzburg algebras are a class of 3-CY dg algebras\, which have attracted attention for their use in the categorification of cluster alge bras. Given a marked surface with a triangulation\, there is an associated Ginzburg algebra G. I will begin by describing how its derived category D ^perf(G) can be glued from the derived categories of the relative Ginzburg algebras of the ideal triangles of the triangulation. We will see that th e passage to Amiot's cluster category\, defined as the quotient D^perf(G)/ D^fin(G)\, does not commute with this gluing. As we will discuss\, this ca n fixed by instead starting with the relative Ginzburg algebra of the tria ngulation and again applying Amiot's quotient formula. Remarkably\, this r esulting relative version of cluster category turns out to be equivalent t o the 1-periodic topological Fukaya category of the surface.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/76/ END:VEVENT BEGIN:VEVENT SUMMARY:Chris Brav (HSE Moscow) DTSTART;VALUE=DATE-TIME:20220110T130000Z DTEND;VALUE=DATE-TIME:20220110T140000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/77 DESCRIPTION:Title: Non-commutative string topology\nby Chris Brav (HSE Mos cow) as part of Paris algebra seminar\n\n\nAbstract\nWe explain how relati ve Calabi-Yau structures on dg functors\, more generally relative orientat ions\, give a non-commutative generalisation of oriented manifolds with bo undary. We then construct genus zero string topology operations on the rel ative Hochschild homology HH_*(C\,D) of a dg functor D —> C equipped wit h a relative orientation. More precisely\, we prove a relative version of the cyclic Deligne conjecture\, stating that this shifted relative Hochsch ild homology carries a natural structure of framed E_2-algebra. Examples i nclude 1) the functor of induction of local systems for the inclusion of t he boundary into an oriented manifold with boundary\, in which case the re lative Hochschild homology is identified with the relative loop homology 2 ) the functor of pushforward of coherent sheaves for the inclusion of the anti-canonical divisor into a variety\, in which case relative Hochschild homology can be related to differential forms\, and 3) various examples co ming from representation theory.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/77/ END:VEVENT BEGIN:VEVENT SUMMARY:Nicholas Williams (Cologne) DTSTART;VALUE=DATE-TIME:20220207T130000Z DTEND;VALUE=DATE-TIME:20220207T140000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/78 DESCRIPTION:Title: Equivalence of maximal green sequences\nby Nicholas Wil liams (Cologne) as part of Paris algebra seminar\n\n\nAbstract\nIt is natu ral to study the set of maximal green sequences of an algebra under an equ ivalence relation. The resulting set of equivalence classes has the struct ure of a poset\; it is a lattice in type A\, where the equivalence classes are in bijection with triangulations of three-dimensional cyclic polytope s. There are at least four appealing ways of defining an equivalence relat ion on maximal green sequences: commutation\, exchange pairs\, tau-rigid s ummands\, and bricks. The main result of my talk will be that the first th ree methods define the same equivalence relation\, while the fourth does n ot. This gives a surprising lack of duality between bricks\, which corresp ond to simples\, and tau-rigid summands\, which correspond to projectives. This is a report on joint work in progress with Mikhail Gorsky.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/78/ END:VEVENT BEGIN:VEVENT SUMMARY:Véronique Bazier-Matte (Connecticut) DTSTART;VALUE=DATE-TIME:20220214T130000Z DTEND;VALUE=DATE-TIME:20220214T140000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/79 DESCRIPTION:Title: Connection between knot theory and Jacobian algebras\nb y Véronique Bazier-Matte (Connecticut) as part of Paris algebra seminar\n \n\nAbstract\nThis is joint work with Ralf Schiffler.\nIn knot theory\, it is known that we can compute the Alexander polynomial of a knot from the lattice of Kauffman states of a knot diagram. Recently\, my collaborator a nd I associated a quiver with a knot diagram. From this quiver\, one can o btain a Jacobian algebra. It appears that the lattice of submodules of ind ecomposable modules over this algebra is in bijection with the lattice of Kauffman states. This bijection allows us to compute the Alexander polynom ial of a knot with a specialization of the F-polynomial of any indecomposa ble module over this algebra.\nAfter a brief introduction to knot theory\, I will explain how to compute an Alexander polynomial from a F-polynomial .\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/79/ END:VEVENT BEGIN:VEVENT SUMMARY:Gonçalo Tabuada (Warwick) DTSTART;VALUE=DATE-TIME:20220221T130000Z DTEND;VALUE=DATE-TIME:20220221T140000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/80 DESCRIPTION:Title: Jacques Tits motivic measure\nby Gonçalo Tabuada (Warw ick) as part of Paris algebra seminar\n\n\nAbstract\nThe Grothendieck ring of varieties\, introduced in a letter from Alexander Grothendieck to Jean -Pierre Serre (August 16th 1964)\, plays an important role in algebraic ge ometry. However\, despite the efforts of several mathematicians\, the stru cture of this ring still remains poorly understood. In order to capture so me of the flavor of Grothendieck’s ring of varieties\, a few motivic mea sures have been built throughout the years. In this talk I will present a new motivic measure\, called the Jacques Tits motivic measure\, and descri be some of its numerous applications.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/80/ END:VEVENT BEGIN:VEVENT SUMMARY:Pierre-Guy Plamondon (Versailles) DTSTART;VALUE=DATE-TIME:20220228T130000Z DTEND;VALUE=DATE-TIME:20220228T140000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/81 DESCRIPTION:Title: Cluster algebras\, categorification\, and some configuratio n spaces\nby Pierre-Guy Plamondon (Versailles) as part of Paris algebr a seminar\n\n\nAbstract\nThe real part of the configuration space M_{0\,n} of n points on a projective line has a connected component which is close ly related to the associahedron. As an affine variety\, it is defined by explicit equations which are in close connection with exchange relations f or cluster variables in type A. This has been generalized to all Dynkin t ypes.\n\nIn this talk\, we will construct an affine variety associated to any representation-finite finite-dimensional algebra over an algebraically closed field. The equations defining the variety will be obtained from t he F-polynomials of indecomposable modules over the algebra. This general izes previous results\, which can be recovered by applying our constructio n to Jacobian algebras in Dynkin types.\n\nThis talk is based on an ongoin g project with Nima Arkani-Hamed\, Hadleigh Frost\, Giulio Salvatori and H ugh Thomas.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/81/ END:VEVENT BEGIN:VEVENT SUMMARY:Léa Bittmann (Edinburgh) DTSTART;VALUE=DATE-TIME:20220425T120000Z DTEND;VALUE=DATE-TIME:20220425T130000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/82 DESCRIPTION:Title: A Schur-Weyl duality between Double Affine Hecke Algebras a nd quantum groups\nby Léa Bittmann (Edinburgh) as part of Paris algeb ra seminar\n\nLecture held in hybrid.\n\nAbstract\nSchur-Weyl duality is o ften used to relate type A Lie groups (or quantum groups) to symmetric gro ups (or Hecke algebras). In this talk\, I will use ribbon calculus and ske in modules to describe an instance of this Schur-Weyl duality between repr esentations of the type A quantum group at roots of unity and representati ons of the Double Affine Hecke Algebra. This is based on joint work with A . Chandler\, A. Mellit and C. Novarini.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/82/ END:VEVENT BEGIN:VEVENT SUMMARY:Thomas Bitoun (Calgary) DTSTART;VALUE=DATE-TIME:20220516T120000Z DTEND;VALUE=DATE-TIME:20220516T130000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/83 DESCRIPTION:Title: On centralizers in Azumaya domains\nby Thomas Bitoun (C algary) as part of Paris algebra seminar\n\nLecture held in hybrid.\n\nAbs tract\nWe prove a positive characteristic analogue of the classical result that the centralizer of a nonconstant differential operator in one variab le is commutative. This leads to a new\, short proof of that classical cha racteristic zero result\, by reduction modulo p. This is joint work with J ustin Desrochers available at https://arxiv.org/abs/2201.04606.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/83/ END:VEVENT BEGIN:VEVENT SUMMARY:Alex Takeda (IHES) DTSTART;VALUE=DATE-TIME:20220307T130000Z DTEND;VALUE=DATE-TIME:20220307T140000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/84 DESCRIPTION:Title: The ribbon quiver complex and the noncommutative Legendre t ransform\nby Alex Takeda (IHES) as part of Paris algebra seminar\n\n\n Abstract\nThe structure of a fully extended oriented 2d TQFT is given by a Frobenius algebra. If one wants to lift this structure to a cohomological field theory\, the correct notion is that of a Calabi-Yau algebra or cate gory\; the CohFT operations can be described by a certain graph complex. T here are two different notions of Calabi-Yau structure on categories\, bot h requiring some type of finiteness or dualizability. In this talk I will discuss a variation that works in non-dualizable cases as well\; in this c ase the graphs get replaced by quivers. The resulting complex calculates t he homology of certain moduli spaces of open-closed surfaces\, and can be used to give a fully explicit description of these operations. In the seco nd half of the talk\, I will describe some of these constructions\, includ ing how to produce operations from smooth and/or relative Calabi-Yau struc tures\, and explain how\, in the smooth case\, this can be thought of as a noncommutative version of the Legendre transform. This is joint work with M. Kontsevich and Y. Vlassopoulos.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/84/ END:VEVENT BEGIN:VEVENT SUMMARY:Norihiro Hanihara (Nagoya) DTSTART;VALUE=DATE-TIME:20220321T130000Z DTEND;VALUE=DATE-TIME:20220321T140000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/85 DESCRIPTION:Title: Tilting theory via enhancements\nby Norihiro Hanihara ( Nagoya) as part of Paris algebra seminar\n\n\nAbstract\nTilting theory aim s at giving equivalences among various triangulated categories\, such as d erived categories\, cluster categories\, and singularity categories. Const ructing such an equivalence provides a mutual understanding of these categ ories. In this talk\, we study tilting theory for singularity categories a nd cluster categories from the viewpoint of dg enhancements. We will first review their construction in terms of their enhancements\, and then based on this we explain a general method of giving equivalences between singul arity categories and cluster categories. Our main steps are existence of ( weak) right Calabi-Yau structure on the dg singularity category of commuta tive Gorenstein rings\, and a characterization of dg orbit categories amon g bigraded dg categories. This is a joint work with Osamu Iyama.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/85/ END:VEVENT BEGIN:VEVENT SUMMARY:Jie Pan (Zhejiang U.) DTSTART;VALUE=DATE-TIME:20220314T130000Z DTEND;VALUE=DATE-TIME:20220314T140000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/86 DESCRIPTION:Title: Positivity and polytope basis in cluster algebras via Newto n polytopes\nby Jie Pan (Zhejiang U.) as part of Paris algebra seminar \n\n\nAbstract\nWe work in the generality of a totally sign-skew-symmetric (e.g. skew-symmetrizable) \ncluster algebra of rank $n$. We study the New ton polytopes of $F$-polynomials and\, more generally\, a\nfamily of polyt opes $N_h$ indexed by vectors $h$ in $Z^n$. We use it to give a new proof of Laurent \npositivity and to construct what we call the polytope basis o f the upper cluster algebra. The polytope \nbasis consists of certain univ ersally indecomposable Laurent polynomials. It is strongly positive\nand g eneralizes the greedy basis constructed by Lee-Li-Zelevinsky in rank 2.\nT his is a report on joint work with Fang Li\, cf. arXiv:2201.01440.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/86/ END:VEVENT BEGIN:VEVENT SUMMARY:Asilata Bapat (Australian National U.) DTSTART;VALUE=DATE-TIME:20220328T120000Z DTEND;VALUE=DATE-TIME:20220328T130000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/87 DESCRIPTION:Title: Categorical q-deformed rational numbers via Bridgeland stab ility conditions\nby Asilata Bapat (Australian National U.) as part of Paris algebra seminar\n\n\nAbstract\nWe will discuss new categorical inte rpretations of two distinct q-deformations of the rational numbers. The fi rst one\, introduced by Morier-Genoud and Ovsienko in a different context\ , enjoys fascinating combinatorial\, topological\, and algebraic propertie s. The second one is a natural partner to the first\, and is new. We obtai n these deformations via boundary points of a compactification of the spac e of Bridgeland stability conditions on the 2-Calabi-Yau category of the A 2 quiver. The talk is based on joint work with Louis Becker\, Anand Deopur kar\, and Anthony Licata.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/87/ END:VEVENT BEGIN:VEVENT SUMMARY:Hipolito Treffinger (City University of Paris) DTSTART;VALUE=DATE-TIME:20220404T120000Z DTEND;VALUE=DATE-TIME:20220404T123000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/88 DESCRIPTION:Title: Torsion classes and tau-tilting in higher homological algeb ra\, I\nby Hipolito Treffinger (City University of Paris) as part of P aris algebra seminar\n\nLecture held in hybrid.\n\nAbstract\nHigher homolo gical algebra was introduced by Iyama in the late \n2000's. His point of v iew was that some classical results by Auslander \nand Auslander--Reiten w ere somehow 2-dimensional and should have \nn-dimensional equivalents. Thi s new theory quickly attracted a lot of \nattention\, with many authors ge neralising classical notions to the \nsetting of higher homological algebr a. Examples of such generalisations \nare the introduction of n-abelian ca tegories by Jasso\, n-angulated \ncategories by Geiss--Keller--Oppermann\, and n-torsion classes by Jørgensen.\n\nRecently\, it was shown by Kvamme and\, independently\, by Ebrahimi and \nNasr-Isfahani\, that every small n-abelian category is the \nn-cluster-tilting subcategory of an abelian ca tegory. In this talk\, we \nwill focus on the relation between n-torsion c lasses in an n-abelian \ncategory $\\mathcal{M}$ and (classical) torsion c lasses of the abelian \ncategory $\\mathcal{A}$ in which $\\mathcal{M}$ is embedded. By \nconsidering functorially finite torsion classes\, this wil l allow us to \nrelate n-torsion classes with maximal tau_n-rigid objects in $\\mathcal{M}$.\n\nSome of the results presented in this talk are part of a joint work by \nJ. Asadollahi\, P. Jørgensen\, S. Schroll\, H. Treff inger. The rest \ncorresponds to an ongoing project by J. August\, J. Haug land\, \nK. Jacobsen\, S. Kvamme\,Y. Palu and H. Treffinger.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/88/ END:VEVENT BEGIN:VEVENT SUMMARY:Yann Palu (Amiens) DTSTART;VALUE=DATE-TIME:20220404T123000Z DTEND;VALUE=DATE-TIME:20220404T130000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/89 DESCRIPTION:Title: Torsion classes and tau-tilting in higher homological algeb ra\, II\nby Yann Palu (Amiens) as part of Paris algebra seminar\n\nLec ture held in hybrid.\n\nAbstract\nHigher homological algebra was introduce d by Iyama in the late \n2000's. His point of view was that some classical results by Auslander \nand Auslander--Reiten were somehow 2-dimensional a nd should have \nn-dimensional equivalents. This new theory quickly attrac ted a lot of \nattention\, with many authors generalising classical notion s to the \nsetting of higher homological algebra. Examples of such general isations \nare the introduction of n-abelian categories by Jasso\, n-angul ated \ncategories by Geiss--Keller--Oppermann\, and n-torsion classes by J ørgensen.\n\nRecently\, it was shown by Kvamme and\, independently\, by E brahimi and \nNasr-Isfahani\, that every small n-abelian category is the \ nn-cluster-tilting subcategory of an abelian category. In this talk\, we \ nwill focus on the relation between n-torsion classes in an n-abelian \nca tegory $\\mathcal{M}$ and (classical) torsion classes of the abelian \ncat egory $\\mathcal{A}$ in which $\\mathcal{M}$ is embedded. By \nconsidering functorially finite torsion classes\, this will allow us to \nrelate n-to rsion classes with maximal tau_n-rigid objects in $\\mathcal{M}$.\n\nSome of the results presented in this talk are part of a joint work by \nJ. Asa dollahi\, P. Jørgensen\, S. Schroll\, H. Treffinger. The rest \ncorrespon ds to an ongoing project by J. August\, J. Haugland\, \nK. Jacobsen\, S. K vamme\,Y. Palu and H. Treffinger.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/89/ END:VEVENT BEGIN:VEVENT SUMMARY:Peigen Cao (Hebrew University) DTSTART;VALUE=DATE-TIME:20220411T120000Z DTEND;VALUE=DATE-TIME:20220411T130000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/90 DESCRIPTION:Title: On exchange matrices from string diagrams\nby Peigen Ca o (Hebrew University) as part of Paris algebra seminar\n\nLecture held in Zoom.\n\nAbstract\nIn this talk\, we will first recall the constructions o f triangular extension and of source-sink extensio for skew-symmetrizable matrices and some invariants under these constructions. Secondly\, we will recall the string diagrams introduced by Shen-Weng\, which are very usefu l to describe many interesting skew-symmetrizable matrices closely related with Lie theory. Thirdly\, we will sketch the proof of our main result: t he skew-symmetrizable matrices from string diagrams are in the smallest cl ass of skew-symmetrizable matrices containing the (1 times 1) zero matrix and closed under mutations and source-sink extensions. This result applies to the exchange matrices of cluster algebras from double Bruhat cells\, u nipotent cells\, double Bott-Samelson cells among others. Finally\, some i mmediate applications regarding reddening sequences and non-degenerate pot entials for many quivers from Lie theory are given.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/90/ END:VEVENT BEGIN:VEVENT SUMMARY:Bruno Vallette (Sorbonne Paris Nord) DTSTART;VALUE=DATE-TIME:20220523T120000Z DTEND;VALUE=DATE-TIME:20220523T130000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/91 DESCRIPTION:Title: Pre-Calabi-Yau algebras and homotopy double Poisson gebras< /a>\nby Bruno Vallette (Sorbonne Paris Nord) as part of Paris algebra semi nar\n\n\nAbstract\nWe prove that the notion of a curved pre-Calabi–Yau a lgebra is equivalent to the notion of a curved homotopy double Poisson geb ra\, thereby settling the equivalence between the two ways to define deriv ed noncommutative Poisson structures. We actually prove that the respectiv e differential graded Lie algebras controlling both deformation theories a re isomorphic. This allows us to apply the recent developments of the prop eradic calculus in order to establish the homotopical properties of curved pre-Calabi–Yau algebras: infini-morphisms\, homotopy transfer theorem\, formality\, Koszul hierarchy\, and twisting procedure. (Joint work with J ohan Leray available at arxiv.org/abs/2203.05062).\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/91/ END:VEVENT BEGIN:VEVENT SUMMARY:Tasuki Kinjo (IPMU) DTSTART;VALUE=DATE-TIME:20220502T120000Z DTEND;VALUE=DATE-TIME:20220502T130000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/92 DESCRIPTION:Title: Deformed Calabi--Yau completion and its application to DT t heory\nby Tasuki Kinjo (IPMU) as part of Paris algebra seminar\n\n\nAb stract\nIn this talk\, we investigate an application of the theory of defo rmed Calabi--Yau completion to enumerative geometry. The notion of Calabi- -Yau completion was first introduced by Keller as a non-commutative analog ue of the canonical bundle. In the same paper\, he also introduced a defor med version of the Calabi--Yau completion.\nWe will explain that the defor med Calabi--Yau completion is a non-commutative analogue of an affine bund le modeled on the canonical bundle. Combining this observation with a rece nt work of Bozec--Calaque--Scherotzke\, we prove that the moduli space of coherent sheaves on a certain non-compact Calabi--Yau threefold is describ ed as the critical locus inside a smooth moduli space. This description ha s several applications in Donaldson--Thomas theory including Toda's \\chi- independence conjecture of Gopakumar--Vafa invariants for arbitrary local curves. By dimensional reduction\, it implies (and extends) Hausel--Thadde us's cohomological \\chi-independence conjecture for Higgs bundles.\n\nThi s talk is based on a joint work with Naruki Masuda and another joint work with Naoki Koseki.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/92/ END:VEVENT BEGIN:VEVENT SUMMARY:Florian Naef DTSTART;VALUE=DATE-TIME:20220509T120000Z DTEND;VALUE=DATE-TIME:20220509T130000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/93 DESCRIPTION:Title: The (non-)homotopy invariance of the string coproduct\n by Florian Naef as part of Paris algebra seminar\n\n\nAbstract\nA Calabi-Y au structure on a smooth algebra allows one to identify Hochschild homolog y with Hochschild cohomology. With this identification Hochschild homology acquires an additional Gerstenhaber algebra structure. One way to formula te the amount of structure one has on Hochschild homology is to encode it into a 2d TFT. This explains some of the string topology operations on the free loop space of a manifold\, but not the string coproduct. If the alge bra has additional structure (trivialization of its Hattori-Stalling Euler characteristic) one obtains an extra secondary operation on Hochschild ho mology\, which recovers the string coproduct. Finally\, in the free loop s pace setting\, this additional structure can either be recovered from inte rsection theory of the manifold or from its underlying simple homotopy typ e\, thus relating the two. Using this last relation one can express the di fference between the string coproduct of two homotopic but not necessarily homeomorphic manifolds in terms of Whitehead torsion.\nThis is joint work with Pavel Safronov\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/93/ END:VEVENT BEGIN:VEVENT SUMMARY:Jeremy Rickard (Bristol) DTSTART;VALUE=DATE-TIME:20220606T120000Z DTEND;VALUE=DATE-TIME:20220606T130000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/94 DESCRIPTION:Title: Generating the derived category\nby Jeremy Rickard (Bri stol) as part of Paris algebra seminar\n\n\nAbstract\nThe unbounded derive d category of (right) modules over a ring is a triangulated category with infinite products and coproducts. As a triangulated category with coproduc ts it is easy to see that it is generated by the projective modules\, and similarly it is generated as a triangulated category with products by the injective modules.\n\nI will discuss the question of whether it is generat ed as a triangulated category with coproducts by the injective modules\, o r as a triangulated category with products by the projective (or flat) mod ules. I will describe the relationship with the finitistic dimension conje cture\, as well as some more recent results.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/94/ END:VEVENT BEGIN:VEVENT SUMMARY:Yuya Mizuno (Osaka Metropolitan University) DTSTART;VALUE=DATE-TIME:20220613T120000Z DTEND;VALUE=DATE-TIME:20220613T130000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/95 DESCRIPTION:Title: g-simplicial complex and silting theory\nby Yuya Mizuno (Osaka Metropolitan University) as part of Paris algebra seminar\n\n\nAbs tract\nFor a finite dimensional algebra $A$\, the 2-term silting complexes of $A$ give a simplicial complex $\\Delta(A)$\, which is called the g-sim plicial complex.\nWe study several properties of $\\Delta(A)$ and\, in par ticular\, we give tilting theoretic interpretations of the $h$-vectors and the Dehn-Sommerville equations of $\\Delta(A)$.\nConsequently\, we can e xplain a close correspondence between torsion classes and wide subcategori es\, which can be regarded as a refinement of the Koenig-Yang corresponden ce.\nThis is joint work with Aoki-Higashitani-Iyama-Kase\, cf. https://arx iv.org/pdf/2203.15213.pdf\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/95/ END:VEVENT BEGIN:VEVENT SUMMARY:Jens Niklas Eberhardt (Bonn) DTSTART;VALUE=DATE-TIME:20220530T120000Z DTEND;VALUE=DATE-TIME:20220530T130000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/96 DESCRIPTION:Title: Motivic Springer Theory\nby Jens Niklas Eberhardt (Bonn ) as part of Paris algebra seminar\n\n\nAbstract\nAlgebras and their repre sentations can often be constructed geometrically in terms of convolution of cycles. \nFor example\, the Springer correspondence describes how irred ucible representations of a Weyl group can be realised in terms of a convo lution action on the vector spaces of irreducible components of Springer f ibers. Similar situations yield the affine Hecke algebra\, quiver Hecke al gebra (KLR algebra)\, quiver Schur algebra or Soergel bimodules.\nIn this spirit\, we show that these algebras and their representations can be real ised in terms of certain equivariant motivic sheaves called Springer motiv es.\nOn our way\, we will discuss weight structures and their applications to motives.\nThis is joint work with Catharina Stroppel.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/96/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexander Shapiro (Edinburgh) DTSTART;VALUE=DATE-TIME:20220620T120000Z DTEND;VALUE=DATE-TIME:20220620T130000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/97 DESCRIPTION:Title: Positive representation theory\nby Alexander Shapiro (E dinburgh) as part of Paris algebra seminar\n\n\nAbstract\nThe notions of a modular tensor category\, 2d topological modular functor\, and 3d topolog ical quantum field theory are essentially equivalent. Fock and Goncharov c onjectured that the quantised higher Teichmüller theory gives rise to an analogue of a modular functor. Their construction in turn yields a family of "positive" representations of quantum groups. I will argue that these r epresentations provide a compelling first step towards constructing an ana logue of a modular tensor category. This talk will be based on joint works with Gus Schrader.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/97/ END:VEVENT BEGIN:VEVENT SUMMARY:Daping Weng (UC Davis) DTSTART;VALUE=DATE-TIME:20220627T120000Z DTEND;VALUE=DATE-TIME:20220627T130000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/98 DESCRIPTION:Title: Grid plabic graphs\, Legendrian weaves\, and (quasi-)cluste r structures\nby Daping Weng (UC Davis) as part of Paris algebra semin ar\n\n\nAbstract\nGiven a plabic graph on R^2\, we can choose a conormal l ift of its zig-zag strands to the unit cotangent bundle of R^2\, obtaining a Legendrian link. If the plabic graph satisfies a “grid” condition\, its Legendrian link admits a natural embedding into the standard contact R^3. We study the Kashiwara-Schapira moduli space of microlocal rank 1 she aves associated with the Legendrian link\, and construct a natural (quasi- )cluster structure on this moduli space using Legendrian weaves. In partic ular\, we prove that any braid variety associated with (beta Delta) for a 3-strand braid beta admits cluster structures with an explicit constructio n of initial seeds. We also construct Donaldson-Thomas transformations for these moduli spaces and prove that the upper cluster algebra equals its c luster algebra. In this talk\, I will introduce the theoretical background and describe the basic combinatorics for constructing Legendrian weaves a nd the (quasi-)cluster structures from a grid plabic graph. This is based on joint work with Roger Casals\, cf. https://arxiv.org/abs/2204.13244.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/98/ END:VEVENT BEGIN:VEVENT SUMMARY:Sibylle Schroll (Cologne) DTSTART;VALUE=DATE-TIME:20220704T120000Z DTEND;VALUE=DATE-TIME:20220704T130000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/99 DESCRIPTION:Title: Recollements of derived categories of graded gentle algebra s\nby Sibylle Schroll (Cologne) as part of Paris algebra seminar\n\n\n Abstract\nGraded gentle algebras are classical objects in representation t heory. They are quadratic monomial algebras making them particularly amena ble to study and they appear in many different areas of mathematics such a s in cluster theory\, in N=2 gauge theories and in homological mirror symm etry of surfaces. \nIn this talk\, we give a construction of a partial cof ibrant dg algebra resolution of a graded quadratic monomial algebra induci ng an explicit recollement of their derived categories. We show that for g raded gentle algebras\, both the left and the right side of such a recolle ment corresponds to cutting the underlying surface which can be associated to a graded gentle algebra. In the case of homologically smooth and prope r graded gentle algebras this recollement can be restricted to the derived categories with finite total cohomology\, thus inducing a recollement of the corresponding partially wrapped Fukaya categories. We give some conseq uences of this construction such as the existence of full exceptional sequ ences\, silting objects and simple minded collections. This is joint work with Wen Chang and Haibo Jin https://arxiv.org/abs/2206.11196.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/99/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniel Labardini-Fragoso (UNAM) DTSTART;VALUE=DATE-TIME:20221107T130000Z DTEND;VALUE=DATE-TIME:20221107T140000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/100 DESCRIPTION:Title: Revisiting Derksen-Weyman-Zelevinsky's mutations\nby D aniel Labardini-Fragoso (UNAM) as part of Paris algebra seminar\n\nLecture held in room 01 of the Institut Henri Poincaré\, Paris\, France.\n\nAbst ract\nThe mutation theory of quivers with potential and their representati ons\, developed around 15 years ago by Derksen-Weyman-Zelevinsky\, has had a profound impact both inside and outside the theory of cluster algebras. In this talk I will present results obtained in joint works with Geiss an d Schröer\, and with de Laporte\, about some interesting behaviors of DWZ 's mutations of representations. Namely\, despite needing several non-cano nical choices of linear-algebraic data in order to be performed\, they can always be arranged so as to become regular maps on dense open subsets of representation spaces rep(Q\,S\,d). As a consequence\, one obtains the inv ariance of Geiss-Leclerc-Schröer's 'generic basis' under mutations even i n the Jacobi-infinite case\, thus generalizing a result of Plamondon. Furt hermore\, given two distinct vertices k\, \\ell of a quiver with potential (Q\,S)\, the k-th mutation of representations takes the \\ell-th indecomp osable projective over (Q\,S) to the \\ell-th indecomposable projective ov er \\mu_k(Q\,S). When a certain 'optimization' condition is satisfied by \ \ell\, this allows to compute certain 'Landau-Ginzburg potentials' as F-po lynomials of projective representations.\n\nIn-person talk at the room 01 of the Institut Henri Poincaré\, Paris\, France\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/100/ END:VEVENT BEGIN:VEVENT SUMMARY:Greg Muller (Oklahoma) DTSTART;VALUE=DATE-TIME:20221010T120000Z DTEND;VALUE=DATE-TIME:20221010T130000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/101 DESCRIPTION:Title: Juggler's friezes\nby Greg Muller (Oklahoma) as part o f Paris algebra seminar\n\n\nAbstract\nFrieze patterns are infinite strips of numbers satisfying certain determinantal identities. Originally motiva ted by Gauss’ “miraculous pentagram” identities\, these patterns hav e since been connected to triangulations\, integrable systems\, representa tion theory\, and cluster algebras. In this talk\, we will review a few ch aracterizations and constructions of frieze patterns\, as well as a genera lization which allows friezes with a “ragged edge” described by a jugg ling function. These “juggler’s friezes” correspond to special point s in positroid varieties\, in direct analogy with how classical friezes co rrespond to special points in Grassmannians.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/101/ END:VEVENT BEGIN:VEVENT SUMMARY:Linhui Shen (Michigan State) DTSTART;VALUE=DATE-TIME:20221017T120000Z DTEND;VALUE=DATE-TIME:20221017T130000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/102 DESCRIPTION:Title: Cluster Nature of Quantum Groups\nby Linhui Shen (Mich igan State) as part of Paris algebra seminar\n\n\nAbstract\nWe present a r igid cluster model to realize the quantum group $U_q(g)$ for $g$ of type A DE. That is\, we prove that there is a natural Hopf algebra isomorphism fr om the quantum group to a quotient algebra of the Weyl group invariants of a Fock-Goncharov quantum cluster algebra. By applying the quantum duality of cluster algebras\, we show that the quantum group admits a cluster can onical basis $\\Theta$ whose structural coefficients are in $\\mathbb{N}[q ^{\\frac{1}{2}}\, q^{-\\frac{1}{2}}]$. The basis $\\Theta$ satisfies an in variance property under Lusztig's braid group action\, the Dynkin automorp hisms\, and the star anti-involution.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/102/ END:VEVENT BEGIN:VEVENT SUMMARY:Slava Pimenov (Nottingham) DTSTART;VALUE=DATE-TIME:20221003T120000Z DTEND;VALUE=DATE-TIME:20221003T130000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/103 DESCRIPTION:Title: Planar Prop of Differential Operators of Associative Algeb ras\nby Slava Pimenov (Nottingham) as part of Paris algebra seminar\n\ nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/103/ END:VEVENT BEGIN:VEVENT SUMMARY:Eleven speakers DTSTART;VALUE=DATE-TIME:20220905T120000Z DTEND;VALUE=DATE-TIME:20220905T130000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/104 DESCRIPTION:Title: Algebra days in Paris\nby Eleven speakers as part of P aris algebra seminar\n\n\nAbstract\nYou may be interested in the eleven ta lks delivered on September 5 and 6 at the Algebra days in Paris.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/104/ END:VEVENT BEGIN:VEVENT SUMMARY:Mikhail Kapranov (Yale and IPMU) DTSTART;VALUE=DATE-TIME:20220912T120000Z DTEND;VALUE=DATE-TIME:20220912T130000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/105 DESCRIPTION:Title: Perverse sheaves and schobers on symmetric products\nb y Mikhail Kapranov (Yale and IPMU) as part of Paris algebra seminar\n\n\nA bstract\nThe talk\, based on joint work in progress with V. Schechtman\, w ill first recall our description of perverse sheaves on $Sym^n(\\mathbb{C} )$\, the symmetric product of the complex line with its natural stratifica tion by multiplicities. This description proceeds in terms of contingency matrices\, which are certain integer matrices appearing (besides their ori gin in statistics) in three different contexts:\n\n- A natural cell decomp osition of $Sym^n(\\mathbb{C})$.\n\n- Compatibility of multiplication and comultiplication in $\\mathbb{Z}_+$-graded Hopf algebras.\n\n- Parabolic B ruhat decomposition for $GL_n$.\n\nPerverse sheaves on $Sym^n(\\mathbb{C}) $ are described in terms of certain data of mixed functoriality on conting ency matrices which we call Janus sheaves. I will then explain our approac h to categorifying the concept of Janus sheaves\, in which sums are replac ed by filtrations with respect to the Bruhat order. Such data can be calle d Janus schobers. Examples can be obtained from $\\mathbb{Z}_+$-graded Hop f categories\, a concept going back to Crane-Frenkel\, of which we conside r two examples related to representations of groups $GL_n$ over finite fie lds (Joyal-Street) and $p$-adic fields (Bernstein-Zelevinsky). [This talk is kindly shared by Noncommutative shape s.]\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/105/ END:VEVENT BEGIN:VEVENT SUMMARY:Amnon Neeman (Australian National University) DTSTART;VALUE=DATE-TIME:20220926T120000Z DTEND;VALUE=DATE-TIME:20220926T130000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/106 DESCRIPTION:Title: Two results\, both developments of a 2015 article by Kraus e\nby Amnon Neeman (Australian National University) as part of Paris a lgebra seminar\n\n\nAbstract\nIn 2020\, the pandemic hit\, and all around the globe we went into lockdowns of various description. During the first lockdown I carefully read Krause's 2015 article "Deriving Auslander's form ula".\n\nIn this talk\, I will outline how the ideas of Krause's paper und erpin two articles written in 2020 in collaboration with Canonaco and Stel lari. One is about the uniqueness of enhancements of large classes of tria ngulated categories\, while the second offers a counterexample to certain vanishing conjectures in negative K-theory. [This talk is kindly shared by Representation theory and triangulated categories.]\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/106/ END:VEVENT BEGIN:VEVENT SUMMARY:Liran Shaul (Prague) DTSTART;VALUE=DATE-TIME:20220919T120000Z DTEND;VALUE=DATE-TIME:20220919T130000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/107 DESCRIPTION:Title: The finitistic dimension conjecture via DG-rings\nby L iran Shaul (Prague) as part of Paris algebra seminar\n\n\nAbstract\nThe fi nitistic dimension of a ring A is defined to be the supremum of projective dimensions among all A-modules of finite projective dimension. It is an o pen problem whether this quantity is finite for finite dimensional algebra s over a field and for artin algebras.\n\nIn this talk\, I will explain a new approach for studying the finiteness of the finitistic dimension by em bedding the ring A inside a nicely behaved differential graded algebra\, a nd using relation between this DG-algebra and A to deduce results about th e finitistic dimension.\nAs an application of these methods\, I will expla in how to generalize a recent sufficient condition of Rickard\, for FPD(A) <∞ in terms of generation of D(A) from finite dimensional algebras over a field to all left perfect rings which admit a dualizing complex.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/107/ END:VEVENT BEGIN:VEVENT SUMMARY:Julia Sauter (Bielefeld) DTSTART;VALUE=DATE-TIME:20221024T120000Z DTEND;VALUE=DATE-TIME:20221024T130000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/108 DESCRIPTION:Title: Tilting theory in exact categories\nby Julia Sauter (B ielefeld) as part of Paris algebra seminar\n\n\nAbstract\nWe define tiltin g subcategories in arbitrary exact categories to archieve the following. F irstly: Unify existing definitions of tilting subcategories to arbitrary e xact categories. Discuss standard results for tilting subcategories: Ausla nder correspondence\, Bazzoni description of the perpendicular category. S econdly: We treat the question of induced derived equivalences separately - given a tilting subcategory T\, we ask if a functor on the perpendicular category induces a derived equivalence to a (certain) functor category ov er T. If this is the case\, we call the tilting subcategory ideq tilting. We prove a generalization of Miyashita's theorem (which is itself a genera lization of a well-known theorem of Brenner-Butler) and characterize exact categories with enough projectives allowing ideq tilting subcategories. I n particular\, this is always fulfilled if the exact category is abelian w ith enough projectives.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/108/ END:VEVENT BEGIN:VEVENT SUMMARY:Sota Asai (Osaka) DTSTART;VALUE=DATE-TIME:20221031T130000Z DTEND;VALUE=DATE-TIME:20221031T140000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/109 DESCRIPTION:Title: TF equivalence classes and canonical decompositions for E- tame algebras\nby Sota Asai (Osaka) as part of Paris algebra seminar\n \n\nAbstract\nThis is joint work with Osamu Iyama. Let $A$ be a finite dim ensional algebra over an algebraically closed field. Then the numerical to rsion pairs of Baumann-Kamnitzer-Tingley give an equivalence relation on t he real Grothendieck group of finitely generated projective $A$-modules\, which is called TF equivalence. By results of Yurikusa and Bruestle-Smith- Treffinger\, we have that the g-vector cone of each 2-term presilting comp lex is a TF equivalence class. To get more TF equivalence classes\, we can use canonical decompositions of elements in the (integral) Grothendieck g roup of finitely generated projectives introduced by Derksen-Fei. We have showed that the cone defined by the canonical decomposition of each elemen t is contained in some single TF equivalence class. Moreover\, we have als o obtained that\, if $A$ is an E-tame algebra\, then this cone is precisel y a TF equivalence class. In this talk\, I will explain these results and some important steps to prove them.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/109/ END:VEVENT BEGIN:VEVENT SUMMARY:Ivan Marin (Amiens and CNRS) DTSTART;VALUE=DATE-TIME:20221114T130000Z DTEND;VALUE=DATE-TIME:20221114T140000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/110 DESCRIPTION:Title: Geometric realization via random variables\nby Ivan Ma rin (Amiens and CNRS) as part of Paris algebra seminar\n\nLecture held in room 01 of the Institut Henri Poincaré\, Paris\, France.\n\nAbstract\nTop ological spaces up to (weak) equivalences are\nfaithfully represented by s implicial combinatorial\nstructures. Through an identification of the\n$n$ -dimensional simplex with the space of probability\nmeasures on a finite s et of size $n+1$\, we investigate\nwhat happens when it is replaced by the \nspace of random variables that naturally lies 'above' it.\nBy this proce dure\, we obtain in particular a simple description\nof the classifying se t of a (discrete) group\, and also\na new concept of geometric realization . This new one\nalso induces an equivalence of categories up to homotopy\n with simplicial sets and topological spaces. The 'probability-law'\nmap th en defines a natural transformation between the\ntwo corresponding Quillen equivalences.\n\nIn-person talk at the room 01 of the Institut Henri Poin caré\, Paris\, France\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/110/ END:VEVENT BEGIN:VEVENT SUMMARY:Euiyong Park (Seoul) DTSTART;VALUE=DATE-TIME:20221205T130000Z DTEND;VALUE=DATE-TIME:20221205T140000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/111 DESCRIPTION:Title: Extended crystal structures of Hernandez-Leclerc categorie s\nby Euiyong Park (Seoul) as part of Paris algebra seminar\n\n\nAbstr act\nIn this talk\, we will discuss the categorical crystal structure on t he Hernandez-Leclerc category $\\mathscr{C}_\\mathfrak{g}^0$. We define ex tended crystals for quantum groups and show that there is a braid group ac tion on extended crystals. We then explain how the set of the isomorphism classes of simple modules in $\\mathscr{C}_\\mathfrak{g}^0$ has an extend ed crystal structure\, and discuss the braid group action from the viewpoi nt of the Hernandez-Leclerc category $\\mathscr{C}_\\mathfrak{g}^0$. This talk is based on joint work with M. Kashiwara (arXiv: 2111.07255 and 2207. 11644).\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/111/ END:VEVENT BEGIN:VEVENT SUMMARY:Gustavo Jasso and Fernando Muro (Lund and Sevilla) DTSTART;VALUE=DATE-TIME:20221121T130000Z DTEND;VALUE=DATE-TIME:20221121T140000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/112 DESCRIPTION:Title: The triangulated Auslander-Iyama correspondence\, I\nb y Gustavo Jasso and Fernando Muro (Lund and Sevilla) as part of Paris alge bra seminar\n\n\nAbstract\nIn these two talks\, we will start by introduci ng a result which establishes the existence and uniqueness of (DG) enhance ments for triangulated categories which admit an additive generator whose endomorphism algebra is finite-dimensional (over a perfect field). We will then present a generalisation of this result that allows us to treat a la rger class of triangulated categories\, which instead admit a generator wi th a strong regularity property (a so-called dZ-cluster tilting object). W e will also explain how our result\, combined with crucial theorems of Aug ust and Hua-Keller\, leads to a positive solution of the Donovan-Wemyss Co njecture for contraction algebras as observed by Keller. We will also comm ent on some details about the proof.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/112/ END:VEVENT BEGIN:VEVENT SUMMARY:Fernando Muro and Gustavo Jasso (Sevilla and Lund) DTSTART;VALUE=DATE-TIME:20221128T130000Z DTEND;VALUE=DATE-TIME:20221128T140000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/113 DESCRIPTION:Title: The triangulated Auslander-Iyama correspondence\, II\n by Fernando Muro and Gustavo Jasso (Sevilla and Lund) as part of Paris alg ebra seminar\n\n\nAbstract\nIn these two talks\, we will start by introduc ing a result which establishes the existence and uniqueness of (DG) enhanc ements for triangulated categories which admit an additive generator whose endomorphism algebra is finite-dimensional (over a perfect field). We wil l then present a generalisation of this result that allows us to treat a l arger class of triangulated categories\, which instead admit a generator w ith a strong regularity property (a so-called dZ-cluster tilting object). We will also explain how our result\, combined with crucial theorems of Au gust and Hua-Keller\, leads to a positive solution of the Donovan-Wemyss C onjecture for contraction algebras as observed by Keller. We will also com ment on some details about the proof.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/113/ END:VEVENT BEGIN:VEVENT SUMMARY:Raphaël Rouquier (UCLA) DTSTART;VALUE=DATE-TIME:20221212T130000Z DTEND;VALUE=DATE-TIME:20221212T140000Z DTSTAMP;VALUE=DATE-TIME:20221209T214505Z UID:paris-algebra-seminar/114 DESCRIPTION:Title: Coherent realizations of 2-representations\nby Raphaë l Rouquier (UCLA) as part of Paris algebra seminar\n\n\nAbstract\n2-repres entations of Kac-Moody algebras arise algebraically and as categories of c onstructible sheaves. We will discuss two settings involving coherent shea ves: derived cotangent bundles to spaces of quiver representations and spa ces of quasi-maps in flag varieties.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/114/ END:VEVENT END:VCALENDAR