BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
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BEGIN:VEVENT
SUMMARY:Hipolito Treffinger (University of Leicester\, UK)
DTSTART:20200514T120000Z
DTEND:20200514T130000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/1
DESCRIPTION:Title: R
epresentation theoretic aspects of scattering diagrams\nby Hipolito Tr
effinger (University of Leicester\, UK) as part of Longitudinal Algebra an
d Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nThe notion of algeb
raic scattering diagram associated to any finite dimensional algebra was r
ecently introduced by Bridgeland as an algebraic construction of the celeb
rated cluster scattering diagrams of Gross\, Hacking\, Keel and Kontsevich
. In this talk\, after briefly recalling the construction of scattering di
agrams given by Bridgeland\, we will show how the homological aspects of t
he module category determine several properties of the support of the scat
tering diagrams. In particular\, we will show that chambers in the scatter
ing diagram of an algebra are in one-to-one correspondence with certain t
orsion pairs in its module category. This is joint work with Thomas Brustl
e and David Smith. Based on this characterisation\, we will discuss how th
e study of torsion pairs in the module category of algebras can play a key
role in the calculation of Donaldson-Thomas invariants for certain Calabi
-Yau threefolds.\n
LOCATION:https://researchseminars.org/talk/LAGOON/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Takeda (IHES\, France)
DTSTART:20200521T120000Z
DTEND:20200521T130000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/2
DESCRIPTION:Title: G
luing relative stability conditions along pushouts\nby Alex Takeda (IH
ES\, France) as part of Longitudinal Algebra and Geometry Open ONline Semi
nar (LAGOON)\n\n\nAbstract\nIn this talk I will discuss the results of arX
iv:1811.10592 and some later developments\, concerning how to produce Brid
geland stability conditions on certain categories from using a local-to-gl
obal principle. The example of particular interest will be the topological
Fukaya category of a marked surface\, and the description of the local da
ta is inspired by the construction of stability conditions on such categor
ies using quadratic differentials by Haiden\, Katzarkov and Kontsevich. As
an application of this method\, we show that one can understand all the c
omponents of the stability space of such categories\, and that in suitable
cases the whole space is described by these HKK stability conditions.\n
LOCATION:https://researchseminars.org/talk/LAGOON/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bernhard Keller (Université Paris Diderot - Paris 7\, France)
DTSTART:20200528T120000Z
DTEND:20200528T130000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/3
DESCRIPTION:Title: G
rassmannian braiding categorified\nby Bernhard Keller (Université Par
is Diderot - Paris 7\, France) as part of Longitudinal Algebra and Geometr
y Open ONline Seminar (LAGOON)\n\n\nAbstract\nChris Fraser has discovered
an action of the extended affine braid group on d strands on the Grassmann
ian cluster algebra of k-subspaces in n-space\, where d is the least commo
n divisor of k and n. We lift this action to the corresponding cluster cat
egory first constructed by Geiss-Leclerc-Schröer in 2008. For this\, we u
se Jensen-King-Su's description of this category as a singularity category
in the sense of Buchweitz/Orlov. We conjecture an action of the same brai
d group on the cluster algebra associated with an arbitrary pair of Dynkin
diagrams whose Coxeter numbers are k and n. This is a report on ongoing j
oint work with Chris Fraser.\n
LOCATION:https://researchseminars.org/talk/LAGOON/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Balazs Szendroi (University of Oxford\, UK)
DTSTART:20200604T120000Z
DTEND:20200604T130000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/4
DESCRIPTION:Title: H
ilbert schemes of points on singular surfaces: combinatorics\, geometry\,
and representation theory\nby Balazs Szendroi (University of Oxford\,
UK) as part of Longitudinal Algebra and Geometry Open ONline Seminar (LAGO
ON)\n\n\nAbstract\nGiven a smooth algebraic surface S over the complex num
bers\, the Hilbert scheme of points of S is the starting point for many in
vestigations\, leading in particular to generating functions with modular
behaviour and Heisenberg algebra representations. I will explain aspects o
f a similar story for surfaces with rational double points\, with links to
algebraic combinatorics and the representation theory of affine Lie algeb
ras. I will in particular recall our 2015 conjecture concerning the genera
ting function of the Euler characteristics of the Hilbert scheme for this
singular case\, and aspects of more recent work that lead to a very recent
proof of the conjecture by Nakajima. Joint work with Gyenge and Nemethi\,
respectively Craw\, Gammelgaard and Gyenge.\n
LOCATION:https://researchseminars.org/talk/LAGOON/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Qiu Yu (Tsinghua University Beijing\, China)
DTSTART:20200611T120000Z
DTEND:20200611T130000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/5
DESCRIPTION:Title: G
raded decorated marked surfaces: Calabi-Yau-X categories of gentle algebra
s\nby Qiu Yu (Tsinghua University Beijing\, China) as part of Longitud
inal Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nMoti
vated by q-deforming of stability conditions and categories\, we study the
Calabi-Yau-X categories of gentle algebras from graded decorated marked s
urfaces. The string model in this case unifies the Calabi-Yau-3 case in th
e prequels and the usual/Calabi-Yau-infinity case (via Lagrangian immersio
n). This is a joint work with Akishi Ikeda and Yu Zhou.\n
LOCATION:https://researchseminars.org/talk/LAGOON/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wendy Lowen (University of Antwerp\, Belgium)
DTSTART:20200625T120000Z
DTEND:20200625T130000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/6
DESCRIPTION:Title: L
inear quasi-categories as templicial modules\nby Wendy Lowen (Universi
ty of Antwerp\, Belgium) as part of Longitudinal Algebra and Geometry Open
ONline Seminar (LAGOON)\n\n\nAbstract\n(joint work with Arne Mertens) We
introduce a notion of enriched infinity categories over a given monoidal c
ategory\, in analogy with quasi-categories over the category of sets. We m
ake use of certain colax monoidal functors\, which we calltemplicial objec
ts\, as a replacement of simplicial objects that respects the monoidal str
ucture. We relate the resulting enriched quasi-categories to nonassociativ
e Frobenius monoidal functors\, allowing us to prove that the free templic
ial module over an ordinary quasi-category is a linear quasi-category. To
any dg category we associate a linear quasi-category\, the linear dg nerve
\, which enhances the classical dg nerve\, and we argue that linear quasi-
categories can be seen as relaxations of dg-categories.\n
LOCATION:https://researchseminars.org/talk/LAGOON/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hiraku Nakajima (Kavli IPMU\, Tokyo\, Japan)
DTSTART:20200702T120000Z
DTEND:20200702T130000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/7
DESCRIPTION:Title: E
uler numbers of Hilbert schemes of points on simple surface singularities
and quantum dimensions of standard modules of quantum affine algebras\
nby Hiraku Nakajima (Kavli IPMU\, Tokyo\, Japan) as part of Longitudinal A
lgebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nBalazs exp
lained his conjecture with Gyenge and Nemethi on\nEuler numbers of Hilbert
schemes on June 4. I proved it by showing that\nquantum dimensions of sta
ndard modules of quantum affine algebras are\nalways 1. This remarkable pr
operty is the simplest case of a conjecture\non quantum dimensions of Kiri
llov-Reshetikhin modules proposed by Kuniba\nin 93\, which is still open f
or E7\,8 in general. In this talk\, I will\nemphasize on representation th
eoretic aspects to minimize overlaps with\nBalazs' talk.\n
LOCATION:https://researchseminars.org/talk/LAGOON/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lara Bossinger (UNAM Oaxaca\, Mexico)
DTSTART:20200618T150000Z
DTEND:20200618T160000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/8
DESCRIPTION:Title: F
amilies of Gröbner degenerations\nby Lara Bossinger (UNAM Oaxaca\, Me
xico) as part of Longitudinal Algebra and Geometry Open ONline Seminar (LA
GOON)\n\n\nAbstract\nIn this talk I will present a construction of one fla
t family that combines many Gröbner degenerations. More precisely\, for a
(weighted) homogeneous ideal we consider a maximal cone in its Gröbner f
an. Associated to that cone we define a flat family that contains various
special fibers associated to the initial degenerations of the cone and all
its faces. This construction has several interesting applications. Most s
urprisingly\, it recovers the recursive construction of universal coeffici
ents for cluster algebras in a non-recursive way for the Grassmannians Gr(
2\,n) and Gr(3\,6). If time permits I will present another application exp
laining how to recover Kaveh-Manon's toric equivariant families arising fr
om a collection of nice cones in the tropicalization of an ideal. This tal
k is based on joint work in progress with F. Mohammadi and A. Nájera Chá
vez.\n
LOCATION:https://researchseminars.org/talk/LAGOON/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Polishchuk (University of Oregon\, USA)
DTSTART:20200709T150000Z
DTEND:20200709T160000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/9
DESCRIPTION:Title: G
eometry of the Associative Yang-Baxter equation\nby Alexander Polishch
uk (University of Oregon\, USA) as part of Longitudinal Algebra and Geomet
ry Open ONline Seminar (LAGOON)\n\n\nAbstract\nI will describe the connect
ion\, discovered jointly with Yanki Lekili\, between Associative Yang-Baxt
er equation (AYBE) and pairs of 1-spherical objects in A-infinity categori
es. I will then explain how such pairs arise from noncommutative orders ov
er singular curves\, in particular\, how to get all nondegenerate trigonom
etric solutions of the AYBE in this way. If time allows\, I will talk abou
t the Lie analog of this story for the classical Yang-Baxter equation.\n
LOCATION:https://researchseminars.org/talk/LAGOON/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Markus Reineke (Universität Bochum\, Germany)
DTSTART:20200716T120000Z
DTEND:20200716T130000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/10
DESCRIPTION:Title:
Fano quiver moduli\nby Markus Reineke (Universität Bochum\, Germany)
as part of Longitudinal Algebra and Geometry Open ONline Seminar (LAGOON)\
n\n\nAbstract\nWe construct a large class of quiver moduli spaces with are
Fano varieties\, by studying global sections of line bundles on quiver mo
duli and identifying a special class of stabilities. We discuss several cl
asses of examples (e.g. toric varieties\, point configuration spaces\, Kro
necker moduli).\n
LOCATION:https://researchseminars.org/talk/LAGOON/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:2020 Categorifications in Representation Theory
DTSTART:20200917T120000Z
DTEND:20200917T130000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/11
DESCRIPTION:Title:
Categorifications in Representation Theory Conference at Leicester (Sep 15
-17)\nby 2020 Categorifications in Representation Theory as part of Lo
ngitudinal Algebra and Geometry Open ONline Seminar (LAGOON)\n\nAbstract:
TBA\n
LOCATION:https://researchseminars.org/talk/LAGOON/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laura Schaposnik (University of Illinois at Chicago\, USA)
DTSTART:20200723T120000Z
DTEND:20200723T130000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/12
DESCRIPTION:Title:
On Generalized Hyperpolygons\nby Laura Schaposnik (University of Illin
ois at Chicago\, USA) as part of Longitudinal Algebra and Geometry Open ON
line Seminar (LAGOON)\n\n\nAbstract\nIn this talk we will introduce genera
lized hyperpolygons\, which arise as Nakajima-type representations of a co
met-shaped quiver\, following a recent work joint with Steven Rayan. After
showing how to identify these representations with pairs of polygons\, we
shall associate to the data an explicit meromorphic Higgs bundle on a gen
us g Riemann surface\, where g is the number of loops in the comet. We sha
ll see that\, under certain assumptions on flag types\, the moduli space o
f generalized hyperpolygons admits the structure of a completely integrabl
e Hamiltonian system. Time permitting\, we shall conclude the talk by ment
ioning some partial results on current work on the construction of triple
branes (in the sense of Kapustin-Witten mirror symmetry)\, and dualities b
etween tame and wild Hitchin systems (in the sense of Painlevé transcende
nts).\n
LOCATION:https://researchseminars.org/talk/LAGOON/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Solotar (University of Buenos Aires\, Argentina)
DTSTART:20200903T120000Z
DTEND:20200903T130000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/13
DESCRIPTION:Title:
A cup-cap duality in Koszul calculus\nby Andrea Solotar (University of
Buenos Aires\, Argentina) as part of Longitudinal Algebra and Geometry Op
en ONline Seminar (LAGOON)\n\n\nAbstract\nIn this talk I will introduce a
cup-cap duality in the Koszul calculus of N-homogeneous algebras following
https://arxiv.org/abs/2007.00627. As an application of this duality\, it
follows that the graded symmetry of the Koszul cap product is a consequenc
e of the graded commutativity of the Koszul cup product. I will also comme
nt on a conceptual approach to this problem that may lead to a proof of th
e graded commutativity\, based on derived categories in the framework of D
G algebras and DG bimodules. This is joint work with Roland Berger.\n
LOCATION:https://researchseminars.org/talk/LAGOON/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhengfang Wang (University of Stuttgart\, Germany)
DTSTART:20200910T120000Z
DTEND:20200910T130000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/14
DESCRIPTION:Title:
Deformations of path algebras of quivers with relations\nby Zhengfang
Wang (University of Stuttgart\, Germany) as part of Longitudinal Algebra a
nd Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nIn this talk\, we
provide a very explicit method to describe deformations of path algebras o
f quivers with relations. This method is based on a combinatorial descript
ion of an L-infinity algebra constructed from Chouhy-Solotar’s projectiv
e resolution. As an application\, we show that the variety associated to m
onomial algebras constructed by Green-Hille-Schroll is actually given by t
he Maurer--Cartan equation of the L-infinity algebra. This is joint work w
ith Severin Barmeier.\n
LOCATION:https://researchseminars.org/talk/LAGOON/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alisa Keating (University of Cambridge\, UK)
DTSTART:20200924T120000Z
DTEND:20200924T130000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/15
DESCRIPTION:Title:
Homological mirror symmetry for log Calabi-Yau surfaces\nby Alisa Keat
ing (University of Cambridge\, UK) as part of Longitudinal Algebra and Geo
metry Open ONline Seminar (LAGOON)\n\n\nAbstract\nGiven a log Calabi-Yau s
urface Y with maximal boundary D\, I'll explain how to construct a mirror
Landau-Ginzburg model\, and sketch a proof of homological mirror symmetry
for these pairs when (Y\,D) is distinguished within its deformation class
(this is mirror to an exact manifold). I'll explain how to relate this to
the total space of the SYZ fibration predicted by Gross--Hacking--Keel\, a
nd\, time permitting\, explain ties with earlier work of Auroux--Katzarkov
--Orlov and Abouzaid. Joint work with Paul Hacking.\n
LOCATION:https://researchseminars.org/talk/LAGOON/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Wemyss (University of Glasgow\, UK)
DTSTART:20201029T120000Z
DTEND:20201029T130000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/16
DESCRIPTION:Title:
Contraction algebras\, plumbings and flops\nby Michael Wemyss (Univers
ity of Glasgow\, UK) as part of Longitudinal Algebra and Geometry Open ONl
ine Seminar (LAGOON)\n\n\nAbstract\nI will explain how certain symmetric N
akayama algebras (under the disguise of "contraction algebras") control an
d prove theorems about geometric objects on both sides of mirror symmetry.
As part of this\, I will explain our symplectic geometry model\, our alg
ebraic geometry model\, and then how the contraction algebra relates them.
The cohomology of objects in the underlying categories are naturally mod
ules for the associated contraction algebra\, and I will explain how to us
e this information to obtain otherwise tricky results\, such as a classifi
cation of spherical (and more generally\, fat-spherical) objects. This ha
s purely topological corollaries. One feature\, which I will probably glo
ss over but is actually fundamental\, is that our categories have a depend
ence on the characteristic of the ground field. This is joint work with I
van Smith (arXiv:2010.10114).\n\nThursday 29th October 2020\, 12:00 – 13
:00 (GMT)\nhttps://us02web.zoom.us/j/89958893469?pwd=aWFWQXZnMXczUFdJc282b
Wx3bE5Idz09\nMeeting ID: 899 5889 3469\nPasscode: Lagoon\n
LOCATION:https://researchseminars.org/talk/LAGOON/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Karin Baur (University of Leeds\, UK and University of Graz\, Aust
ria)
DTSTART:20201001T110000Z
DTEND:20201001T120000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/17
DESCRIPTION:Title:
Structure of Grassmannian cluster categories\nby Karin Baur (Universit
y of Leeds\, UK and University of Graz\, Austria) as part of Longitudinal
Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nThe categ
ory of Cohen Macaulay modules over a quotient of a preprojective algebra p
rovides an additive categorification of Scott’s cluster algebra structur
e of the coordinate ring of the Grassmannian of k-subspaces in n-space\, b
y work of Jensen\, King and Su. Under this correspondence\, rigid indecomp
osable objects map to cluster variables. A special role is played by rank
1 indecomposables which correspond bijectively to Plücker coordinates. Th
ese are in fact all indecomposables in case k=2. In the other finite types
(i.e. $(k\,n)\\in \\{(3\,6)\,(3\,7)\,(3\,8)\\}$)\, there are also rank 2
and rank 3 rigid indecomposables. In general\, the Grassmannian categories
are not well understood. We provide characterisations for these low rank
modules in infinite types. This is joint work with Dusko Bogdanic and Ana
Garcia Elsener and with Bogdanic\, Garcia Elsener and Jianrong Li.\n
LOCATION:https://researchseminars.org/talk/LAGOON/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrey Lazarev (Lancaster University\, UK)
DTSTART:20201008T110000Z
DTEND:20201008T120000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/18
DESCRIPTION:Title:
Koszul duality for dg-categories and infinity-categories\nby Andrey La
zarev (Lancaster University\, UK) as part of Longitudinal Algebra and Geom
etry Open ONline Seminar (LAGOON)\n\n\nAbstract\nDifferential graded (dg)
Koszul duality is a certain adjunction between the category of dg algebras
and conilpotent dg coalgebras that becomes an equivalence on the levels o
f homotopy categories. More precisely\, this adjunction is a Quillen equiv
alence of the corresponding closed model categories. Various versions of t
his result exist and play important roles in rational homotopy theory\, de
formation theory\, representation theory and other related fields. We exte
nd it to a Quillen equivalence between dg categories (generalizing dg alge
bras) and a class of dg coalgebras\, more general than conilpotent ones. A
s applications we describe explicitly and conceptually Lurie’s dg nerve
functor as well as its adjoint and characterize derived categories of (\\i
nfty\,1)-categories as derived categories of comodules over simplicial cha
in coalgebras.(joint work with J. Holstein)\n
LOCATION:https://researchseminars.org/talk/LAGOON/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giulia Saccà (Collège de France and Columbia University\, USA)
DTSTART:20201203T170000Z
DTEND:20201203T180000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/19
DESCRIPTION:Title:
Hodge numbers of OG10 via Ngô strings\nby Giulia Saccà (Collège de
France and Columbia University\, USA) as part of Longitudinal Algebra and
Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nI will talk on joint
work with M. de Cataldo and A. Rapagnetta\, in which we compute the Hodge
numbers of the 10-dimensional hyperkähler manifold known as OG10. The mai
n technique is the use of Ngô's support theorem\, applied to a natural La
grangian fibration on a certain projective model of OG10\, together with t
he study of the geometry of the fibration itself.\n
LOCATION:https://researchseminars.org/talk/LAGOON/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fabrizio Catanese (University of Bayreuth\, Germany)
DTSTART:20201015T110000Z
DTEND:20201015T120000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/20
DESCRIPTION:Title:
Topologically trivial automorphisms of compact Kähler surfaces and manifo
lds\nby Fabrizio Catanese (University of Bayreuth\, Germany) as part o
f Longitudinal Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbst
ract\nThe abstract can be downloaded here: \nhttps://drive.google.com/file
/d/1B6aZ-46iUgPic9YJyJ5lGnr2MsvP3lvl/view\n
LOCATION:https://researchseminars.org/talk/LAGOON/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yukinobu Toda (Kavli IPMU\, Tokyo\, Japan)
DTSTART:20201105T120000Z
DTEND:20201105T130000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/21
DESCRIPTION:Title:
On d-critical birational geometry and categorical DT theories\nby Yuki
nobu Toda (Kavli IPMU\, Tokyo\, Japan) as part of Longitudinal Algebra and
Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nIn this talk\, I wil
l explain an idea of analogue of birational geometry for \nJoyce's d-criti
cal loci\, and categorical Donaldson-Thomas theories \non Calabi-Yau 3-fo
lds. The motivations of this framework include \ncategorifications of wall
-crossing formulas of DT invariants and also \na d-critical analogue of D/
K conjecture in birational geometry. \nThe main result is to realize the a
bove story for local surfaces. \nI will show the window theorem for catego
rical DT theories on local surfaces\nand apply it to categorify wall-cross
ing invariance of genus zero GV invariants\, \nMNOP/PT correspondence\, et
c.\n
LOCATION:https://researchseminars.org/talk/LAGOON/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Greenlees (University of Warwick\, UK)
DTSTART:20201119T120000Z
DTEND:20201119T130000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/22
DESCRIPTION:Title:
The singularity category of C^*(BG)\nby John Greenlees (University of
Warwick\, UK) as part of Longitudinal Algebra and Geometry Open ONline Sem
inar (LAGOON)\n\n\nAbstract\n[joint work with G.Stevenson and D.Benson] Fo
r an ordinary commutative Noetherian ring R we would define the singularit
y category to be the quotient of the (derived category of) finitely genera
ted modules modulo the (derived category of) fg projective modules [``the
bounded derived category modulo compact objects’’]. For a ring spectr
um like C^*(BG) (coefficients in a field of characteristic p) it is easy t
o define the module category and the compact objects\, but finitely genera
ted objects need a new definition. The talk will describe the definition a
nd show that the singularity category is trivial exactly when G is p-nilpo
tent. We will go on to describe the singularity category for groups with c
yclic Sylow p-subgroup.\n\nMeeting Link\nThursday 19th November 2020\, 12
:00 – 13:00 (GMT)\nhttps://us02web.zoom.us/j/89958893469?pwd=aWFWQXZnMXc
zUFdJc282bWx3bE5Idz09\nMeeting ID: 899 5889 3469\nPasscode: Lagoon\n
LOCATION:https://researchseminars.org/talk/LAGOON/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lang Mou (HMI Bonn\, Germany)
DTSTART:20201022T110000Z
DTEND:20201022T120000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/23
DESCRIPTION:Title:
Caldero–Chapoton formulas for generalized cluster algebras from orbifold
s\nby Lang Mou (HMI Bonn\, Germany) as part of Longitudinal Algebra an
d Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nTo a marked bordere
d surface with orbifold points of order 3\, we associated a quiver (with l
oops) with potential. We then connect the cluster structure of the corresp
onding skew-symmetrizable matrix with the stability conditions and the $\\
tau$-tiliting theory of the Jacobian algebra. Finally we provide Caldero
–Chapoton type formulas for cluster monomials of the generalized cluster
algebra of Chekhov and Shapiro associated to the surface. This is joint w
ork with Labardini-Fragoso\n
LOCATION:https://researchseminars.org/talk/LAGOON/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ralph Kaufmann (Purdue University\, USA)
DTSTART:20201210T120000Z
DTEND:20201210T130000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/24
DESCRIPTION:Title:
Categorical Interactions in Algebra\, Geometry and Representation Theory\nby Ralph Kaufmann (Purdue University\, USA) as part of Longitudinal Al
gebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nThere are s
everal fundamental interactions between combinatorics\, algebra and geomet
ry\, where the combinatorial structures give representations and suitably
interpreted encode cells for a geometric realization. A prime example of t
his is Deligne's conjecture\, where the representation of certain graphs y
ields actions on the Hochschild complex and geometrically these graphs can
be considered as graphs dual to a system of arcs on a surface. There is a
way to encode the combinatorial structures into categorical ones\, the so
-called Feynman categories. The representations in this setting functors o
ut of them. More generally they yield the representations can also be alge
bras of certain types. In the functorial formalism one has restriction\, r
eduction and Frobenius reciprocity. To make these geometric\, one can use
a so-called W-construction. For trees and graphs\, this program leads to t
he construction of moduli spaces of graphs and Riemann surfaces. These are
versions of the commutative and associative geometries studied by Kontsev
ich. Staying inside the algebraic world\, one can use functors to enrich F
eynman categories. The enriched categories play the role of algebras and t
he representations are modules - all with possible higher operations. The
enrichment is made by using a plus construction\, which has a connection t
o bi-algebras and Hopf algebras based on the morphisms of a Feynman catego
ry.\n\nMeeting Link\nhttps://us02web.zoom.us/j/89958893469?pwd=aWFWQXZnMXc
zUFdJc282bWx3bE5Idz09\nMeeting ID: 899 5889 3469\nPasscode: Lagoon\n
LOCATION:https://researchseminars.org/talk/LAGOON/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Evgeny Shinder (University of Sheffield\, UK)
DTSTART:20201126T120000Z
DTEND:20201126T130000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/25
DESCRIPTION:Title:
Birationality centers\, rationality problems and Cremona groups\nby Ev
geny Shinder (University of Sheffield\, UK) as part of Longitudinal Algebr
a and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nI will introduc
e a framework to account for the ambiguity of stable birational types of a
sequence of centers for birational transformations. I will explain in whi
ch settings the introduced invariants are nonvanishing\, and give applicat
ions to the structure of Cremona groups over various fields. This is joint
work in progress with Hsueh-Yung Lin and Susanna Zimmermann.\n\nMeeting L
ink\nhttps://us02web.zoom.us/j/89958893469?pwd=aWFWQXZnMXczUFdJc282bWx3bE5
Idz09\nMeeting ID: 899 5889 3469\nPasscode: Lagoon\n
LOCATION:https://researchseminars.org/talk/LAGOON/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amihay Hanany (Imperial College London\, UK)
DTSTART:20201112T120000Z
DTEND:20201112T130000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/26
DESCRIPTION:Title:
Coulomb branch\nby Amihay Hanany (Imperial College London\, UK) as par
t of Longitudinal Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\nA
bstract\nThe Coulomb branch is a symplectic singularity that appears in th
e physics study of gauge theories (more precisely in 3d N=4 supersymmetric
gauge theories). A recent (2013) progress in understanding the Coulomb br
anch was when a combinatorial formula for this singularity was introduced\
, named the monopole formula. This raised excitement both in physics and i
n mathematics.It plays an important role in a collection of physical pheno
mena which were hard to solve previously\, and it gives a new construction
of geometric singularities that opens new directions of study in represen
tation theory. This talk will focus on the monopole formula for a quiver a
nd will discuss the different objects and features which arise from the qu
iver.\n
LOCATION:https://researchseminars.org/talk/LAGOON/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dan Kaplan (University of Birmingham\, UK)
DTSTART:20210128T120000Z
DTEND:20210128T130000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/28
DESCRIPTION:Title:
Multiplicative preprojective algebras in geometry and topology\nby Dan
Kaplan (University of Birmingham\, UK) as part of Longitudinal Algebra an
d Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nIn 2006\, Crawley-B
oevey and Shaw defined the multiplicative preprojective algebra (MPA) to s
tudy certain character varieties. More recently\, MPAs appeared in work of
Etgü--Lekili in the study of Fukaya categories of 4-manifolds. Nice prop
erties of the (additive) preprojective algebra are expected to hold for MP
As\, but most proof techniques are not available. In joint work with Travi
s Schedler\, we define the strong free product property\, following older
work of Anick. Using this property\, we prove MPAs are 2-Calabi--Yau algeb
ras for quivers containing a cycle. Moreover\, using a result of Bocklandt
--Galluzzi--Vaccarino\, we prove the formal local structure of multiplicat
ive quiver varieties is isomorphic to that of a (usual) quiver variety. In
this talk\, I'll survey these ideas and illustrate them in small examples
.\n
LOCATION:https://researchseminars.org/talk/LAGOON/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bertrand Toën (CNRS\, Université de Toulouse\, France)
DTSTART:20210211T120000Z
DTEND:20210211T130000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/29
DESCRIPTION:Title:
Foliations on schemes\nby Bertrand Toën (CNRS\, Université de Toulou
se\, France) as part of Longitudinal Algebra and Geometry Open ONline Semi
nar (LAGOON)\n\n\nAbstract\nIn this talk I will present a notion of foliat
ions on\narbitrary schemes (possibly of positive or mixed characteristics)
\, based on techniques\nfrom derived algebraic geometry. As an instance of
application I will explain\nhow Baum-Bott's existence of residues for sin
gular holomorphic\nfoliations can be extended to the positive characterist
ic setting.\n\nhttps://us02web.zoom.us/j/87160036709\nMeeting ID: 871 6003
6709\nPasscode: LAGOON\n
LOCATION:https://researchseminars.org/talk/LAGOON/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Merlin Christ (University of Hamburg\, Germany)
DTSTART:20210204T120000Z
DTEND:20210204T130000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/30
DESCRIPTION:Title:
A gluing construction for Ginzburg algebras of triangulated surfaces\n
by Merlin Christ (University of Hamburg\, Germany) as part of Longitudinal
Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nGinzburg
algebras associated to triangulated surfaces are a class of 3-Calabi-Yau
dg-algebras which categorify the cluster algebras of the underlying marked
surfaces. In this talk\, we will discuss a description of these Ginzburg
algebras in terms of the global sections of a constructible cosheaf of dg-
categories (modelling a perverse Schober). This cosheaf description shows
that the Ginzburg algebras arise via the gluing of relative versions of Gi
nzburg algebras associated to the faces of the triangulation along their c
ommon edges. The definition of the cosheaf is inspired by a result of Ivan
Smith\, by which the finite derived category of such a Ginzburg algebra e
mbeds into the Fukaya category of a Calabi-Yau 3-fold equipped with a Lefs
chetz fibration to the surface.\n
LOCATION:https://researchseminars.org/talk/LAGOON/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paolo Stellari (University of Milano\, Italy)
DTSTART:20210218T120000Z
DTEND:20210218T130000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/31
DESCRIPTION:Title:
Uniqueness of enhancements for derived and geometric categories\nby Pa
olo Stellari (University of Milano\, Italy) as part of Longitudinal Algebr
a and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nIn this talk we
address several open questions and generalize the existing results about
the uniqueness of enhancements for triangulated categories which arise as
derived categories of abelian categories or from geometric contexts. If ti
me permits\, we will also discuss applications to the description of exact
equivalences. This is joint work with A. Canonaco and A. Neeman.\n
LOCATION:https://researchseminars.org/talk/LAGOON/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chelsea Walton (Rice University\, USA)
DTSTART:20210701T140000Z
DTEND:20210701T150000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/32
DESCRIPTION:Title:
Frobenius algebras galore\nby Chelsea Walton (Rice University\, USA) a
s part of Longitudinal Algebra and Geometry Open ONline Seminar (LAGOON)\n
\n\nAbstract\nIn this talk\, I’ll chat about wonderful algebraic structu
res that were discovered in the early 1900’s: Frobenius algebras. I will
survey the 100+ year history of the development and uses of these structu
res\, ending with very recent research results from joint work with Harshi
t Yadav.\n\nMeeting Link\nThursday\, 15:00 - 16:00 (BST\, UK Time)\nhttps
://us02web.zoom.us/j/87160036709?pwd=aGtBdkx4VDFuY0l2UlkzRFdiYUF3dz09 \nMe
eting ID: 871 6003 6709\nPasscode: LAGOON\n
LOCATION:https://researchseminars.org/talk/LAGOON/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Claudia Scheimbauer (TU München\, Germany)
DTSTART:20210225T120000Z
DTEND:20210225T130000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/33
DESCRIPTION:Title:
Derived symplectic geometry and AKSZ topological field theories\nby Cl
audia Scheimbauer (TU München\, Germany) as part of Longitudinal Algebra
and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nDerived algebraic
geometry and derived symplectic geometry in the sense of Pantev-Toen-Vaqu
ié-Vezzosi allows for a reinterpretation/analog of the classical AKSZ con
struction for certain $\\sigma$-models. After recalling this procedure I w
ill explain how it can be extended to give a fully extended oriented TFT i
n the sense of Lurie with values in a higher category whose objects are $n
$-shifted symplectic derived stacks and (higher) morphisms are (higher) La
grangian correspondences. It is given by taking mapping stacks with a fixe
d target building and describes ``semi-classical TFTs". This is joint work
in progress with Damien Calaque and Rune Haugseng.\n\nMeeting Link\nThurs
day 18 February\, 12:00 - 13:00 (GMT)\nhttps://us02web.zoom.us/j/87160036
709\nMeeting ID: 871 6003 6709\nPasscode: LAGOON\n
LOCATION:https://researchseminars.org/talk/LAGOON/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Letterio Gatto (Polytechnic University of Turin\, Italy)
DTSTART:20210318T120000Z
DTEND:20210318T130000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/34
DESCRIPTION:Title:
HiDEAs to work with\nby Letterio Gatto (Polytechnic University of Turi
n\, Italy) as part of Longitudinal Algebra and Geometry Open ONline Semina
r (LAGOON)\n\n\nAbstract\nHiDEA is the acronym of Higher Derivations on Ex
terior Algebra\, a project I am currently working on together with many c
ollaborators\, such as O. Behzad & A. Nasrollah Nejad (Iran)\, L. Rowen &
I. Scherbak (Israel)\, A. Contiero\, P. Salehyan & R. Vidal Martins (Brasi
l)\, S. Amukugu\, M. Mugochi & G. Marelli (Namibia). Originally introduced
by Hasse & Schmidt (1937) to extend Taylor expansions of analytic functi
ons and Wronskians in in the realm of positive characteristic commutative
algebra\, the notion of Higher Order derivations (Hasse-Schmidt derivatio
n in the sequel) provides an extremely rich theory when applied to the sup
er--commutative situation supplied by exterior algebras of free modules. T
he purpose of this talk is to advertise HiDEAs practise\, focusing on its
main tool\, the so-called integration by parts formula. The latter shows
how the theory is concerned with multilinear algebra (via an extension of
the Cayley-Hamilton theorem for possible infinite dimensional vector space
s)\, with intersection theory of Grassmannians (Schubert Calculus via Pier
i's & Giambelli's formula)\, with Representation Theory and Mathematical P
hysics\, given the spontaneously arising of the vertex operators occurring
in the boson-fermion correspondence from the so-called Schubert Derivati
ons. The talk aims to be general\, non specialistic and self--contained\,
requiring no more than basics in multilinear algebra (exterior algebras)\
, elementary calculus (Taylor expansions) and a little routine combinator
ics (formal power series\, partitions\, symmetric functions).\n\nhttps://u
s02web.zoom.us/j/87160036709\nMeeting ID: 871 6003 6709\nPasscode: LAGOON\
n
LOCATION:https://researchseminars.org/talk/LAGOON/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandra Zvonareva (University of Stuttgart\, Germany)
DTSTART:20210311T120000Z
DTEND:20210311T130000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/35
DESCRIPTION:Title:
Derived equivalence classification of Brauer graph algebras\nby Alexan
dra Zvonareva (University of Stuttgart\, Germany) as part of Longitudinal
Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nIn this t
alk\, I will explain the classification of Brauer graph algebras up to der
ived equivalence. These algebras first appeared in representation theory o
f finite groups and can be defined for any suitably decorated graph on an
oriented surface. The classification relies on the connection between Brau
er graph algebras and gentle algebras and the classification of the mappin
g class group orbits of the homotopy classes of line fields on surfaces. W
e consider A-infinity trivial extensions of partially wrapped Fukaya categ
ories associated to surfaces with boundary\, this construction naturally e
nlarges the class of Brauer graph algebras and provides a way to construct
derived equivalences. This is based on joint work with Sebastian Opper.\n
LOCATION:https://researchseminars.org/talk/LAGOON/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sebastian Opper (Charles University Prague\, Czech Republic)
DTSTART:20210304T120000Z
DTEND:20210304T130000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/36
DESCRIPTION:Title:
Spherical objects on cycles of projective lines and transitivity\nby S
ebastian Opper (Charles University Prague\, Czech Republic) as part of Lon
gitudinal Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\
nPolishchuk showed that spherical objects in the derived category of any c
ycle of projective lines yield solutions of the associative Yang-Baxter eq
uation which raises the question whether one can classify spherical object
s. He further posed the question whether the group of derived auto-equiva
lences of a cycle acts transitively on isomorphism classes of spherical ob
jects. Partial solutions to both problems were given in works of Burban-Kr
eussler and Lekili-Polishchuk. A theorem of Burban-Drozd establishes a co
nnection between the derived category of any cycle of projective lines wit
h the derived category of a certain gentle algebra which can be modeled by
a (toplogical) surface and which allows us to translate algebraic informa
tion in the derived category such as objects into geometric information on
the surface such as curves. I will explain how the result of Burban-Drozd
can be used to find a similar model for the derived category of a cycle.
Afterwards we discuss how this can be exploited to classify spherical obje
cts and establish transitivity. Further applications include a description
of the group of derived auto-equivalences of a cycle and faithfulness of
a certain group action as defined by Sibilla.\n
LOCATION:https://researchseminars.org/talk/LAGOON/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Valery Lunts (Indiana University\, USA)
DTSTART:20210415T140000Z
DTEND:20210415T150000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/37
DESCRIPTION:Title:
Subcategories of derived categories on affine schemes and projective curve
s\nby Valery Lunts (Indiana University\, USA) as part of Longitudinal
Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nI will re
port on my joint recent work with Alexey Elagin (arXiv:2007.02134 \, arXiv
:2002.06416\, arXiv:1711.01492).\nThe famous theorem of Hopkins-Neeman giv
es a simple geometric classification of thick subcategories of the categor
y Perf(X) for an affine noetherian scheme X. It is natural to ask if there
is a similar classification of thick subcategories of D^b(cohX) (for an a
ffine X). I will discuss some positive and some negative results in this d
irection. In a different situation: surprisingly one is able to classify (
up to equivalence) all thick subcategories of D^b(cohC) for a smooth proje
ctive curve.\n\nhttps://us02web.zoom.us/j/87160036709 \nMeeting ID: 871 6
003 6709\nPasscode: LAGOON\n
LOCATION:https://researchseminars.org/talk/LAGOON/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Severin Barmeier (University of Freiburg\, Germany)
DTSTART:20210422T110000Z
DTEND:20210422T120000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/38
DESCRIPTION:Title:
Scattering amplitudes from derived categories and cluster categories\n
by Severin Barmeier (University of Freiburg\, Germany) as part of Longitud
inal Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nScat
tering amplitudes are physical observables which play a central role in in
terpreting scattering experiments at particle colliders. In recent years a
new perspective on scattering amplitudes has revealed a fascinating link
to various mathematical structures\, such as positive Grassmannians and cl
uster algebras. In this talk I will explain this connection from the point
of view of derived and cluster categories of type A quivers\, from which
the formulae for scattering amplitudes can be obtained from projectives of
hearts of intermediate t-structures. This talk is based on arXiv:2101.028
84 joint with Koushik Ray.\n
LOCATION:https://researchseminars.org/talk/LAGOON/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Okke van Garderen (University of Glasgow\, UK)
DTSTART:20210429T110000Z
DTEND:20210429T120000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/39
DESCRIPTION:Title:
Stability\, duality\, and DT invariants for flopping curves\nby Okke v
an Garderen (University of Glasgow\, UK) as part of Longitudinal Algebra a
nd Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nThreefold flops ar
e birational surgeries on a contractible curve that connect minimal models
of threefolds\, and are therefore crucial to the minimal model program. T
o examine these flops one would like to compute their Donaldson-Thomas inv
ariants\, which are virtual counts of semistable objects in the derived ca
tegory. In this talk I will explain how to determine the semistable object
s supported on a flopping curve by showing that their K-theory classes are
dual to a hyperplane arrangement induced by tilting complexes. I will als
o show how this duality can be categorified to give a full description of
the (3-Calabi-Yau) deformation theory of these objects\, which has various
implications for the DT theory.\n\nhttps://us02web.zoom.us/j/87160036709
\nMeeting ID: 871 6003 6709\nPasscode: LAGOON\n
LOCATION:https://researchseminars.org/talk/LAGOON/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ana Ros Camacho (Cardiff University\, UK)
DTSTART:20210506T110000Z
DTEND:20210506T120000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/40
DESCRIPTION:Title:
On the Landau-Ginzburg/conformal field theory correspondence\nby Ana R
os Camacho (Cardiff University\, UK) as part of Longitudinal Algebra and G
eometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nThe Landau-Ginzburg/co
nformal field theory (LG/CFT) correspondence is a result from the theoreti
cal physics literature dating back to the late 80s-early 90s\, which in pa
rticular predicts a certain relation between categories of matrix factoriz
ations and categories of representations of vertex operator algebras. Curr
ently we lack a precise mathematical statement for this physics result\, b
ut fortunately we have some examples available that we will review during
this talk\, as well as some current work in progress towards more. This is
joint work with I. Runkel\, A. Davydov et al.\n
LOCATION:https://researchseminars.org/talk/LAGOON/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Markus Szymik (NTNU Trondheim\, Norway)
DTSTART:20210603T110000Z
DTEND:20210603T120000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/41
DESCRIPTION:Title:
A homological stroll into the algebraic theories of racks and quandles
\nby Markus Szymik (NTNU Trondheim\, Norway) as part of Longitudinal Algeb
ra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nRacks and quan
dles are rudimentary algebraic structures akin to groups and tied to symme
try. I will begin my presentation with an introduction to these concepts\,
focussing on their ubiquity in geometry and topology. Current development
s illustrate how an interplay between conceptual curiosity and computation
al aspiration can substantially progress our understanding of such structu
res. I will take a homological vantage point and weave a narrative around
some recent joint work with Tyler Lawson and Victoria Lebed.\n\nhttps://us
02web.zoom.us/j/87160036709 Meeting ID: 871 6003 6709 Passcode: LAGOON\n
LOCATION:https://researchseminars.org/talk/LAGOON/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matt Booth (University ofd Antwerp\, Belgium)
DTSTART:20210513T110000Z
DTEND:20210513T120000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/42
DESCRIPTION:Title:
Topological Hochschild cohomology for schemes\nby Matt Booth (Universi
ty ofd Antwerp\, Belgium) as part of Longitudinal Algebra and Geometry Ope
n ONline Seminar (LAGOON)\n\n\nAbstract\nTopological Hochschild cohomology
is a sort of refinement of usual Hochschild cohomology that incorporates
data from stable homotopy theory. Instead of working over a base ring\, on
e works over the sphere spectrum\, which is a commutative ring in an appro
priate sense. I'll give a quick introduction to spectral algebra and THH^*
. Then I'll define the THH^* of a scheme in a `derived noncommutative' way
- i.e. using appropriate dg categories of sheaves - and explain some inva
riance results\, which in the non-topological setting are due to Lowen and
Van den Bergh via Keller. I'll discuss some toy non-affine computations\,
and time permitting I'll talk about the relationship to deformation theor
y\, especially in positive characteristic. This is joint work with Dmitry
Kaledin and Wendy Lowen.\n\nhttps://us02web.zoom.us/j/87160036709 \nMeeti
ng ID: 871 6003 6709\nPasscode: LAGOON\n
LOCATION:https://researchseminars.org/talk/LAGOON/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fabian Haiden (University of Oxford\, UK)
DTSTART:20210610T110000Z
DTEND:20210610T120000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/43
DESCRIPTION:Title:
New 3CY categories of topological surfaces\nby Fabian Haiden (Universi
ty of Oxford\, UK) as part of Longitudinal Algebra and Geometry Open ONlin
e Seminar (LAGOON)\n\n\nAbstract\nTo a topological surface\, perhaps with
certain markings\, one can attach several different triangulated categorie
s whose objects are\, roughly speaking\, curves on the surface. One such e
xample is the Fukaya category of the surface\, another is the 3-d Calabi-Y
au (3CY) category of an ideal triangulation. These have proven useful\, am
ong other things\, in the study of Bridgeland stability conditions and the
representation theory of finite-dimensional algebras. In the recent prepr
int arXiv:2104.06018 I introduce yet another class of triangulated A-infin
ity categories of surfaces. The motivation for constructing them was to ex
tend the work of Bridgeland-Smith on stability conditions and quadratic di
fferentials to the finite area case (e.g. holomorphic differentials). They
are closely related to the existing triangulated categories of surfaces a
nd clarify the relation between them. Their construction involves some alg
ebraic tricks\, such as twisted complexes and modules over curved A-infini
ty categories\, which will be discussed in detail.\n\nhttps://us02web.zoom
.us/j/87160036709?pwd=aGtBdkx4VDFuY0l2UlkzRFdiYUF3dz09 \nMeeting ID: 871 6
003 6709\nPasscode: LAGOON\n
LOCATION:https://researchseminars.org/talk/LAGOON/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergey Mozgovoy (Trinity College Dublin\, Ireland)
DTSTART:20210520T110000Z
DTEND:20210520T120000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/44
DESCRIPTION:Title:
DT invariants of some 3CY quotients\nby Sergey Mozgovoy (Trinity Colle
ge Dublin\, Ireland) as part of Longitudinal Algebra and Geometry Open ONl
ine Seminar (LAGOON)\n\n\nAbstract\nGiven a finite subgroup of SL3\, the c
orresponding quotient singularity has a natural non-commutative crepant re
solution\, the skew group algebra. By the result of Ginzburg\, this crepan
t resolution is Morita equivalent to the Jacobian algebra of the McKay qui
ver equipped with a canonical potential. We will discuss refined DT invari
ants of such Jacobian algebras for the cases of finite subgroups of SL2 an
d SO3\, where the quotient singularity admits a small crepant resolution a
nd the McKay quiver is symmetric.\n\nhttps://us02web.zoom.us/j/87160036709
\nMeeting ID: 871 6003 6709\nPasscode: LAGOON\n
LOCATION:https://researchseminars.org/talk/LAGOON/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yilin Wu (Université Paris Diderot - Paris 7\, France)
DTSTART:20210624T110000Z
DTEND:20210624T120000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/46
DESCRIPTION:Title:
Derived equivalences from mutations of ice quivers with potential\nby
Yilin Wu (Université Paris Diderot - Paris 7\, France) as part of Longitu
dinal Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nIn
2009\, Keller and Yang categorified quiver mutation by interpreting it in
terms of equivalences between derived categories. Their approach was base
d on Ginzburg’s Calabi--Yau algebras and on Derksen--Weyman--Zelevinsky
’s mutation of quivers with potential. Recently\, Matthew Pressland has
generalized mutation of quivers with potential to that of ice quivers with
potential. We will explain how his rule yields derived equivalences betwe
en the associated relative Ginzburg algebras\, which are special cases of
Yeung’s deformed relative Calabi–Yau completions arising in the theory
of relative Calabi--Yau structures due to Toën and Brav--Dyckerhoff. We
will illustrate our results on examples arising in the work of Baur--King-
-Marsh on dimer models and cluster categories of Grassmannians. If time pe
rmits\, we will also sketch a categorification of mutation at frozen verti
ces as it appears in recent work of Fraser--Sherman-Bennett on positroid c
luster structures.\n\nMeeting Link\nThursday\, 12:00 - 13:00 (BST\, UK Ti
me)\nhttps://us02web.zoom.us/j/87160036709?pwd=aGtBdkx4VDFuY0l2UlkzRFdiYUF
3dz09 \nMeeting ID: 871 6003 6709\nPasscode: LAGOON\n
LOCATION:https://researchseminars.org/talk/LAGOON/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Pauksztello (Lancaster University\, UK)
DTSTART:20210617T110000Z
DTEND:20210617T120000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/47
DESCRIPTION:Title:
Functorially finite hearts\, simple-minded systems and negative cluster ca
tegories\nby David Pauksztello (Lancaster University\, UK) as part of
Longitudinal Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstra
ct\nSimple-minded systems (SMSs) were introduced by Koenig-Liu as an abstr
action of nonprojective simple modules in stable module categories: the id
ea was to use SMSs as a way to get around the lack of projective generator
s to help develop a Morita theory for stable module categories. Recent dev
elopments have shown that SMSs in negative Calabi-Yau categories admit mut
ation theories and combinatorics that are highly suggestive of cluster-til
ting theory. In this talk\, we explain one such development: that negative
Calabi-Yau orbit categories of bounded derived categories of acyclic quiv
ers serve as categorical models of positive Fuss-Catalan combinatorics and
one can think of SMSs as negative cluster-tilting objects. Along the way
\, we will make use of the rather surprising observation that in a triangu
lated category of finite homological dimension\, functorial finiteness of
the heart of a t-structure is related to the property of the heart having
enough injectives and enough projectives. This is surprising because it sa
ys that some feature of how a heart behaves within an ambient triangulated
category can be detected intrinsically in the heart. This talk is based o
n joint work with Raquel Coelho Simoes and David Ploog.\n
LOCATION:https://researchseminars.org/talk/LAGOON/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pedro Tamaroff (MPIMiS\, Leipzig\, Germany)
DTSTART:20211007T110000Z
DTEND:20211007T120000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/48
DESCRIPTION:Title:
Minimal models for monomial algebras\nby Pedro Tamaroff (MPIMiS\, Leip
zig\, Germany) as part of Longitudinal Algebra and Geometry Open ONline Se
minar (LAGOON)\n\n\nAbstract\nWe will explain how to obtain the minimal mo
del of a monomial associative algebra A\, as in [1]. This multiplicative r
esolution has for generators the Anick chains of A\, and as a differential
a combinatorial `cutting' operation that splits such chains into `smaller
' ones. Along with the formalism of Anick chains\, our results make use of
the algebraic discrete Morse theory of Jöllenbeck--Welker and Sköldberg
\, and the general theory of A_infty-(co)algebras. We aim to also mention
certain open questions and conjectures that emerged from [1] and related w
ork [2] with Dotsenko and Gélinas\, and how one could begin elucidating s
imilar results for other algebraic structures\, where it is known the beha
viour of the minimal model is already pathological. \n\n[1] Minimal models
for monomial algebras\, Homology\, Homotopy and Applications Volume 23 (2
021) no. 1\, pp. 341 – 366. (arXiv:1804.01435)\n\n[2] Finite generation
for Hochschild cohomology of Gorenstein monomial algebras\, preprint arXiv
:1909.00487\n
LOCATION:https://researchseminars.org/talk/LAGOON/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shunsuke Kano (Tohoku University\, Japan)
DTSTART:20211014T110000Z
DTEND:20211014T120000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/49
DESCRIPTION:Title:
Categorical dynamical systems arising from sign-stable mutation loops\
nby Shunsuke Kano (Tohoku University\, Japan) as part of Longitudinal Alge
bra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nA pair formed
by a triangulated category and an autoequivalence is called a categorical
dynamical system. Its complexity is measured by the so-called categorical
entropy. In this talk\, I will present a computation of the categorical e
ntropies of categorical dynamical systems obtained by lifting a sign-stabl
e mutation loop of a quiver to an autoequivalence of the derived category
of the corresponding Ginzburg dg algebra. The notion of sign-stability is
introduced as ananalogy of the pseudo-Anosov property of mapping classes o
f surfaces. If time permits\, we will discuss the pseudo-Anosovness of the
autoequivalences constructed.\n
LOCATION:https://researchseminars.org/talk/LAGOON/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiao-Wu Chen (USTC Hefei\, China)
DTSTART:20211021T110000Z
DTEND:20211021T120000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/50
DESCRIPTION:Title:
The dg Leavitt path algebra\, singular Yonda category and singularity cate
gory\nby Xiao-Wu Chen (USTC Hefei\, China) as part of Longitudinal Alg
ebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nWe prove tha
t\, for any finite dimensional algebra given by a quiver with relations\,
its dg singularity category is quasi-equivalent to the perfect dg derived
category of the dg Leavitt path algebra of its radical quiver. This result
might be viewed as a deformation of the known description of the dg singu
larity category of a radical-square-zero algebra in terms of a Leavitt pat
h algebra. The main ingredient is a new dg enhancement of the singularity
category\, namely the singular Yoneda dg category\, which is obtained by
a new strict dg localization inverting a natural transformation. This is j
oint with Zhengfang Wang.\n
LOCATION:https://researchseminars.org/talk/LAGOON/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amnon Neeman (Mathematical Sciences Institute\, ANU Canberra\, Aus
tralia)
DTSTART:20211028T110000Z
DTEND:20211028T120000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/51
DESCRIPTION:Title:
Finite approximations as a tool for studying triangulated categories\n
by Amnon Neeman (Mathematical Sciences Institute\, ANU Canberra\, Australi
a) as part of Longitudinal Algebra and Geometry Open ONline Seminar (LAGOO
N)\n\n\nAbstract\nA metric on a category assigns lengths to morphisms\, wi
th the triangle inequality holding. This notion goes back to a 1974 articl
e by Lawvere. We'll begin with a quick review of some basic constructions\
, like forming the Cauchy completion of a category with respect to a metri
c.And then will begin a string of surprising new results. It turns out tha
t\, in a triangulated category with a metric\, there is a reasonable notio
n of Fourier series\, and an approximable triangulated category can be tho
ught of as a category where many objects are the limits of their Fourier e
xpansions. And then come two types of theorems: (1) theorems providing exa
mples\, meaning showing that some category you might naturally want to loo
k at is approximable\, and (2) general structure theorems about approximab
le triangulated categories. And what makes it all interesting is (3) appli
cations. These turn out to include the proof of a conjecture by Bondal and
Van den Bergh\, a major generalization of a theorem of Rouquier's\, and a
short\, sweet proof of Serre's GAGA theorem.\n\nhttps://icms-org-uk.zoom.
us/j/81601767022?pwd=dDZwV1dEeW1STUZkOTUwTlNiVmZodz09\n\nMeeting ID: 816 0
176 7022\nPasscode: LAGOON\n
LOCATION:https://researchseminars.org/talk/LAGOON/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bruno Vallette (Université Sorbonne-Paris Nord\, France)
DTSTART:20211111T120000Z
DTEND:20211111T130000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/52
DESCRIPTION:Title:
Deformation theory of Cohomological Field Theories\nby Bruno Vallette
(Université Sorbonne-Paris Nord\, France) as part of Longitudinal Algebra
and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nIn this talk\, I
will develop the deformation theory of Cohomological Field Theories (CohF
Ts)\, that is algebras over the moduli spaces of stable curves with marked
points. This will lead to two new natural extensions of the notion of a C
ohFT: homotopical (necessary to structure chain-level Gromov--Witten invar
iants) and quantum (with examples found in the works of Buryak--Rossi on i
ntegrable systems). I will introduce a new version of Kontsevich's graph c
omplex\, enriched with tautological classes\, and I will use it to study a
new universal deformation group which acts naturally on the moduli spaces
of quantum homotopy CohFTs. This group is shown to contain both the prou
nipotent Grothendieck--Teichmüller group and the Givental group. (Joint w
ork with Vladimir Dotsenko\, Sergey Shadrin\, Arkady Vaintrob available at
arxiv.org/abs/2006.01649.)\n\nZoom link:\nhttps://icms-org-uk.zoom.us/j/8
1601767022?pwd=dDZwV1dEeW1STUZkOTUwTlNiVmZodz09\nMeeting ID: 816 0176 7022
\nPasscode: LAGOON\n
LOCATION:https://researchseminars.org/talk/LAGOON/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tobias Dyckerhoff (University of Hamburg\, Germany)
DTSTART:20211118T120000Z
DTEND:20211118T130000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/53
DESCRIPTION:Title:
Perverse sheaves and schobers on Riemann surfaces\nby Tobias Dyckerhof
f (University of Hamburg\, Germany) as part of Longitudinal Algebra and Ge
ometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nReporting on joint work
with M. Kapranov\, V. Schechtman\, and Y. Soibelman\, I will explain how
to describe the derived constructible category of a stratified Riemann sur
face as representations of the so-called paracyclic category of the surfac
e. This allows for geometric depictions of the various t-structures of int
erest (including the perverse one) and their interplay with Verdier dualit
y. We will then discuss how this leads to an approach to categorified perv
erse sheaves (perverse schobers) and provide some examples.\n\nZoom link:
https://icms-org-uk.zoom.us/j/81601767022?pwd=dDZwV1dEeW1STUZkOTUwTlNiVmZo
dz09 Meeting ID: 816 0176 7022 Passcode: LAGOON\n
LOCATION:https://researchseminars.org/talk/LAGOON/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Véronique Bazier-Matte (University of Connecticut\, USA)
DTSTART:20211104T120000Z
DTEND:20211104T130000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/54
DESCRIPTION:Title:
Triangulations of the Möbius strip and its connections with quasi-cluster
algebras\nby Véronique Bazier-Matte (University of Connecticut\, USA
) as part of Longitudinal Algebra and Geometry Open ONline Seminar (LAGOON
)\n\n\nAbstract\nIn 2015\, Dupont and Palesi defined quasi-cluster algebra
s\, which are cluster algebras arising from surfaces\, orientable or not.
They proved that the only quasi-cluster algebras with a finite number of c
lusters are the ones arising from the Möbius strip. In this talk\, we wil
l define quasi-cluster algebras\, list some of their properties and count
the number of clusters in a quasi-cluster algebra arising from a Möbius s
trip\, i.e. the number of triangulations of the Möbius strip.\n
LOCATION:https://researchseminars.org/talk/LAGOON/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marcy Robertson (University of Melbourne\, Australia)
DTSTART:20211125T120000Z
DTEND:20211125T130000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/55
DESCRIPTION:Title:
A topological characterization of the Kashiwara-Vergne groups\nby Marc
y Robertson (University of Melbourne\, Australia) as part of Longitudinal
Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nSolutions
to the Kashiwara--Vergne equations in noncommutative geometry are a "high
er dimensional" version of Drinfeld associators. In this talk we build on
work of Bar-Natan and Dancso and identify solutions of the Kashiwara--Verg
ne equations with isomorphisms of (completed) wheeled props of "welded tan
gled foams" -- a class of knotted surfaces in $\\mathbb{R}^4$. As a conseq
uence\, we identify the symmetry groups of the Kashiwara-Vergne equations
with automorphisms of our (completed) wheeled props. This talk is aimed a
t a general audience and I will not assume familiarity with the Kashiwara-
Vergne equations\, Drinfeld associators or wheeled props. Includes joint w
ork with Z. Dancso and I. Halacheva.\n\nZoom link: https://icms-org-uk.zoo
m.us/j/81601767022?pwd=dDZwV1dEeW1STUZkOTUwTlNiVmZodz09 Meeting ID: 816 01
76 7022 Passcode: LAGOON\n
LOCATION:https://researchseminars.org/talk/LAGOON/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeremy Brightbill (UC Santa Barbara\, USA)
DTSTART:20211209T160000Z
DTEND:20211209T170000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/56
DESCRIPTION:Title:
Higher simple-minded systems in negative Calabi-Yau categories.\nby Je
remy Brightbill (UC Santa Barbara\, USA) as part of Longitudinal Algebra a
nd Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nHigher simple-mind
ed systems are collections of objects in a negative Calabi-Yau category wh
ose behavior mimics that of simple modules. Under certain hypotheses the
collection of all simple-minded systems admits a theory of mutations. In
this talk\, we shall discuss how to construct many examples of negative Ca
labi-Yau categories using the so-called "dg-stable category". For a concre
te example\, we consider the dg-stable category of a negatively-graded Bra
uer tree algebra. Using a combinatorial model\, we classify the simple-mi
nded systems of this category and describe its mutation theory.\n
LOCATION:https://researchseminars.org/talk/LAGOON/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alberto Canonaco (University of Pavia\, Italy)
DTSTART:20220203T120000Z
DTEND:20220203T130000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/57
DESCRIPTION:Title:
Dg enhancements of triangulated categories and their uniqueness\nby Al
berto Canonaco (University of Pavia\, Italy) as part of Longitudinal Algeb
ra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nIt is well kno
wn that often some intrinsic defects of triangulated categories can be avo
ided by enhancing them to suitable higher categorical structures\, like (p
retriangulated) dg categories. However\, despite significant progress made
in recent years\, the relation between the triangulated and the dg level
is not yet completely clear\, and some foundational questions have receive
d only partial answers so far. After presenting the general picture\, I wi
ll report on a joint work (partly in progress) with Neeman and Stellari ab
out uniqueness of dg enhancements.\n\nMeeting Link\nhttps://icms-org-uk.zo
om.us/j/82901356928?pwd=NmNReXc5U1M0MUFScEVLMEtyaU56dz09 \nMeeting ID: 829
0135 6928\nPasscode: LAGOON22\n
LOCATION:https://researchseminars.org/talk/LAGOON/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nick Sheridan (University of Edinburgh\, UK)
DTSTART:20220310T120000Z
DTEND:20220310T130000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/58
DESCRIPTION:Title:
The Gamma and SYZ conjectures\nby Nick Sheridan (University of Edinbur
gh\, UK) as part of Longitudinal Algebra and Geometry Open ONline Seminar
(LAGOON)\n\n\nAbstract\nI will give some background on the Gamma Conjectur
e\, which says that mirror symmetry does *not* respect integral cycles: ra
ther\, the integral cycles on a complex manifold correspond to integral cy
cles on the symplectic mirror\, multiplied by a certain transcendental cha
racteristic class called the Gamma class. In the second part of the talk I
will explain a new geometric approach to the Gamma Conjecture\, which is
based on the SYZ viewpoint on mirror symmetry. We find that the appearance
of zeta(k) in the asymptotics of period integrals arises from the codimen
sion-k singular locus of the SYZ fibration. This is based on joint work wi
th Abouzaid\, Ganatra\, and Iritani.\n\nMeeting Link\nhttps://icms-org-uk.
zoom.us/j/82901356928?pwd=NmNReXc5U1M0MUFScEVLMEtyaU56dz09 \nMeeting ID: 8
29 0135 6928\nPasscode: LAGOON22\n
LOCATION:https://researchseminars.org/talk/LAGOON/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matt Pressland (University of Glasgow\, UK)
DTSTART:20220210T120000Z
DTEND:20220210T130000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/59
DESCRIPTION:Title:
Grassmannian twists categorified\nby Matt Pressland (University of Gla
sgow\, UK) as part of Longitudinal Algebra and Geometry Open ONline Semina
r (LAGOON)\n\n\nAbstract\nThe Grassmannian of k-dimensional subspaces of a
n n-dimensional space carries a birational automorphism called the twist (
or sometimes the Donaldson–Thomas transformation)\, defined by Berenstei
n–Fomin–Zelevinsky and Marsh–Scott. This automorphism respects the c
luster algebra structure on the coordinate ring\, being a quasi-cluster au
tomorphism in the sense of Fraser. By work of Muller–Speyer\, similar re
sults hold for positroid strata in the Grassmannian. The cluster algebras
in this picture have been categorified\, by Jensen–King–Su in the case
of the full Grassmannian\, and by myself for more general (connected) pos
itroid varieties. In this talk I will report on joint work with İlke Çan
akçı and Alastair King\, in which we describe the twist in terms of thes
e categorifications. The key ingredient is provided by perfect matching mo
dules\, certain combinatorially defined representations for a quiver 'with
faces'\, and I will also explain this construction.\n
LOCATION:https://researchseminars.org/talk/LAGOON/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergey Mozgovoy (Trinity College Dublin\, Ireland)
DTSTART:20220217T120000Z
DTEND:20220217T130000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/60
DESCRIPTION:Title:
Wall-crossing structures arising from surfaces\nby Sergey Mozgovoy (Tr
inity College Dublin\, Ireland) as part of Longitudinal Algebra and Geomet
ry Open ONline Seminar (LAGOON)\n\n\nAbstract\nFamilies of Bridgeland stab
ility conditions induce families of stability data (DT invariants)\, wall-
crossing structures and scattering diagrams on the motivic Hall algebra. T
hese structures can be transferred to the quantum torus if the stability c
onditions of the family have global dimension at most 2. I will discuss ge
ometric stability conditions on a surface with nef anticanonical bundle. T
hese stability conditions have global dimension 2\, hence induce a family
of stability data. I will also discuss the relationship of this family to
the family of stability data associated to a quiver with potential\, with
an emphasis on the projective plane.\n\nhttps://icms-org-uk.zoom.us/j/8290
1356928?pwd=NmNReXc5U1M0MUFScEVLMEtyaU56dz09 \nMeeting ID: 829 0135 6928\n
Passcode: LAGOON22\n
LOCATION:https://researchseminars.org/talk/LAGOON/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sira Gratz (University of Glasgow\, UK)
DTSTART:20220224T120000Z
DTEND:20220224T130000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/61
DESCRIPTION:Title:
When Aisles Meet\nby Sira Gratz (University of Glasgow\, UK) as part o
f Longitudinal Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbst
ract\nDiscrete cluster categories of type A are an exciting playing field
on which to learn about infinite rank cluster combinatorics: On the one ha
nd\, they combinatorially behave\, in many ways\, in a familiar finite typ
e A way. On the other hand\, they exhibit new phenomena for which finite t
ype A is “too small”. One such phenomenon is the existence of t-struct
ures. In this talk\, we describe the classification of t-structures in dis
crete cluster categories of type A via decorated non-crossing partitions a
nd explain how they form a lattice under inclusion of aisles – an unusua
l occurrence for t-structures in a triangulated category. This classificat
ion of t-structures can inform our understanding of posets of t-structures
more generally and help to tackle completions of triangulated categories
from a combinatorial perspective. This talk is based on joint work with Al
exandra Zvonareva\, and with Thorsten Holm and Peter Jørgensen.\n
LOCATION:https://researchseminars.org/talk/LAGOON/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eleonore Faber (University of Leeds\, UK)
DTSTART:20220303T120000Z
DTEND:20220303T130000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/62
DESCRIPTION:Title:
Matrix factorizations of some discriminants\nby Eleonore Faber (Univer
sity of Leeds\, UK) as part of Longitudinal Algebra and Geometry Open ONli
ne Seminar (LAGOON)\n\n\nAbstract\nIn this talk\, we consider discriminant
s of complex reflection groups. We identify certain matrix factorizations\
, whose corresponding Cohen-Macaulay modules give a noncommutative resolut
ion of the discriminant. We will in particular consider the family of pseu
do-reflection groups G(r\,p\,n)\, for which one can explicitly determine t
hese matrix factorizations that are indexed by partitions\, using higher S
pecht polynomials (work in progress with Colin Ingalls\, Simon May\, and M
arco Talarico).\n
LOCATION:https://researchseminars.org/talk/LAGOON/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Safronov (University of Edinburgh\, UK)
DTSTART:20220407T110000Z
DTEND:20220407T120000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/64
DESCRIPTION:Title:
Euler structures and noncommutative volume forms\nby Pavel Safronov (U
niversity of Edinburgh\, UK) as part of Longitudinal Algebra and Geometry
Open ONline Seminar (LAGOON)\n\n\nAbstract\nCalabi-Yau structures on dg ca
tegories provide a noncommutative analog of symplectic structures. In this
talk I will introduce a noncommutative analog of volume forms called nonc
ommutative Euler structures. I will give some examples of these and relate
noncommutative Euler structures to string topology-type operations. An ap
plication of these ideas is the proof that the Goresky--Hingston string co
product on the homology of free loop space is not homotopy invariant. If I
have time\, I will also discuss how Euler structures give rise to volume
forms on derived mapping stacks. This is a report on work in progress join
t with Florian Naef.\n\nZOOM Meeting Link\nhttps://icms-org-uk.zoom.us/j/8
2901356928?pwd=NmNReXc5U1M0MUFScEVLMEtyaU56dz09 \nPassword: LAGOON22\n
LOCATION:https://researchseminars.org/talk/LAGOON/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Labardini-Fragoso (UNAM Mexico City\, Mexico)
DTSTART:20220317T120000Z
DTEND:20220317T130000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/65
DESCRIPTION:Title:
Gentle algebras arising from surfaces with orbifold points\nby Daniel
Labardini-Fragoso (UNAM Mexico City\, Mexico) as part of Longitudinal Alge
bra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nSome years ag
o\, Diego Velasco and I associated a gentle algebra to each triangulation
of a polygon with one orbifold point of order three\, and showed that the
\\tau-tilting combinatorics of this gentle algebra coincides with the comb
inatorics of flips of triangulations. Moreover\, we showed that whenever o
ne mutates support \\tau-tilting pairs\, the corresponding Caldero-Chapoto
n functions obey a generalized cluster exchange formula\, which means that
the Caldero-Chapoton algebra is isomorphic to a generalized cluster algeb
ra of Chekhov-Shapiro. Generalizing the aforementioned work\, in ongoing c
ollaboration Lang Mou and I associate a gentle algebra to each triangulati
on of any unpunctured surface with orbifold points of order three. We are
able to define generalized reflection functors and DWZ-like mutations of r
epresentations. This is somewhat surprising\, since the quivers we conside
r are allowed to have loops\, and the matrix-mutation classes of their ske
w-symmetrizable matrices may fail to have acyclic representatives.\n\nMeet
ing Link\nhttps://icms-org-uk.zoom.us/j/82901356928?pwd=NmNReXc5U1M0MUFScE
VLMEtyaU56dz09 \nMeeting ID: 829 0135 6928\nPasscode: LAGOON22\n
LOCATION:https://researchseminars.org/talk/LAGOON/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Asilata Bapat (Mathematical Sciences Institute\, ANU Canberra\, Au
stralia)
DTSTART:20220331T110000Z
DTEND:20220331T120000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/66
DESCRIPTION:Title:
The sphere of spherical objects\nby Asilata Bapat (Mathematical Scienc
es Institute\, ANU Canberra\, Australia) as part of Longitudinal Algebra a
nd Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nConsider the 2-Cal
abi--Yau triangulated category arising from the zigzag algebra of the An q
uiver. The braid group acts on this category by twists in spherical object
s. Given a Bridgeland stability condition\, we describe how to realise the
spherical objects as a dense subset of a piecewise-linear manifold. This
manifold is canonically associated to the category\, and the braid group a
cts on it piecewise-linearly. We also describe how the manifold transforms
under wall-crossings of the stability condition. The talk is based on joi
nt work with Anand Deopurkar and Anthony M. Licata.\n\nZOOM Meeting Link\n
https://icms-org-uk.zoom.us/j/82901356928?pwd=NmNReXc5U1M0MUFScEVLMEtyaU56
dz09 \nPassword: LAGOON22\n
LOCATION:https://researchseminars.org/talk/LAGOON/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fernando Muro (Universidad de Sevilla\, Spain)
DTSTART:20220324T120000Z
DTEND:20220324T130000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/67
DESCRIPTION:Title:
Enhanced n-angulated categories\nby Fernando Muro (Universidad de Sevi
lla\, Spain) as part of Longitudinal Algebra and Geometry Open ONline Semi
nar (LAGOON)\n\n\nAbstract\nThese categories were introduced by Geiss\, Ke
ller\, and Oppermann in order to encode the behaviour of n-cluster tilting
subcategories of triangulated categories. In this talk I will define diff
erential graded enhancements for these categories\, analogous to those of
Bondal and Kapranov for triangulated categories. I will present an existen
ce and uniqueness theorem for n-angulated enhancements which holds\, for i
nstance\, for the additivization of an n-cluster tilting object. As a coro
llary\, I will deduce that a triangulated category with a (higher) cluster
tilting object has a unique triangulated enhancement. This is joint work
with Gustavo Jasso(Lund).\n\nMeeting Link\nhttps://icms-org-uk.zoom.us/j/8
2901356928?pwd=NmNReXc5U1M0MUFScEVLMEtyaU56dz09 \nMeeting ID: 829 0135 692
8\nPasscode: LAGOON22\n
LOCATION:https://researchseminars.org/talk/LAGOON/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chrysostomos Psaroudakis (Aristotle University of Thessaloniki\, G
reece)
DTSTART:20220505T110000Z
DTEND:20220505T120000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/68
DESCRIPTION:Title:
Homological invariants of the arrow removal operation\nby Chrysostomos
Psaroudakis (Aristotle University of Thessaloniki\, Greece) as part of Lo
ngitudinal Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract
\nSeveral homological conjectures in representation theory are related wit
h specific problems concerning the homological behaviour and the structure
theory of finite dimensional algebras. In joint work with Edward Green an
d Oyvind Solberg we developed new reduction techniques (vertex removal ope
ration and arrow removal operation) on quotients of path algebras for test
ing the finiteness of the finitistic dimension. In this talk\, we will rev
iew these operations and we will focus on the arrow removal operation. In
particular\, we will show that Gorensteinness\, singularity categories and
the finite generation condition Fg for the Hochschild cohomology are inva
riants under the arrow removal operation for a finite dimensional algebra.
This is joint work with Karin Erdmann and Oyvind Solberg.\n\nMeeting Link
\nhttps://uni-koeln.zoom.us/j/91875528987?pwd=TjNZV1lNdVJNOWUrR2xNalRuQWk3
dz09\n\nMeeting ID: 918 7552 8987\nPassword: LAGOON2022\n
LOCATION:https://researchseminars.org/talk/LAGOON/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Severin Barmeier (University of Cologne\, Germany)
DTSTART:20220512T110000Z
DTEND:20220512T120000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/69
DESCRIPTION:Title:
Deformations of categories of coherent sheaves via quivers with relations<
/a>\nby Severin Barmeier (University of Cologne\, Germany) as part of Long
itudinal Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\n
In this talk I will explain how to use the deformation theory of path alge
bras of quivers with relations to give a concrete and complete description
of the deformation theory of the Abelian category coh(X) of coherent shea
ves on any separated Noetherian scheme X. Deformations of coh(X) are a gen
erous source of interesting examples of noncommutative schemes arising as
an amalgamation of classical deformations of X\, quantizations of Poisson
structures on X and twists of the structure sheaf. Lowen and Van den Bergh
showed that the deformation theory of coh(X) is equivalent to the deforma
tion theory of a certain associative algebra\, namely the "diagram algebra
" associated to the restriction of the structure sheaf to any affine open
cover. When X is Noetherian\, this associative algebra and its deformation
s can be described concretely via a finite quiver with relations. This tal
k is based on arXiv:2107.07490 and arXiv:2002.10001 both joint with Zhengf
ang Wang.\n\nMeeting Link\nhttps://uni-koeln.zoom.us/j/91875528987?pwd=TjN
ZV1lNdVJNOWUrR2xNalRuQWk3dz09\n\nMeeting ID: 918 7552 8987\nPassword: LAGO
ON2022\n
LOCATION:https://researchseminars.org/talk/LAGOON/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Imma Gálvez Carrillo (UPC Barcelona\, Spain)
DTSTART:20220519T110000Z
DTEND:20220519T120000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/70
DESCRIPTION:Title:
Combinatorial bialgebras and decomposition spaces\nby Imma Gálvez Car
rillo (UPC Barcelona\, Spain) as part of Longitudinal Algebra and Geometry
Open ONline Seminar (LAGOON)\n\n\nAbstract\nDecomposition spaces (introdu
ced independently by Dyckerhoff and Kapranov under the name 2-Segal spaces
) are simplicial spaces with a certain exactness property that models coas
sociativity in the same way that usual Segal spaces capture associative co
mposition. I will talk about joint work with Joachim Kock and Andrew Tonks
on the application of decomposition spaces in "categorified" or "objectiv
e" algebra. As motivating examples\, I will discuss decomposition spaces
for many classical combinatorial Hopf algebras\, such as those of symmetri
c functions.\n\nMeeting Link uni-koeln.zoom.us/j/91875528987?pwd=TjNZV1lNd
VJNOWUrR2xNalRuQWk3dz09\n\nMeeting ID: 918 7552 8987 Password: LAGOON2022\
n
LOCATION:https://researchseminars.org/talk/LAGOON/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shengyuan Huang (University of Birmingham\, UK)
DTSTART:20220526T110000Z
DTEND:20220526T120000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/72
DESCRIPTION:Title:
The HKR isomorphism and Hochschild cohomology\nby Shengyuan Huang (Uni
versity of Birmingham\, UK) as part of Longitudinal Algebra and Geometry O
pen ONline Seminar (LAGOON)\n\n\nAbstract\nFor a smooth scheme X\, the HKR
isomorphism identifies the Hochschild cohomology of X with the cohomology
of polyvector fields as vector spaces. This isomorphism is known as the c
lassical HKR isomorphism for the diagonal embedding: X in X\\timesX. We di
scuss the generalization of the HKR isomorphism to arbitrary closed embedd
ings and the corresponding functoriality property. Then we recall the gene
ralization of the HKR isomorphism to orbifolds. We apply all the results a
bove to study the product structure of orbifold Hochschild cohomology.\n\n
Meeting Link\nhttps://uni-koeln.zoom.us/j/91875528987?pwd=TjNZV1lNdVJNOWUr
R2xNalRuQWk3dz09\n\nMeeting ID: 918 7552 8987\nPassword: LAGOON2022\n
LOCATION:https://researchseminars.org/talk/LAGOON/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jongmyeong Kim (IBS Center for Geometry and Physics\, South Korea)
DTSTART:20220623T110000Z
DTEND:20220623T120000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/73
DESCRIPTION:Title:
Categorical entropy\, (co-)t-structures and ST-triples\nby Jongmyeong
Kim (IBS Center for Geometry and Physics\, South Korea) as part of Longitu
dinal Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nIn
this talk\, we study a dynamical property of an exact endofunctor F of a t
riangulated category D using the notion of categorical entropy introduced
by Dimitrov–Haiden–Katzarkov–Kontsevich. In particular\, we consider
the following question: Given full triangulated subcategories A and B of
D such that F restricts to A and B\, how the categorical entropies of the
restricted functors are related? To answer this question\, we will introdu
ce new entropy-type invariants using bounded (co-)t-structures and see the
ir basic properties. We then apply these results to answer our question fo
r the case where our A and B form an ST-triple in which case A has a bound
ed t-structure and B has a bounded co-t-structure which are\, in some sens
e\, dual to each other.\n\nMeeting Link\nhttps://uni-koeln.zoom.us/j/91875
528987?pwd=TjNZV1lNdVJNOWUrR2xNalRuQWk3dz09\n\nMeeting ID: 918 7552 8987\n
Password: LAGOON2022\n
LOCATION:https://researchseminars.org/talk/LAGOON/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Gorsky (Laboratoire de Mathématiques de Versailles\, Fran
ce)
DTSTART:20220707T110000Z
DTEND:20220707T120000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/74
DESCRIPTION:Title:
Cluster structures on braid varieties\nby Mikhail Gorsky (Laboratoire
de Mathématiques de Versailles\, France) as part of Longitudinal Algebra
and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nA braid variety i
s a certain affine algebraic variety associated with a \nsimply-connected
simple algebraic group G and a positive braid of the \ncorresponding type.
These varieties generalise open Richardson varieties \nand appear in the
context of symplectic topology and in the study of \nlink invariants such
as HOMFLY-PT polynomials and Khovanov-Rozansky \nhomology.\nIn this talk\,
I will give a proof of the existence of cluster \nA-structures and cluste
r Poisson structures on any braid variety. I will \nsketch an explicit con
struction of cluster seeds involving the \ndiagrammatic calculus of weaves
and a tropicalization of Lustig's \ncoordinates. These cluster algebras a
re local acyclic and equal their \nupper cluster algebras. The main result
also proves the conjecture of B. \nLeclerc on the existence of cluster al
gebra structures on the coordinate \nrings of open Richardson varieties in
simply laced types. The talk is \nbased on joint work with Roger Casals\,
Eugene Gorsky\, Ian Le\, Linhui \nShen\, and José Simental.\n\nMeeting L
ink\nhttps://uni-koeln.zoom.us/j/91875528987?pwd=TjNZV1lNdVJNOWUrR2xNalRuQ
Wk3dz09\n\nMeeting ID: 918 7552 8987\nPassword: LAGOON2022\n
LOCATION:https://researchseminars.org/talk/LAGOON/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andy Tonks (Universidad de Málaga\, Spain)
DTSTART:20220630T110000Z
DTEND:20220630T120000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/75
DESCRIPTION:Title:
On some generalisations of Baues-Wirsching cohomology\nby Andy Tonks (
Universidad de Málaga\, Spain) as part of Longitudinal Algebra and Geomet
ry Open ONline Seminar (LAGOON)\n\n\nAbstract\nI will discuss the (co)homo
logy of categories of Baues-Wirsching\, and how it is related to several o
ther (co)homologies\, new and old: of decomposition spaces\, of 2-categori
es (and higher) and of simplicial sets. Joint work and work in progress wi
th I Gálvez-Carrillo\, F Neumann and S Paoli.\n\nMeeting Link\nhttps://un
i-koeln.zoom.us/j/91875528987?pwd=TjNZV1lNdVJNOWUrR2xNalRuQWk3dz09\n\nMeet
ing ID: 918 7552 8987\nPassword: LAGOON2022\n
LOCATION:https://researchseminars.org/talk/LAGOON/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolò Sibilla (SISSA\, Italy)
DTSTART:20221013T110000Z
DTEND:20221013T120000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/76
DESCRIPTION:Title:
Fukaya category of surfaces and pants decomposition'\nby Nicolò Sibil
la (SISSA\, Italy) as part of Longitudinal Algebra and Geometry Open ONlin
e Seminar (LAGOON)\n\n\nAbstract\nIn this talk I will explain some results
joint with James Pascaleff on the Fukaya category of Riemann surfaces. I
will explain a local-to-global principle which allows us to reduce the cal
culation of the Fukaya category of surfaces of genus g greater than one to
the case of the pair-of-pants\, and which holds both in the punctured and
in the compact case. The starting point are the sheaf-theoretic methods w
hich are available in the exact setting\, and which I will review at the b
eginning of the talk. This result has several interesting consequences for
HMS and geometrization of objects in the Fukaya category. I will conclude
the talk hinting at more recent developments\, related to work of Max Jef
fs on the Fukaya category of singular surfaces\, and conjectures of Lekili
-Ueda. The talk is based on ArXiv 1604.06448\, 2103.03366 and 2208.03896.\
n\nMeeting Link\n\nhttps://uni-koeln.zoom.us/j/91875528987?pwd=TjNZV1lNdVJ
NOWUrR2xNalRuQWk3dz09\n\nMeeting ID: 918 7552 8987\nPassword: LAGOON2022\n
LOCATION:https://researchseminars.org/talk/LAGOON/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilaria Di Dedda (King's College London\, UK)
DTSTART:20221020T110000Z
DTEND:20221020T120000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/77
DESCRIPTION:Title:
A symplectic interpretation of Auslander correspondence\nby Ilaria Di
Dedda (King's College London\, UK) as part of Longitudinal Algebra and Geo
metry Open ONline Seminar (LAGOON)\n\n\nAbstract\nAuslander correspondence
establishes a bijection between the class of algebras of finite represent
ation type and the class of Auslander algebras\, with both families consid
ered up to Morita equivalence. This allows one to study the representation
theory of the former via the homological properties of the latter. The ai
m of this talk is to give a symplectic interpretation to this corresponden
ce when the algebra of finite representation type is the path algebra of t
he quiver of Dynkin type A_n. This result relies on a realisation of Ausla
nder algebras of type A as Fukaya-Seidel categories of a family of Lefsche
tz fibrations.\n\nhttps://uni-koeln.zoom.us/j/91875528987?pwd=TjNZV1lNdVJN
OWUrR2xNalRuQWk3dz09\n\nMeeting ID: 918 7552 8987\nPassword: LAGOON2022\n
LOCATION:https://researchseminars.org/talk/LAGOON/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anya Nordskova (UHasselt\, Belgium)
DTSTART:20221117T120000Z
DTEND:20221117T130000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/78
DESCRIPTION:Title:
Derived Picard groups of representation-finite symmetric algebras\nby
Anya Nordskova (UHasselt\, Belgium) as part of Longitudinal Algebra and Ge
ometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nI will talk about my wo
rk on computing the derived Picard groups of a particular class of symmetr
ic representation-finite algebras of type D. We obtain an explicit descrip
tion of these groups via generators and relations. In particular\, we prov
e that these groups are generated by spherical twists along a collection o
f 0-spherical objects\, the shift and\, roughly speaking\, outer automorph
isms of the algebras. One of the key ingredients in the proof is the faith
fulness of braid group actions by spherical twists along ADE configuration
s of 0-spherical objects. Another part of the strategy is based on the fac
t that symmetric representation-finite algebras are tilting-connected. To
apply this result we in particular develop a combinatorial-geometric model
for silting mutations in type D\, generalising the classical concepts of
Brauer trees and Kauer moves. I will also discuss possible directions in w
hich the result might be extended to a more general categorical context.\n
\nMeeting Link\n\nhttps://uni-koeln.zoom.us/j/91875528987?pwd=TjNZV1lNdVJN
OWUrR2xNalRuQWk3dz09\n\nMeeting ID: 918 7552 8987\nPassword: LAGOON2022\n
LOCATION:https://researchseminars.org/talk/LAGOON/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Brav (Higher School of Economics\, Moscow\, Russia)
DTSTART:20221124T120000Z
DTEND:20221124T130000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/79
DESCRIPTION:Title:
Poisson brackets and the string Lie algebra of a Calabi-Yau category\n
by Chris Brav (Higher School of Economics\, Moscow\, Russia) as part of Lo
ngitudinal Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract
\nGoldman defined a symplectic structure on the moduli space of local syst
ems on a closed oriented surface\, constructed a collection of natural Ham
iltonians on the moduli space by taking trace of monodromy around loops on
the surface\, and computed Poisson brackets among these Hamiltonians in t
erms of what is now called the Goldman bracket on free homotopy classes of
loops. Chas and Sullivan generalized the Goldman bracket to a string brac
ket on the degree-shifted equivariant homology of the free loop space of a
closed oriented manifold of any dimension\, but the compatibility with th
e corresponding shifted-symplectic geometry on the moduli space of local s
ystems remained mostly conjectural. We generalize these results of Goldman
and of Chas-Sullivan to higher dimensional ’non-commutative’ closed o
riented manifolds in the form of smooth Calabi-Yau categories. Our main re
sults are the description of a chain-level ’string Lie bracket’ on cyc
lic chains of a smooth Calabi-Yau category and the intertwining of this st
ring Lie bracket on cyclic chains with the shifted Poisson bracket on func
tions on the moduli space of objects in the category.\n\nMeeting Link\n\nh
ttps://uni-koeln.zoom.us/j/91875528987?pwd=TjNZV1lNdVJNOWUrR2xNalRuQWk3dz0
9\n\nMeeting ID: 918 7552 8987 Password: LAGOON2022\n
LOCATION:https://researchseminars.org/talk/LAGOON/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victoria Hoskins (Radboud University Nijmegen\, Netherlands)
DTSTART:20221110T120000Z
DTEND:20221110T130000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/80
DESCRIPTION:Title:
Motivic mirror symmetry for Higgs bundles\nby Victoria Hoskins (Radbou
d University Nijmegen\, Netherlands) as part of Longitudinal Algebra and G
eometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nModuli spaces of Higgs
bundles for Langlands dual groups are conjecturally related by a form of
mirror symmetry. For SL_n and PGL_n\, Hausel and Thaddeus conjectured a to
pological mirror symmetry given by an equality of (twisted orbifold) Hodge
numbers\, which was proven by Groechenig--Wyss--Ziegler and also Maulik--
Shen. We lift this to an isomorphism of Voevodsky motives\, and thus in pa
rticular an equality of (twisted orbifold) rational Chow groups. Our metho
d is based on Maulik and Shen's approach to the Hausel--Thaddeus conjectur
e\, as well as showing certain motives are abelian\, in order to use conse
rvativity of the Betti realisation on abelian motives. This is joint work
with Simon Pepin Lehalleur.\n\nMeeting Link\nhttps://uni-koeln.zoom.us/j/9
1875528987?pwd=TjNZV1lNdVJNOWUrR2xNalRuQWk3dz09\n\nMeeting ID: 918 7552 89
87\nPassword: LAGOON2022\n
LOCATION:https://researchseminars.org/talk/LAGOON/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Barbieri (University of Padova\, Italy)
DTSTART:20221201T120000Z
DTEND:20221201T130000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/81
DESCRIPTION:Title:
Categories associated with weighted marked surfaces and their stability ma
nifold\nby Anna Barbieri (University of Padova\, Italy) as part of Lon
gitudinal Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\
nIn a paper in 2015\, Bridgeland and Smith identified some moduli spaces o
f meormorphic quadratic differentials with simple zeroes on a Riemann surf
ace with some spaces of stability conditions on certain categories. This i
dentification passes through associating a quiver with potential and a Gin
zburg category to a triangulation of a marked bordered surface defined by
a quadratic differential. I will review this correspondence and discuss ho
w the picture changes when quadratic differentials with zeroes of arbitrar
y order are considered. This involves the study of Verdier quotients of Gi
nzburg categories and their t-structures. The talk is based on a joint wor
k with M.Moeller\, Y.Qiu\, and J.So.\n\nMeeting Link\n\nuni-koeln.zoom.us/
j/91875528987?pwd=TjNZV1lNdVJNOWUrR2xNalRuQWk3dz09\n\nMeeting ID: 918 7552
8987 Password: LAGOON2022\n
LOCATION:https://researchseminars.org/talk/LAGOON/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hanwool Bae (Seoul National University\, South Korea)
DTSTART:20221103T120000Z
DTEND:20221103T130000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/82
DESCRIPTION:Title:
Cluster categories from Fukaya categories\nby Hanwool Bae (Seoul Natio
nal University\, South Korea) as part of Longitudinal Algebra and Geometry
Open ONline Seminar (LAGOON)\n\n\nAbstract\nThe wrapped Fukaya category o
f the plumbing X of the cotangent bundles of spheres along a tree T is sho
wn to be quasi-equivalent to the dg category of dg modules over the Ginzbu
rg dg algebra associated to a quiver Q whose underlying graph is T. In th
is talk\, I will first discuss that the quotient of the wrapped Fukaya cat
egory W of X by its compact Fukaya category F is equivalent to the Amiot
–Guo–Keller cluster category associated to Q\, and a certain generator
L of W becomes a cluster-tilting object of W/F. Then using the minimal mo
del of the Ginzburg dg algebra computed by Hermes\, in the case the tree T
is given by a Dynkin diagram of type A\,D or E\, I will explain how to sh
ow that the endomorphism algebra of L in the quotient category W/F is isom
orphic to the path algebra of a certain quiver with relations. This talk i
s based on a joint work with Wonbo Jeong and Jongmyeong Kim.\n
LOCATION:https://researchseminars.org/talk/LAGOON/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiaofa Chen (Université Paris Cité\, France)
DTSTART:20221027T110000Z
DTEND:20221027T120000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/83
DESCRIPTION:Title:
On exact dg categories\nby Xiaofa Chen (Université Paris Cité\, Fran
ce) as part of Longitudinal Algebra and Geometry Open ONline Seminar (LAGO
ON)\n\n\nAbstract\nIn this talk\, we propose a framework of dg enhancement
s\, which we call exact dg categories\, for a certain class of extriangula
ted categories\, which we call algebraic. The motivation comes from typica
l examples like Yilin Wu’s Higgs categories and Haibo Jin’s categories
of dg Cohen-Macaulay modules. We will present several results concerning
the dg nerve\, the dg derived category\, tensor products and functor dg ca
tegories with exact target. We will conclude by computing the lattice of a
ll exact structures on dg categories satisfying certain strong finiteness
conditions.\n\nMeeting Link\n\nhttps://uni-koeln.zoom.us/j/91875528987?pwd
=TjNZV1lNdVJNOWUrR2xNalRuQWk3dz09\n\nMeeting ID: 918 7552 8987\nPassword:
LAGOON2022\n
LOCATION:https://researchseminars.org/talk/LAGOON/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jasper van de Kreeke (KDV Amsterdam\, Netherlands)
DTSTART:20221215T120000Z
DTEND:20221215T130000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/84
DESCRIPTION:Title:
Deformation theory of gentle algebras\nby Jasper van de Kreeke (KDV Am
sterdam\, Netherlands) as part of Longitudinal Algebra and Geometry Open O
Nline Seminar (LAGOON)\n\n\nAbstract\nGentle algebras are discrete models
for Fukaya categories of punctured surfaces. How to deform them? We will s
tart with one specific deformation\, motivated by Seidel's relative Fukaya
categories. We will classify the entire deformation theory of gentle alge
bras and prove that their Hochschild DGLA is formal. We will comment on de
formed mirror symmetry and related work of Barmeier-Schroll-Wang. On a tec
hnical level\, this talk teaches us A∞-deformations\, L∞-algebras\, Ka
deishvili constructions and Koszul duality. This work is part of my PhD th
esis supervised by Raf Bocklandt.\n
LOCATION:https://researchseminars.org/talk/LAGOON/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhengfang Wang (University of Stuttgart\, Germany)
DTSTART:20221208T120000Z
DTEND:20221208T130000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/85
DESCRIPTION:Title:
A-infinity deformations of extended Khovanov arc algebras and Stroppel's c
onjecture\nby Zhengfang Wang (University of Stuttgart\, Germany) as pa
rt of Longitudinal Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\n
Abstract\nExtended Khovanov arc algebras K_m^n are introduced by Stroppel
when studying parabolic category O. They naturally appear in different sub
jects (including representation theory and symplectic geometry) and have m
any nice algebraic properties\, for example they are Koszul and quasi-here
ditary. In this talk\, we will first give the diagrammatic description of
K_m^n due to Brundan-Stroppel. Then\, by writing K_m^n as the path algebra
of a quiver with relations\, we show that the Koszul dual of K_m^n admits
a natural reduction system satisfying diamond condition\, by relating the
number of the associated "irreducible paths" to the Kazhdan-Lusztig polyn
omials. We also explain how to apply this reduction system to study Stropp
el's conjecture. As a result\, we show that K_m^n is not intrinsically for
mal for m\, n>1. This is joint work with S. Barmeier.\n\nMeeting Link\n\nh
ttps://uni-koeln.zoom.us/j/91875528987?pwd=TjNZV1lNdVJNOWUrR2xNalRuQWk3dz0
9\n\nMeeting ID: 918 7552 8987\nPassword: LAGOON2022\n
LOCATION:https://researchseminars.org/talk/LAGOON/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Naoki Koseki (University of Liverpool\, UK)
DTSTART:20230927T120000Z
DTEND:20230927T130000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/86
DESCRIPTION:Title:
Symmetric products of dg categories and semi-orthogonal decompositions
\nby Naoki Koseki (University of Liverpool\, UK) as part of Longitudinal A
lgebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nThe notion
of symmetric products of a dg category was introduced by Ganter and Kapra
nov. I will explain how a semi-orthogonal decomposition (SOD) of an origin
al dg category induces an SOD on the symmetric products. This is a general
ization of the direct sum decomposition of the symmetric product of a dire
ct sum of two vector spaces.\nThe main application is the construction of
various interesting SODs on the derived categories of the Hilbert schemes
of points on surfaces.\n\nThe Zoomlink is as follows:\nhttps://uni-koeln.z
oom.us/j/91875528987?pwd=US8wdjNrWjl5dXNQSVRzREhoRE1PUT09\nMeeting ID: 918
7552 8987\nPassword: LAGOON\n
LOCATION:https://researchseminars.org/talk/LAGOON/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yu Qiu (Tsinghua University\, China)
DTSTART:20231025T120000Z
DTEND:20231025T130000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/87
DESCRIPTION:Title:
On cluster braid groups\nby Yu Qiu (Tsinghua University\, China) as pa
rt of Longitudinal Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\n
Abstract\nWe introduce cluster braid groups\, with motivations coming from
the study of stability conditions and quadratic differentials. In the Cox
eter–Dynkin case\, they are naturally isomorphic to the corresponding br
aid groups (1407.5986 and 2310.02871). In the surface case\, they are natu
rally isomorphic to braid twist groups (1407.0806\, 1703.10053 and 1805.00
030).\n\nThe Zoom link is as follows:\n \nhttps://uni-koeln.zoom.us/j/9187
5528987?pwd=US8wdjNrWjl5dXNQSVRzREhoRE1PUT09\n\nMeeting ID: 918 7552 8987\
nPassword: LAGOON\n
LOCATION:https://researchseminars.org/talk/LAGOON/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laura Pertusi (University of Milano\, Italy)
DTSTART:20231129T130000Z
DTEND:20231129T140000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/88
DESCRIPTION:Title:
Non-commutative abelian surfaces and generalized Kummer varieties\nby
Laura Pertusi (University of Milano\, Italy) as part of Longitudinal Algeb
ra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nA hyperkaehler
manifold is a compact complex simply connected Kaehler manifold whose spa
ce of holomorphic two-forms is generated by a symplectic form\, unique up
to scalar multiplication. Together with complex tori and irreducible Calab
i--Yau manifolds\, they are building blocks for compact Kaehler manifolds
with trivial first Chern class. In dimension two hyperkaehler manifolds ar
e K3 surfaces\, while finding examples in higher dimensions is a challengi
ng problem. In this talk we will construct new families of hyperkahler man
ifolds of generalized Kummer type via moduli spaces of stable objects in a
noncommutative deformation of the bounded derived category of an abelian
surface. This work in progress is joint with Arend Bayer\, Alex Perry and
Xiaolei Zhao.\n\nhttps://uni-koeln.zoom.us/j/91875528987?pwd=US8wdjNrWjl5d
XNQSVRzREhoRE1PUT09\n\nMeeting ID: 918 7552 8987\nPassword: LAGOON\n
LOCATION:https://researchseminars.org/talk/LAGOON/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jaiung Jun (State University of New York\, USA)
DTSTART:20231220T130000Z
DTEND:20231220T140000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/89
DESCRIPTION:Title:
Quiver representations over ${\\mathbb F}_1$\nby Jaiung Jun (State Uni
versity of New York\, USA) as part of Longitudinal Algebra and Geometry Op
en ONline Seminar (LAGOON)\n\n\nAbstract\nA quiver is a directed graph\, a
nd a representation of a quiver assigns a vector space to each vertex and
a linear map to each arrow. Quiver representations over ${\\mathbb F}_1$\,
"the field with one element"\, can be considered as a combinatorial model
of quiver representations over a field\, where vector spaces and linear m
aps are replaced by ${\\mathbb F}_1$-vector spaces and ${\\mathbb F}_1$-li
near maps. I will introduce several aspects of quiver representations over
${\\mathbb F}_1$\, and its potential applications. This is joint work wit
h Jaehoon Kim and Alex Sistko.\n\nhttps://uni-koeln.zoom.us/j/91875528987?
pwd=US8wdjNrWjl5dXNQSVRzREhoRE1PUT09\n\nMeeting ID: 918 7552 8987 Password
: LAGOON\n
LOCATION:https://researchseminars.org/talk/LAGOON/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucy Yang (Columbia University\, New York\, USA)
DTSTART:20240131T130000Z
DTEND:20240131T140000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/90
DESCRIPTION:Title:
Categorical dynamics on stable module categories\nby Lucy Yang (Columb
ia University\, New York\, USA) as part of Longitudinal Algebra and Geomet
ry Open ONline Seminar (LAGOON)\n\n\nAbstract\nGiven a mathematical object
X and an endomorphism f of X\, entropy assigns to this pair a number h(f)
measuring the dynamical complexity of f. Initially defined for measure sp
aces and topological spaces\, it has also been generalized by Dimitrov--Ha
iden--Katzarkov--Kontsevich to measure the complexity of endomorphisms of
stable ∞-categories. I will discuss a result showing that the categorica
l polynomial entropy of a twist functor on stable module categories of cer
tain algebras A of cohomology operations over a field k reflects the compl
exity of A: it is at least one less than the Krull dimension of H*(A\;k)\,
generalizing results of Fan--Fu--Ouchi. We will then discuss work in pro
gress to bring this dynamicalperspective to homotopy theory.\n\nhttps://un
i-koeln.zoom.us/j/91875528987?pwd=US8wdjNrWjl5dXNQSVRzREhoRE1PUT09\n\nMeet
ing ID: 918 7552 8987 Password: LAGOON\n
LOCATION:https://researchseminars.org/talk/LAGOON/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nadia Romero (Universidad de Guanajuato\, Mexico)
DTSTART:20240228T130000Z
DTEND:20240228T140000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/91
DESCRIPTION:Title:
Hochschild cohomology for functors on linear symmetric monoidal categories
\nby Nadia Romero (Universidad de Guanajuato\, Mexico) as part of Long
itudinal Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\n
Let X be an essentially small symmetric monoidal category enriched in R-Mo
d\, with R a commutative ring with identity. Under these conditions\, the
category F\, of R-linear functors from X to R-Mod\, becomes an abelian sym
metric monoidal category\, also enriched in R-Mod. The fact that F is mono
idal and abelian at the same time allows for a nice theory of modules over
the monoids in F\, in particular it allows for a nice and easy definition
of an internal hom functor. In this talk\, we will see how this internal
hom is the key to define a Hochschild cohomology theory in F.\n\nhttps://u
ni-koeln.zoom.us/j/91875528987?pwd=US8wdjNrWjl5dXNQSVRzREhoRE1PUT09\n\nMee
ting ID: 918 7552 8987\nPassword: LAGOON\n
LOCATION:https://researchseminars.org/talk/LAGOON/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emmanuele Pavia (SISSA\, Italy)
DTSTART:20240327T130000Z
DTEND:20240327T140000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/92
DESCRIPTION:Title:
Sheaves of categories over topological and coaffine stacks\nby Emmanue
le Pavia (SISSA\, Italy) as part of Longitudinal Algebra and Geometry Open
ONline Seminar (LAGOON)\n\n\nAbstract\nStarting from any sufficiently nic
e topological space X\, one can produce two different (derived) stacks def
ined over a field k of characteristic 0: the Betti stack X_B\, which bears
information on the underlying homotopy type of X\, and the coaffine stack
cSpec(C*(X\; k)) on the commutative algebra C*(X\; k) of k-valued singula
r cochains on X\, which behaves as the affinization of the Betti stack X_B
. In this talk\, I shall apply the technical machinery of sheaves of (∞-
)categories on derived stacks as developed in Gaitsgory’s work to the ca
se of Betti stacks and their associated coaffine stacks. We shall see how
sheaves of categories on X_B are intimately related to categorified local
systems over the original space X and to homotopy-coherent actions of topo
logical groups on k-linear ∞-categories. At the very end\, I shall brief
ly describe how sheaves of categories on X_B and on cSpec(C*(X\; k)) inter
act\, and how such interaction can be interpreted as an instance of higher
Koszul duality. This talk is based on upcoming joint work with J. Pascale
ff and N. Sibilla.See abstract under 'Paper link' below.\n\nLive stream: h
ttps://uni-koeln.zoom.us/j/91875528987?pwd=US8wdjNrWjl5dXNQSVRzREhoRE1PUT0
9\n\nMeeting ID: 918 7552 8987\nPassword: LAGOON\n
LOCATION:https://researchseminars.org/talk/LAGOON/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pieter Belmans (University of Luxembourg\, Luxembourg)
DTSTART:20240424T120000Z
DTEND:20240424T130000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/93
DESCRIPTION:Title:
Hochschild cohomology of Hilbert schemes of points\nby Pieter Belmans
(University of Luxembourg\, Luxembourg) as part of Longitudinal Algebra an
d Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nI will present a fo
rmula describing the Hochschild cohomology of symmetric quotient stacks\,
computing the Hochschild–Kostant–Rosenberg decomposition of this orbif
old. Through the Bridgeland–King–Reid–Haiman equivalence this allows
the computation of Hochschild cohomology of Hilbert schemes of points on
surfaces. These computations explain how this invariant behaves differentl
y from say Betti or Hodge numbers\, which have been studied intensively in
the past 30 years\, and it allows for new deformation-theoretic results.
This is joint work with Lie Fu and Andreas Krug.\n\nThe Zoom link is\n \nh
ttps://uni-koeln.zoom.us/j/91875528987?pwd=US8wdjNrWjl5dXNQSVRzREhoRE1PUT0
9\n\nMeeting ID: 918 7552 8987\nPassword: LAGOON\n
LOCATION:https://researchseminars.org/talk/LAGOON/93/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Davide Favero (University of Minnesota\, USA)
DTSTART:20240529T120000Z
DTEND:20240529T130000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/94
DESCRIPTION:Title:
Homotopy path algebras and resolutions\nby Davide Favero (University o
f Minnesota\, USA) as part of Longitudinal Algebra and Geometry Open ONlin
e Seminar (LAGOON)\n\n\nAbstract\nA homotopy path algebra is like a direct
ed version of the group ring on a fundamental group. One can imagine a di
rected graph (quiver) embedded in a topological space and consider the pat
h algebra up to homotopy. Alternatively\, one can think of homotopy class
es of directed paths in a stratified topological space. I will introduce
homotopy path algebras and describe their connections to mirror symmetry a
nd resolutions of coherent sheaves on toric varieties.\n
LOCATION:https://researchseminars.org/talk/LAGOON/94/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Merlin Christ (Institut de Mathématiques de Jussieu\, France)
DTSTART:20240626T120000Z
DTEND:20240626T130000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/95
DESCRIPTION:Title:
Relative graded Brauer graph algebras and stability conditions\nby Mer
lin Christ (Institut de Mathématiques de Jussieu\, France) as part of Lon
gitudinal Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\
nWe consider a class of dg-algebras which generalize Brauer graph algebras
\, called relative graded Brauer graph algebras. Their Koszul dual dg-alge
bras are given by finite group quotients of relative Ginzburg algebras ass
ociated with n-angulated surfaces. By constructing a partial geometric mod
el of the derived category\, we fully describe the finite heart tilting th
eory. This leads to a description of the space of Bridgeland stability con
ditions in terms of quadratic differentials. Based on joint work with Y. Q
iu and F. Haiden.\n\nhttps://uni-koeln.zoom.us/j/91875528987?pwd=US8wdjNrW
jl5dXNQSVRzREhoRE1PUT09\n\nMeeting ID: 918 7552 8987\nPassword: LAGOON\n
LOCATION:https://researchseminars.org/talk/LAGOON/95/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alekos Robotis (Cornell University\, USA)
DTSTART:20241030T130000Z
DTEND:20241030T140000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/96
DESCRIPTION:Title:
Partial compactification of the stability manifold by categorical decompos
itions\nby Alekos Robotis (Cornell University\, USA) as part of Longit
udinal Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nI
will discuss new geometric-categorical structures on triangulated categori
es that give a partial compactification of spaces of stability conditions.
This is based on joint work with Daniel Halpern-Leistner.\n\nhttps://uni-
koeln.zoom.us/j/91875528987?pwd=US8wdjNrWjl5dXNQSVRzREhoRE1PUT09\n\nMeetin
g ID: 918 7552 8987\nPassword: LAGOON\n
LOCATION:https://researchseminars.org/talk/LAGOON/96/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonas Schnitzer (University of Pavia\, Italy)
DTSTART:20241127T130000Z
DTEND:20241127T140000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/97
DESCRIPTION:Title:
Global homotopies for differential Hochschild cohomologies\nby Jonas S
chnitzer (University of Pavia\, Italy) as part of Longitudinal Algebra and
Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nIt is well known tha
t the Hochschild–Kostant–Rosenberg map from multivector fields to diff
erential Hochschild cochains is a quasi-isomorphism. Nevertheless\, it is
sometimes desirable to not only know the cohomology itself\, but also find
reasonable formulas for primitives of exact cochains. In my talk I will e
xplain how to construct a quasi-inverse of the Hochschild–Kostant–Rose
nberg map and a homotopy to turn all the maps into a deformation retract.
The difference to already existing attempts is that our construction is pe
rformed globally and enjoys nice properties regarding symmetries. Moreove
r\, the idea of this construction allows for generalizations in various di
rections. This is a joint work with Marvin Dippell\, Chiara Esposito and S
tefan Waldmann.\n\nhttps://uni-koeln.zoom.us/j/91875528987?pwd=US8wdjNrWjl
5dXNQSVRzREhoRE1PUT09\n\nMeeting ID: 918 7552 8987\nPassword: LAGOON\n
LOCATION:https://researchseminars.org/talk/LAGOON/97/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Burban (University of Paderborn\, Germany)
DTSTART:20241218T130000Z
DTEND:20241218T140000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/98
DESCRIPTION:Title:
Exceptional hereditary non-commutative curves and real curve orbifolds
\nby Igor Burban (University of Paderborn\, Germany) as part of Longitudin
al Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nAn exc
eptional hereditary non-commutative curve over an algebraically closed fie
ld is a weighted projective line of Geigle and Lenzing. However\, over arb
itrary fields\, the theory of exceptional curves is significantly richer.
In my talk I am going to explain the definition\, examples and key propert
ies of these classes of non-commutative curves\, including their invariant
s and relation to squid algebras and canonical algebras.\n\nhttps://uni-ko
eln.zoom.us/j/91875528987?pwd=US8wdjNrWjl5dXNQSVRzREhoRE1PUT09\n\nMeeting
ID: 918 7552 8987\nPassword: LAGOON\n
LOCATION:https://researchseminars.org/talk/LAGOON/98/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Barbieri (University of Verona\, Italy)
DTSTART:20250129T130000Z
DTEND:20250129T140000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/99
DESCRIPTION:Title:
A compactification of the stability space for the Aₙ-quiver\nby Anna
Barbieri (University of Verona\, Italy) as part of Longitudinal Algebra a
nd Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nThe space of Bridg
eland stability conditions is a non-compact complex manifold attached to a
triangulated category D\, parametrizing some t-structures of the category
. In this talk I will propose a notion of multi-scale stability conditions
that gives a smooth compactification of an appropriate quotient of the st
ability manifold of the Ginzburg category of type Aₙ and a partial compa
ctification for other Ginzburg categories attached to quivers with potenti
al from triangulated marked Riemann surfaces. Based on a joint work with M
. Möller and J. So.\n\nhttps://uni-koeln.zoom.us/j/91875528987?pwd=US8wdj
NrWjl5dXNQSVRzREhoRE1PUT09\n\nMeeting ID: 918 7552 8987 Password: LAGOON\n
LOCATION:https://researchseminars.org/talk/LAGOON/99/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julian Holstein (University of Hamburg\, Germany)
DTSTART:20250226T130000Z
DTEND:20250226T140000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/100
DESCRIPTION:Title: Curvature\, Koszul duality and Calabi–Yau structures\nby Julian Hol
stein (University of Hamburg\, Germany) as part of Longitudinal Algebra an
d Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nI will talk about t
wo aspects of Koszul duality. Firstly\, Koszul duality for dg categories p
rovides a way of modelling dg categories as certain curved coalgebras. Thi
s is a linearization of the correspondence of simplicial categories as sim
plicial sets (quasi-categories) and curved coalgebras have better formal p
roperties than dg categories. Secondly\, Koszul duality exchanges two self
-dualities: smooth and proper Calabi–Yau structures. This is a generaliz
ation and conceptual explanation of the following phenomenon: For a topolo
gical space X with the homotopy type of a finite complex having an oriente
d Poincaré duality structure (with local coefficients) is equivalent to h
aving a smooth Calabi–Yau structure on the dg algebra of chains on the b
ased loop space of X. A similar phenomenon occurs for Lie algebras. This i
s joint work with Andrey Lazarev and with Manuel Rivera\, respectively.\n\
nhttps://uni-koeln.zoom.us/j/91875528987?pwd=US8wdjNrWjl5dXNQSVRzREhoRE1PU
T09\n\nMeeting ID: 918 7552 8987\nPassword: LAGOON\n
LOCATION:https://researchseminars.org/talk/LAGOON/100/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Wemyss (University of Glasgow\, UK)
DTSTART:20250430T120000Z
DTEND:20250430T130000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/101
DESCRIPTION:Title: The classification of 3-fold flops via Jacobi algebras\nby Michael We
myss (University of Glasgow\, UK) as part of Longitudinal Algebra and Geom
etry Open ONline Seminar (LAGOON)\n\n\nAbstract\nThe talk will give an ove
rview of the analytic classification of smooth\, simple\, 3-fold flops. T
here are three main aspects: (1) reducing the problem to the classificatio
n of certain noncommutative finite dimensional algebras\, (2) a full under
standing of those algebras\, then lastly (3) building the associated geome
try for each algebra in that class. There are various bonus corollaries.
The talk will be algebraic\, and so will focus mostly on (1) and (2)\, wh
ere new techniques in A∞ algebras and in noncommutative standard bases w
ill be explained. Perhaps the main point is that a new invariant of Jacob
i algebras on the two-loop quiver called the "algebraic length" will be in
troduced\, and I will speculate on how general this construction really is
. Part (1) is joint with Joe Karmazyn and Emma Lepri\, the rest is joint
with Gavin Brown.\n
LOCATION:https://researchseminars.org/talk/LAGOON/101/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Travis Schedler (Imperial College London\, UK)
DTSTART:20250625T120000Z
DTEND:20250625T130000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/103
DESCRIPTION:Title: Creating quantum projective spaces by deforming q-symmetric algebras\
nby Travis Schedler (Imperial College London\, UK) as part of Longitudinal
Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nI will e
xplain how to construct new "quantum projective spaces"\, in the form of K
oszul\, Calabi–Yau algebras with the Hilbert series of a polynomial ring
. To do so we deform the relations of toric ones — q-symmetric algebras
— using a diagrammatic calculus. Such deformations are unobstructed unde
r suitable nondegeneracy conditions\, which also guarantee that the algebr
as are Kontsevich's canonical quantizations of corresponding quadratic Po
isson structures. This produces the first broad class of quadratic Poisson
structures for which his quantization can be computed and shown to conver
ge\, as he conjectured in 2001. On the other hand\, we also give examples
of purely noncommutative deformations\, which cannot be obtained by quanti
zing Poisson structures. This is joint work with Mykola Matviichuk and Bre
nt Pym.\n\nhttps://uni-koeln.zoom.us/j/91875528987?pwd=US8wdjNrWjl5dXNQSVR
zREhoRE1PUT09\n\nMeeting ID: 918 7552 8987\nPassword: LAGOON\n
LOCATION:https://researchseminars.org/talk/LAGOON/103/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nick Williams (University of Cambridge\, UK)
DTSTART:20250528T120000Z
DTEND:20250528T130000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/104
DESCRIPTION:Title: Steenrod operations via higher Bruhat orders\nby Nick Williams (Unive
rsity of Cambridge\, UK) as part of Longitudinal Algebra and Geometry Open
ONline Seminar (LAGOON)\n\n\nAbstract\nThe cohomology of a topological sp
ace has a ring structure via the cup product. The cup product is defined a
t the level of cochains\, where it is not commutative\, but it becomes com
mutative at the cohomology level. At the cochain level\, the lack of commu
tativity is resolved homotopically by an infinite tower of higher products
\, known as the Steenrod cup-i products. This additional structure provide
s more refined information which can be used to tell apart non-homotopy-eq
uivalent spaces. In this talk\, I will explain recent work with Guillaume
Laplante-Anfossi\, where we show how conceptual proofs of the key properti
es of Steenrod's cup-i products can be given using the higher Bruhat order
s of Manin and Schechtman.\n\nhttps://uni-koeln.zoom.us/j/91875528987?pwd=
US8wdjNrWjl5dXNQSVRzREhoRE1PUT09\n\nMeeting ID: 918 7552 8987\nPassword: L
AGOON\n
LOCATION:https://researchseminars.org/talk/LAGOON/104/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jon Pridham (Hodge Institute\, University of Endinburgh\, UK)
DTSTART:20250924T120000Z
DTEND:20250924T130000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/105
DESCRIPTION:Title: Derived deformation functors\, Koszul duality\, and Maurer-Cartan spaces<
/a>\nby Jon Pridham (Hodge Institute\, University of Endinburgh\, UK) as p
art of Longitudinal Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\
nAbstract\nFor Koszul dual pairs (L\, C) of differential graded operads (t
he motivating case being Lie and commutative)\, I will give an overview of
the equivalence between dg L-algebras up to quasi-isomorphism and functor
s on Artinian dg C-algebras satisfying some exactness conditions. The latt
er tend to arise as derived versions of natural deformation functors.\n\nh
ttps://uni-koeln.zoom.us/j/91875528987?pwd=US8wdjNrWjl5dXNQSVRzREhoRE1PUT0
9\n\nMeeting ID: 918 7552 8987\nPassword: LAGOON\n
LOCATION:https://researchseminars.org/talk/LAGOON/105/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sira Gratz (Aarhus University\, Denmark)
DTSTART:20251105T130000Z
DTEND:20251105T140000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/106
DESCRIPTION:Title: An equivalence of graded hypersurface singularities of infinite type A an
d D\nby Sira Gratz (Aarhus University\, Denmark) as part of Longitudin
al Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nThe on
e-dimensional hypersurface singularities of countably infinite Cohen–Mac
aulay type are precisely those of infinite type A and D. They are the infi
nite analogues of simple plane curve singularities\, which have finite Coh
en–Macaulay type and are classified by the finite ADE diagrams. From a c
luster theoretic perspective\, it is natural to study these\, and related\
, singularities with a specific grading. This was pioneered in work by Jen
sen\, King and Su for the finite rank case. We explain how to translate th
is idea to the infinite rank case\, and conclude with a surprising observa
tion: Under this grading\, we find a stable equivalence of graded Cohen–
Macaulay modules for the hypersurface singularities of infinite types A an
d D. This talk is based on two WINART projects\, the first joint with Augu
st\, Cheung\, Faber and Schroll and the second joint with Cummings\, Kirkm
an\, Letz\, Rock and Špenko.\n\nhttps://uni-koeln.zoom.us/j/91875528987?p
wd=US8wdjNrWjl5dXNQSVRzREhoRE1PUT09\n\nMeeting ID: 918 7552 8987\nPassword
: LAGOON\n
LOCATION:https://researchseminars.org/talk/LAGOON/106/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Timothy Logvinenko (Cardiff University\, UK)
DTSTART:20251210T130000Z
DTEND:20251210T140000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/107
DESCRIPTION:Title: Unbounded twisted complexes\nby Timothy Logvinenko (Cardiff Universit
y\, UK) as part of Longitudinal Algebra and Geometry Open ONline Seminar (
LAGOON)\n\n\nAbstract\nThe notion of a (bounded) twisted complex of object
s in a DG category was introduced by Bondal and Kapranov as a tool to stud
y and construct DG enhancements of triangulated categories. It can be view
ed as a lift to the DG enhancement of a bounded complex of objects in the
underlying triangulated category. But what if one needs to work with unbou
nded complexes of objects?\nIn this talk\, I will first give an introducti
on summarising the original theory of bounded twisted complexes. Then I wi
ll explain the difficulties involved in making it work with unbounded comp
lexes\, and how they are dealt with in the resulting theory of unbounded t
wisted complexes due to Rina Anno and I. Finally\, I will talk about some
applications\, such as A-infinity structures in monoidal DG categories and
homotopy idempotents.\n\nTalk postponed to Wednesday December 10!\n\nhttp
s://uni-koeln.zoom.us/j/91875528987?pwd=US8wdjNrWjl5dXNQSVRzREhoRE1PUT09\n
\nMeeting ID: 918 7552 8987 Password: LAGOON\n
LOCATION:https://researchseminars.org/talk/LAGOON/107/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Álvaro Sánchez (Universidad de Murcia\, Spain)
DTSTART:20260128T130000Z
DTEND:20260128T140000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/108
DESCRIPTION:Title: Abstract representation theory of quivers and spectral Picard groups\
nby Álvaro Sánchez (Universidad de Murcia\, Spain) as part of Longitudin
al Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nWhile
the (derived) representation theory of quivers over a field is by now well
-understood\, much less is known when moving to coefficients in the intege
rs or an arbitrary commutative ring. In this talk\, we take a rather radic
al but well-founded approach: it has recently been observed that certain w
ell-known symmetries of categories of representations (tilting results) ar
e actually mere consequences of the stability of the coefficients involved
\, and so they exist in a much broader generality\, often for the correspo
nding representations in any stable homotopy theory — this includes arbi
trary rings\, schemes\, dg algebras\, or ring spectra. For a finite acycli
c quiver Q\, we present here a method for producing universal autoequivale
nces of representations C^Q in any stable ∞-category C\, which are the e
lements of the spectral Picard group of Q. This is based on an abstract eq
uivalence of C^Q with a certain mesh ∞-category of representations of th
e Auslander–Reiten quiver Γ_Q. Then our universal equivalences arise fr
om symmetries of Γ_Q\, and thus yield abstract versions of key functors i
n classical representation theory — e.g. the Auslander-Reiten translatio
n\, the Serre functor\, etc. Moreover\, for representations of trees this
allows us to realize the whole derived Picard group over a field as a fact
or of the spectral Picard group.\n
LOCATION:https://researchseminars.org/talk/LAGOON/108/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tristan Bozec (Université Angers\, France)
DTSTART:20260225T130000Z
DTEND:20260225T140000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/109
DESCRIPTION:Title: TFTs via DAG\nby Tristan Bozec (Université Angers\, France) as part
of Longitudinal Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbs
tract\nOne very nice feature of derived algebraic geometry\, and specifica
lly shifted symplectic geometry\, is how convenient it is to tackle topolo
gical field theories. We will first review the recent history of this appr
oach\, through the fundamental use of mapping stacks and the Betti shape.
We will illustrate our review with many very concrete examples and noncomm
utative applications\, before explaining how the (recently proved) Moore--
Tachikawa conjecture lead us to considering the Dolbeault shape in view of
defining a new TFT associated to Higgs fields. This reports an ongoing co
llaboration with Damien Calaque\, Julien Grivaux and Hugo Pourcelot.\n\nTh
e Zoom link is\n\nhttps://uni-koeln.zoom.us/j/91875528987?pwd=US8wdjNrWjl5
dXNQSVRzREhoRE1PUT09\n\nMeeting ID: 918 7552 8987\nPassword: LAGOON\n
LOCATION:https://researchseminars.org/talk/LAGOON/109/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiao-Wu Chen (University of Science and Technology of China\, Hefe
i\, China)
DTSTART:20260325T130000Z
DTEND:20260325T140000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/110
DESCRIPTION:Title: Frobenius quotients\, inflation categories and weighted projective lines<
/a>\nby Xiao-Wu Chen (University of Science and Technology of China\, Hefe
i\, China) as part of Longitudinal Algebra and Geometry Open ONline Semina
r (LAGOON)\n\n\nAbstract\nBy the work of Kussin\, Lenzing and Meltzer\,
the category of vector bundles on a certain weighted projective line is c
losely related to the graded submodule problem\, studied by Ringel-Schmidm
eier. However\, the connection is quite mysterious. We construct an explic
it functor\, which yields Kussin-Lenzing-Meltzer’s stable equivalence. I
nspired by Demonet-Iyama's work\, we introduce a general notion of Frobeni
us quotients. We use multifold matrix factorizations in the proof. This is
joint with Qiang Dong and Shiquan Ruan.\n\nThe Zoom link is\n\nhttps://un
i-koeln.zoom.us/j/91875528987?pwd=US8wdjNrWjl5dXNQSVRzREhoRE1PUT09\n\nMeet
ing ID: 918 7552 8987\nPassword: LAGOON\n
LOCATION:https://researchseminars.org/talk/LAGOON/110/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Solotar (University of Buenos Aires\, Argentina)
DTSTART:20260429T120000Z
DTEND:20260429T130000Z
DTSTAMP:20260422T225841Z
UID:LAGOON/111
DESCRIPTION:by Andrea Solotar (University of Buenos Aires\, Argentina) as
part of Longitudinal Algebra and Geometry Open ONline Seminar (LAGOON)\n\n
Abstract: TBA\n
LOCATION:https://researchseminars.org/talk/LAGOON/111/
END:VEVENT
END:VCALENDAR