BEGIN:VCALENDAR
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CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Bernhard Keller
DTSTART:20201005T140000Z
DTEND:20201005T150000Z
DTSTAMP:20260416T153226Z
UID:ConRepGeom/1
DESCRIPTION:Title: Introduction to A-infinity structures 1\nby Bernhard Keller as part
of Winter School "Connections between representation theory and geometry"
\n\n\nAbstract\nIn this minicourse\, we will present basic results on A-in
finity \nalgebras\, their modules and their derived categories. We will\ns
tart with two motivating problems from representation theory. Then we \nwi
ll briefly present the topological origin of A-infinity structures. We \nw
ill then define and study A-infinity algebras and their morphisms. Of \nce
ntral importance are the bar construction and Kadeishvili's theorem on \nt
he existence of minimal models. We will then define the derived \ncategory
of an A-infinity algebra or category and describe its full \nsubcategory
generated by the representables using twisted objects.\n
LOCATION:https://researchseminars.org/talk/ConRepGeom/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bernhard Keller
DTSTART:20201007T140000Z
DTEND:20201007T150000Z
DTSTAMP:20260416T153226Z
UID:ConRepGeom/2
DESCRIPTION:Title: Introduction to A-infinity structures 2\nby Bernhard Keller as part
of Winter School "Connections between representation theory and geometry"
\n\n\nAbstract\nIn this minicourse\, we will present basic results on A-in
finity \nalgebras\, their modules and their derived categories. We will\ns
tart with two motivating problems from representation theory. Then we \nwi
ll briefly present the topological origin of A-infinity structures. We \nw
ill then define and study A-infinity algebras and their morphisms. Of \nce
ntral importance are the bar construction and Kadeishvili's theorem on \nt
he existence of minimal models. We will then define the derived \ncategory
of an A-infinity algebra or category and describe its full \nsubcategory
generated by the representables using twisted objects.\n
LOCATION:https://researchseminars.org/talk/ConRepGeom/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Pascaleff
DTSTART:20201007T151500Z
DTEND:20201007T161500Z
DTSTAMP:20260416T153226Z
UID:ConRepGeom/3
DESCRIPTION:Title: Introduction to Fukaya categories 1\nby James Pascaleff as part of
Winter School "Connections between representation theory and geometry"\n\n
\nAbstract\nThis minicourse will provide an introduction to Fukaya categor
ies. I will assume that participants are also attending Keller's course on
$\\mathrm{A}_{\\infty}$ categories.\n\nLecture 1: Basics of symplectic ge
ometry for Fukaya categories. Symplectic manifolds\; Lagrangian submanifol
ds\; exactness conditions\; almost complex structures\; holomorphic maps\;
Maslov indices and gradings.\n\nLecture 2: Floer cohomology and the Fukay
a category. Lagrangian intersection theory\; Floer differential\; $\\mathr
m{A}_{\\infty}$ operations\; Gromov compactification and $\\mathrm{A}_{\\i
nfty}$ equations.\n\nLecture 3: Examples of Fukaya categories. The case of
surfaces\; other cases as time permits.\n
LOCATION:https://researchseminars.org/talk/ConRepGeom/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bernhard Keller
DTSTART:20201009T140000Z
DTEND:20201009T150000Z
DTSTAMP:20260416T153226Z
UID:ConRepGeom/4
DESCRIPTION:Title: Introduction to A-infinity structures 3\nby Bernhard Keller as part
of Winter School "Connections between representation theory and geometry"
\n\n\nAbstract\nIn this minicourse\, we will present basic results on A-in
finity \nalgebras\, their modules and their derived categories. We will\ns
tart with two motivating problems from representation theory. Then we \nwi
ll briefly present the topological origin of A-infinity structures. We \nw
ill then define and study A-infinity algebras and their morphisms. Of \nce
ntral importance are the bar construction and Kadeishvili's theorem on \nt
he existence of minimal models. We will then define the derived \ncategory
of an A-infinity algebra or category and describe its full \nsubcategory
generated by the representables using twisted objects.\n
LOCATION:https://researchseminars.org/talk/ConRepGeom/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Pascaleff
DTSTART:20201009T151500Z
DTEND:20201009T161500Z
DTSTAMP:20260416T153226Z
UID:ConRepGeom/5
DESCRIPTION:Title: Introduction to Fukaya categories 2\nby James Pascaleff as part of
Winter School "Connections between representation theory and geometry"\n\n
\nAbstract\nThis minicourse will provide an introduction to Fukaya categor
ies. I will assume that participants are also attending Keller's course on
$\\mathrm{A}_{\\infty}$ categories.\n\nLecture 1: Basics of symplectic ge
ometry for Fukaya categories. Symplectic manifolds\; Lagrangian submanifol
ds\; exactness conditions\; almost complex structures\; holomorphic maps\;
Maslov indices and gradings.\n\nLecture 2: Floer cohomology and the Fukay
a category. Lagrangian intersection theory\; Floer differential\; $\\mathr
m{A}_{\\infty}$ operations\; Gromov compactification and $\\mathrm{A}_{\\i
nfty}$ equations.\n\nLecture 3: Examples of Fukaya categories. The case of
surfaces\; other cases as time permits.\n
LOCATION:https://researchseminars.org/talk/ConRepGeom/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sibylle Schroll
DTSTART:20201012T140000Z
DTEND:20201012T150000Z
DTSTAMP:20260416T153226Z
UID:ConRepGeom/6
DESCRIPTION:Title: A geometric model for the bounded derived category of a gentle algebra
1\nby Sibylle Schroll as part of Winter School "Connections between re
presentation theory and geometry"\n\n\nAbstract\nGentle algebras are quadr
atic monomial algebras whose representation theory is well understood. In
recent years they have played a central role in several different subject
s such as in cluster algebras where they occur as Jacobian algebras of qui
vers with potentials obtained from triangulations of marked surfaces and i
n the context of homological mirror symmetry where graded gentle algebras
with zero differential appear in the construction of partially wrapped Fuk
aya categories of surfaces with stops. In these lectures we will recall th
e construction of a geometric model for the bounded derived category of an
(ungraded) gentle algebra. We will see how the gentle algebra encodes not
only a marked surface but also a line field on the surface. This line fie
ld allows to define a complete derived invariant for gentle algebras whic
h generalises and completes the well-known derived invariant by Avella-Ala
minos and Geiss. We will give explicit examples relating the introduced ge
ometric model with the description of the partially wrapped Fukaya categor
y in the work of Haiden\, Katzarkov and Kontsevich.\n
LOCATION:https://researchseminars.org/talk/ConRepGeom/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Pascaleff
DTSTART:20201012T151500Z
DTEND:20201012T161500Z
DTSTAMP:20260416T153226Z
UID:ConRepGeom/7
DESCRIPTION:Title: Introduction to Fukaya categories 3\nby James Pascaleff as part of
Winter School "Connections between representation theory and geometry"\n\n
\nAbstract\nThis minicourse will provide an introduction to Fukaya categor
ies. I will assume that participants are also attending Keller's course on
$\\mathrm{A}_{\\infty}$ categories.\n\nLecture 1: Basics of symplectic ge
ometry for Fukaya categories. Symplectic manifolds\; Lagrangian submanifol
ds\; exactness conditions\; almost complex structures\; holomorphic maps\;
Maslov indices and gradings.\n\nLecture 2: Floer cohomology and the Fukay
a category. Lagrangian intersection theory\; Floer differential\; $\\mathr
m{A}_{\\infty}$ operations\; Gromov compactification and $\\mathrm{A}_{\\i
nfty}$ equations.\n\nLecture 3: Examples of Fukaya categories. The case of
surfaces\; other cases as time permits.\n
LOCATION:https://researchseminars.org/talk/ConRepGeom/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sibylle Schroll
DTSTART:20201014T140000Z
DTEND:20201014T150000Z
DTSTAMP:20260416T153226Z
UID:ConRepGeom/8
DESCRIPTION:Title: A geometric model for the bounded derived category of a gentle algebra
2\nby Sibylle Schroll as part of Winter School "Connections between re
presentation theory and geometry"\n\n\nAbstract\nGentle algebras are quadr
atic monomial algebras whose representation theory is well understood. In
recent years they have played a central role in several different subject
s such as in cluster algebras where they occur as Jacobian algebras of qui
vers with potentials obtained from triangulations of marked surfaces and i
n the context of homological mirror symmetry where graded gentle algebras
with zero differential appear in the construction of partially wrapped Fuk
aya categories of surfaces with stops. In these lectures we will recall th
e construction of a geometric model for the bounded derived category of an
(ungraded) gentle algebra. We will see how the gentle algebra encodes not
only a marked surface but also a line field on the surface. This line fie
ld allows to define a complete derived invariant for gentle algebras whic
h generalises and completes the well-known derived invariant by Avella-Ala
minos and Geiss. We will give explicit examples relating the introduced ge
ometric model with the description of the partially wrapped Fukaya categor
y in the work of Haiden\, Katzarkov and Kontsevich.\n
LOCATION:https://researchseminars.org/talk/ConRepGeom/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Smith
DTSTART:20201014T151500Z
DTEND:20201014T161500Z
DTSTAMP:20260416T153226Z
UID:ConRepGeom/9
DESCRIPTION:Title: Plumbings and flops\nby Ivan Smith as part of Winter School "Connec
tions between representation theory and geometry"\n\n\nAbstract\nI will di
scuss geometric models\, in both symplectic and algebraic geometry\, for t
he A-infinity algebras associated to potentials on the oriented two-cycle
quiver\; the models show an interesting dependence on the characteristic o
f the ground field. This talk reports on joint work with Michael Wemyss.\
n
LOCATION:https://researchseminars.org/talk/ConRepGeom/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sibylle Schroll
DTSTART:20201016T140000Z
DTEND:20201016T150000Z
DTSTAMP:20260416T153226Z
UID:ConRepGeom/10
DESCRIPTION:Title: A geometric model for the bounded derived category of a gentle algebra
3\nby Sibylle Schroll as part of Winter School "Connections between r
epresentation theory and geometry"\n\n\nAbstract\nGentle algebras are quad
ratic monomial algebras whose representation theory is well understood. I
n recent years they have played a central role in several different subjec
ts such as in cluster algebras where they occur as Jacobian algebras of qu
ivers with potentials obtained from triangulations of marked surfaces and
in the context of homological mirror symmetry where graded gentle algebras
with zero differential appear in the construction of partially wrapped Fu
kaya categories of surfaces with stops. In these lectures we will recall t
he construction of a geometric model for the bounded derived category of a
n (ungraded) gentle algebra. We will see how the gentle algebra encodes no
t only a marked surface but also a line field on the surface. This line fi
eld allows to define a complete derived invariant for gentle algebras whi
ch generalises and completes the well-known derived invariant by Avella-Al
aminos and Geiss. We will give explicit examples relating the introduced g
eometric model with the description of the partially wrapped Fukaya catego
ry in the work of Haiden\, Katzarkov and Kontsevich.\n
LOCATION:https://researchseminars.org/talk/ConRepGeom/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gustavo Jasso
DTSTART:20201019T140000Z
DTEND:20201019T150000Z
DTSTAMP:20260416T153226Z
UID:ConRepGeom/11
DESCRIPTION:Title: Partially wrapped Fukaya categories of symmetric products of marked di
sks\nby Gustavo Jasso as part of Winter School "Connections between re
presentation theory and geometry"\n\n\nAbstract\nPartially wrapped Fukaya
categories of symmetric products of marked\nsurfaces were introduced by Au
roux so as to give a symplecto-geometric\nintepretation of the bordered He
egaard-Floer homology of Lipshitz\, Ozsv\\'ath\nand Thurston. In this talk
\, I will explain the equivalence between the\npartially wrapped Fukaya ca
tegories of symmetric products of marked\ndisks and the perfect derived ca
tegories of a (discrete) family of\nfinite-dimensional algebras introduced
by Iyama\, the so-called higher\nAuslander algebras of type A. In particu
lar\, I will explain some of the\nrich structure present among these mathe
matical objects as they also\nrelate to the higher Waldhausen S-constructi
ons of Dyckerhoff and Poguntke.\n\nThis is a report with Tobias Dyckerhoff
and Yanki Lekili and also\ncontains work with Dyckerhoff and Walde.\n
LOCATION:https://researchseminars.org/talk/ConRepGeom/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fabian Haiden
DTSTART:20201019T151500Z
DTEND:20201019T161500Z
DTSTAMP:20260416T153226Z
UID:ConRepGeom/12
DESCRIPTION:Title: From Hall algebras to legendrian skein algebras\nby Fabian Haiden
as part of Winter School "Connections between representation theory and ge
ometry"\n\n\nAbstract\nA mysterious relation between Hall algebras of Fuka
ya categories of\nsurfaces and skein algebras was suggested by recent work
of\nMorton-Samuelson and Samuelson-Cooper. I will discuss how this relati
on\ncan be made precise using knot theory of legendrian curves and general
\ngluing properties of skein and Hall algebras. Along the way I aim to\nmo
tivate and review notions such as Hall algebras\, Fukaya categories of\nsu
rfaces\, and skein theory. Based on arXiv:1908.10358\, arXiv:1910.04182\,\
nand ongoing work with Ben Cooper.\n
LOCATION:https://researchseminars.org/talk/ConRepGeom/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tobias Dyckerhof
DTSTART:20201021T140000Z
DTEND:20201021T150000Z
DTSTAMP:20260416T153226Z
UID:ConRepGeom/13
DESCRIPTION:Title: Perverse sheaves and schobers on Riemann surfaces\nby Tobias Dycke
rhof as part of Winter School "Connections between representation theory a
nd geometry"\n\n\nAbstract\nReporting on joint work in progress with M. Ka
pranov\, V.\nSchechtman\, and Y. Soibelman\, I will explain how to describ
e the derived\nconstructible category of a stratified Riemann surface as\n
representations of the so-called paracyclic category of the surface.\nThis
allows for geometric depictions of the various t-structures of\ninterest
(including the perverse one) and their interplay with Verdier\nduality. We
will then discuss how this leads to an approach to\ncategorified perverse
sheaves (perverse schobers) and provide\napplications.\n
LOCATION:https://researchseminars.org/talk/ConRepGeom/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yanki Lekili
DTSTART:20201021T151500Z
DTEND:20201021T161500Z
DTSTAMP:20260416T153226Z
UID:ConRepGeom/14
DESCRIPTION:Title: Homological mirror symmetry for not-so-simple singularities\nby Ya
nki Lekili as part of Winter School "Connections between representation th
eory and geometry"\n\n\nAbstract\nIn a joint work with Ueda\, we outlined
a set of explicit conjectures that precisely explain how homological mirro
r symmetry should work for Milnor fibers of invertible polynomials. We can
prove these conjectures in a number of interesting cases such as the case
of simple singularities (in any dimension)\, when the corresponding categ
ories turns out to be equivalent to the derived category of the Calabi-Yau
completion of the path algebra of Dynkin quivers. In general\, one has to
consider global deformations\, but we can show that the possible deformat
ions are parametrized by a moduli space of $A_\\infty$ structures which we
identify with a certain moduli space of polarized Calabi-Yau varieties. I
will explain the case of the Milnor fiber of $x^4+y^4+z^4$ (and its high
er dimensional generalizations) which is among the cases of not-so-simple
singularities for which we can fully rigorously prove homological mirror s
ymmetry.\n
LOCATION:https://researchseminars.org/talk/ConRepGeom/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Claire Amiot
DTSTART:20201023T140000Z
DTEND:20201023T150000Z
DTSTAMP:20260416T153226Z
UID:ConRepGeom/15
DESCRIPTION:Title: Skew-gentle algebras and surface orbifolds\nby Claire Amiot as par
t of Winter School "Connections between representation theory and geometry
"\n\n\nAbstract\nIn the 80’s\, Reiten and Riedtmann introduced the notio
n of skew-group algebra attached to an algebra with the action of a group
by automorphisms. They studied in particular its representation theory. Sk
ew-gentle algebras were introduced by Geiss and de la Pe\\~na in the 90’
s as certain skew-group algebras of gentle algebras. The aim of this talk
is to show how the geometric model of the derived category of gentle algeb
ras developed by Opper\, Plamondon and Schroll can be adapted to skew-grou
p algebras. \n\nThis is a joint work with Thomas Br{\\"u}stle.\n
LOCATION:https://researchseminars.org/talk/ConRepGeom/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ailsa Keating
DTSTART:20201023T151500Z
DTEND:20201023T161500Z
DTSTAMP:20260416T153226Z
UID:ConRepGeom/16
DESCRIPTION:Title: Homological mirror symmetry for log Calabi-Yau surfaces\nby Ailsa
Keating as part of Winter School "Connections between representation theor
y and geometry"\n\n\nAbstract\nGiven a log Calabi-Yau surface Y with maxim
al boundary D\, I'll explain how to construct a mirror Landau-Ginzburg mod
el\, and sketch a proof of homological mirror symmetry for these pairs whe
n (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\, and\, time permitting\
, explain ties with earlier work of Auroux-Katzarkov-Orlov and Abouzaid. J
oint work with Paul Hacking.\n
LOCATION:https://researchseminars.org/talk/ConRepGeom/16/
END:VEVENT
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