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BEGIN:VEVENT
SUMMARY:Combinatorial actions on quivers and geometric interpretations
DTSTART;VALUE=DATE-TIME:20231220T081000Z
DTEND;VALUE=DATE-TIME:20231220T090000Z
DTSTAMP;VALUE=DATE-TIME:20240907T180522Z
UID:indico-contribution-430-7571@indico.ipmu.jp
DESCRIPTION:Speakers: Amihay Hanany ()\nThe Coulomb branch of 3d N=4 gauge
theory is a new construction of symplectic singularities.\nThis talk will
cover operations on quivers that start with a given symplectic singularit
y and ends with a new symplectic singularity\, while the relation between
the two is understood geometrically.\nThese operations include\n— Quiver
subtraction where the resulting singularity is a degeneration of a bigger
singularity\, thus revealing the stratification of symplectic leaves.\n
— Quiver subtraction where the resulting singularity is a HK quotient.\n
These combinatorial operations extend to orthosymplectic quivers and few e
xamples of this type will be discussed.\nIt is hoped that such operations
can be further extended to Gorenstein singularities.\n\nhttps://indico.ipm
u.jp/event/430/contributions/7571/
LOCATION:Kavli IPMU\, Kashiwa\, Japan Lecture Hall
URL:https://indico.ipmu.jp/event/430/contributions/7571/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Explicit examples of trihedral G-Hilbert schemes
DTSTART;VALUE=DATE-TIME:20231219T073000Z
DTEND;VALUE=DATE-TIME:20231219T080000Z
DTSTAMP;VALUE=DATE-TIME:20240907T180522Z
UID:indico-contribution-430-7560@indico.ipmu.jp
DESCRIPTION:Speakers: Alvaro Nolla de Celis (Madrid)\nIn this talk I will
show how to construct examples of G-Hilb when G is a trihedral group in SL
(3\,C). The calculations are based on the connection between trihedral boa
ts and representations of the McKay quiver\, allowing us to compute explic
itly the exceptional locus of the crepant resolution G-Hlib C^3 \\to C^3/G
and Reid’s recipe for small cases.\n\nhttps://indico.ipmu.jp/event/430/
contributions/7560/
LOCATION:Kavli IPMU\, Kashiwa\, Japan Lecture Hall
URL:https://indico.ipmu.jp/event/430/contributions/7560/
END:VEVENT
BEGIN:VEVENT
SUMMARY:$(1\,2)$-symmetric subgroups of SL$(4\,\\mathbb{C})$
DTSTART;VALUE=DATE-TIME:20231221T081000Z
DTEND;VALUE=DATE-TIME:20231221T090000Z
DTSTAMP;VALUE=DATE-TIME:20240907T180522Z
UID:indico-contribution-430-7562@indico.ipmu.jp
DESCRIPTION:Speakers: Miles Reid (Warwick)\nThe topic is finite diagonal s
ubgroups $A\\subset$SL$(4\,\\mathbb{C})$ and their \\hbox{$A$-Hilbert} sch
emes. As a dimension reducing assumption\, I impose the additional $(1\,2)
$-symmetric condition. The case to bear in mind is $\\frac1r(1\,1\,a\,b)$
with $r = a+b+2$. The ``junior end and all-even'' conditions for the quoti
ent $X=\\mathbb{A}^4/A$ to have a crepant resolution are known from Sarah
Davis's thesis [D].\n\nStudying the $A$-Hilbert scheme $A$-Hilb$\\mathbb{A
}^4$ in the general $(1\,2)$-symmetric case is interesting in its own righ
t\, and provides more detailed insight into case of the crepant resolution
. The variety $Y=A$-Hilb$\\mathbb{A}^4$ is toric\, a union of affine piece
s corresponding to monomomial ideals $I\\subset k[\\mathbb{A}^4]=k[x\,y\,z
\,t]$\, and can be constructed by my 2009 computer algebra routine [M]. In
very many cases $Y$ is nonsingular\, and is a resolution $Y\\to X$ with e
xceptional divisors of discrepancy 0 or 1.\n\nThe calculation of $A$-Hilb$
\\mathbb{A}^4$ mirrors the classical construction of Nakamura [A] and Craw
--Reid [CR]\, with some remarkable modifications.\n\nhttps://indico.ipmu.j
p/event/430/contributions/7562/
LOCATION:Kavli IPMU\, Kashiwa\, Japan Lecture Hall
URL:https://indico.ipmu.jp/event/430/contributions/7562/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cotilting complexes over commutative noetherian rings
DTSTART;VALUE=DATE-TIME:20231218T073000Z
DTEND;VALUE=DATE-TIME:20231218T080000Z
DTSTAMP;VALUE=DATE-TIME:20240907T180522Z
UID:indico-contribution-430-7559@indico.ipmu.jp
DESCRIPTION:Speakers: Tsutomu Nakamura (Mie)\nWe give a nontrivial example
of a cotilting complex that induces a compactly generated t-structure in
the unbounded derived category of a commutative noetherian ring\, and expl
ain its relation with big Cohen-Macaulay modules and Cohen-Macaulay approx
imations. This talk is partly based on joint work with Michal Hrbek and Ja
n Stovicek (arXiv:2207.01309).\n\nhttps://indico.ipmu.jp/event/430/contrib
utions/7559/
LOCATION:Kavli IPMU\, Kashiwa\, Japan Lecture Hall
URL:https://indico.ipmu.jp/event/430/contributions/7559/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Exceptional surfaces in 3-folds and derived symmetries
DTSTART;VALUE=DATE-TIME:20231220T063000Z
DTEND;VALUE=DATE-TIME:20231220T072000Z
DTSTAMP;VALUE=DATE-TIME:20240907T180522Z
UID:indico-contribution-430-7543@indico.ipmu.jp
DESCRIPTION:Speakers: Will Donovan (Tsinghua)\nCrepant resolutions of 3-fo
ld singularities may contain elaborate configurations of exceptional surfa
ces. Using toric cases as a guide\, I review some known contributions of t
hese configurations to the derived autoequivalence group of the resolution
\, in particular from work of Seidel-Thomas\, and discuss work in progress
with Luyu Zheng.\n\nhttps://indico.ipmu.jp/event/430/contributions/7543/
LOCATION:Kavli IPMU\, Kashiwa\, Japan Lecture Hall
URL:https://indico.ipmu.jp/event/430/contributions/7543/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Birational geometry of quiver moduli through Cox rings
DTSTART;VALUE=DATE-TIME:20231219T050000Z
DTEND;VALUE=DATE-TIME:20231219T055000Z
DTSTAMP;VALUE=DATE-TIME:20240907T180522Z
UID:indico-contribution-430-7569@indico.ipmu.jp
DESCRIPTION:Speakers: Ryo Yamagishi (Bath)\nModuli spaces of quiver repres
entations appear in various contexts of mathematics. These spaces depend o
n the choice of stability parameters and\, in many cases\, variation of th
e parameters induces birational transformations such as flops. In this tal
k I will introduce a new method to investigate such transformations using
the Cox rings. We will then see that this method works well especially in
the context of the McKay correspondence and that it is also useful in the
study of a Craw-Ishii type problem.\n\nhttps://indico.ipmu.jp/event/430/co
ntributions/7569/
LOCATION:Kavli IPMU\, Kashiwa\, Japan Lecture Hall
URL:https://indico.ipmu.jp/event/430/contributions/7569/
END:VEVENT
BEGIN:VEVENT
SUMMARY:L-genera and applications
DTSTART;VALUE=DATE-TIME:20231220T010000Z
DTEND;VALUE=DATE-TIME:20231220T015000Z
DTSTAMP;VALUE=DATE-TIME:20240907T180522Z
UID:indico-contribution-430-7561@indico.ipmu.jp
DESCRIPTION:Speakers: Andrei Okounkov (Columbia)\nMy goal in this talk is
to give an accessible discussion of an ongoing research project with David
Kazhdan. In this work\, we define L-function genera and use them in the s
pectral analysis of Eisenstein series and in related problems of enumerati
ve geometry.\n\nhttps://indico.ipmu.jp/event/430/contributions/7561/
LOCATION:Kavli IPMU\, Kashiwa\, Japan Lecture Hall
URL:https://indico.ipmu.jp/event/430/contributions/7561/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Projective crepant resolutions of toric cDV singularities and dime
r combinatorics
DTSTART;VALUE=DATE-TIME:20231222T063000Z
DTEND;VALUE=DATE-TIME:20231222T072000Z
DTSTAMP;VALUE=DATE-TIME:20240907T180522Z
UID:indico-contribution-430-7558@indico.ipmu.jp
DESCRIPTION:Speakers: Yusuke Nakajima (Kyoto Sangyo)\nIt is known that any
projective crepant resolution of a three-dimensional Gorenstein toric sin
gularity can be described as the moduli space of representations of the qu
iver associated to a consistent dimer model for some stability parameter.
The space of stability parameters has the wall-and-chamber structure\, tha
t is\, it is decomposed into chambers separated by walls. The moduli space
s associated to stability parameters contained in the same chamber are iso
morphic\, but a stability parameter contained in another chamber would giv
e a different moduli space. Thus\, it is important to detect the wall-and-
chamber structure of the space of stability parameters to understand the r
elationships among projective crepant resolutions of three-dimensional Gor
enstein toric singularities. \n In this talk\, I observe the wall-and-cham
ber structure for a particular class of three-dimensional Gorenstein toric
singularities called toric compound Du Val (cDV) singularities. In partic
ular\, I will show that zigzag paths of a consistent dimer model associate
d to a toric cDV singularity control the wall-and-chamber structure. This
talk is based on the preprint arXiv:2309.16112.\n\nhttps://indico.ipmu.jp/
event/430/contributions/7558/
LOCATION:Kavli IPMU\, Kashiwa\, Japan Lecture Hall
URL:https://indico.ipmu.jp/event/430/contributions/7558/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tilting theory and g-fans
DTSTART;VALUE=DATE-TIME:20231222T050000Z
DTEND;VALUE=DATE-TIME:20231222T055000Z
DTSTAMP;VALUE=DATE-TIME:20240907T180522Z
UID:indico-contribution-430-7555@indico.ipmu.jp
DESCRIPTION:Speakers: Yuya Mizuno (Osaka Metropolitan)\nThe notion of tilt
ing objects is basic to study the structure of a given derived category. T
he class of silting objects gives a completion of the class of tilting obj
ects from the point of view of mutation\, and they correspond bĳectively
with other important objects in the derived category. The subset of 2-term
silting complexes enjoys especially nice properties\, which is closely re
lated to τ-tilting theory and cluster theory. In this talk\, we discuss t
he notion of g-simplicial complexes\, g-polytopes and g-fans\, which is de
fined from 2-term silting complexes. We study several properties of these
three objects. In particular\, we give tilting theoretic interpretations o
f the h-vectors and Dehn-Sommerville equations of the g-simplicial complex
. Moreover\, we discuss the convexity of the g-polytope and its dual poly
tope.\nThis is a joint work with Aoki-Higashitani-Iyama-Kase.\n\nhttps://i
ndico.ipmu.jp/event/430/contributions/7555/
LOCATION:Kavli IPMU\, Kashiwa\, Japan Lecture Hall
URL:https://indico.ipmu.jp/event/430/contributions/7555/
END:VEVENT
BEGIN:VEVENT
SUMMARY:The Donovan-Wemyss Conjecture via the Derived Auslander-Iyama Corr
espondence
DTSTART;VALUE=DATE-TIME:20231221T050000Z
DTEND;VALUE=DATE-TIME:20231221T055000Z
DTSTAMP;VALUE=DATE-TIME:20240907T180522Z
UID:indico-contribution-430-7550@indico.ipmu.jp
DESCRIPTION:Speakers: Gustavo Jesso (Lund)\nThe Donovan-Wemyss Conjecture
predicts that the isomorphism type of an isolated compound Du Val singular
ity R that admits a crepant resolution is completely determined by the der
ived-equivalence class of any of its contraction algebras. Crucial results
of August\, Hua-Keller and Wemyss reduced the DW conjecture to a problem
closely related the question of uniqueness of enhancements of the singular
ity category of R. I will explain\, based on an observation by Bernhard Ke
ller\, how the DW conjecture follows from a recent theorem of Fernando Mur
o and myself that we call the Derived Auslander-Iyama Correspondence.\n\nh
ttps://indico.ipmu.jp/event/430/contributions/7550/
LOCATION:Kavli IPMU\, Kashiwa\, Japan Lecture Hall
URL:https://indico.ipmu.jp/event/430/contributions/7550/
END:VEVENT
BEGIN:VEVENT
SUMMARY:TF equivalence\, silting theory and canonical decompositions
DTSTART;VALUE=DATE-TIME:20231222T024000Z
DTEND;VALUE=DATE-TIME:20231222T033000Z
DTSTAMP;VALUE=DATE-TIME:20240907T180522Z
UID:indico-contribution-430-7539@indico.ipmu.jp
DESCRIPTION:Speakers: Sota Asai (Tokyo)\nThis talk is based on joint work
with Osamu Iyama. The representation theory of a finite dimensional algebr
a $A$ deals with the category $\\mathsf{mod} A$ of finitely generated $A$-
modules. One of the main topics is torsion pairs in $\\mathsf{mod} A$. Fun
ctorially finite torsion pairs have been well-studied\, but they are too f
ew among all torsion pairs. Thus\, we are now studying a wider class calle
d semistable torsion pairs introduced by Baumann-Kamnitzer-Tingley associa
ted to elements of the real Grothendieck group $K_0(\\mathsf{proj}A)_\\mat
hbb{R}$ of the category of finitely generated projective $A$-modules\, whi
ch is identified with the Euclidean space whose canonical basis is given b
y the isoclasses of indecomposable projective $A$-modules. By using semist
able torsion pairs\, I (Asai) introduced an equivalence relation called TF
equivalence on $K_0(\\mathsf{proj} A)_\\mathbb{R}$. A typical example of
TF equivalence classes is the silting cone $C^\\circ(U)$ generated by the
g-vectors of indecomposable direct summands of each 2-term presilting comp
lex $U$. On the other hand\, there can be other TF equivalence classes. To
study them\, we have found that canonical decompositions introduced by\nD
erksen-Fei is useful. I would like to explain some important properties of
these notions.\n\nhttps://indico.ipmu.jp/event/430/contributions/7539/
LOCATION:Kavli IPMU\, Kashiwa\, Japan Lecture Hall
URL:https://indico.ipmu.jp/event/430/contributions/7539/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mutations of noncommutative crepant resolutions in geometric invar
iant theory
DTSTART;VALUE=DATE-TIME:20231218T024000Z
DTEND;VALUE=DATE-TIME:20231218T033000Z
DTSTAMP;VALUE=DATE-TIME:20240907T180522Z
UID:indico-contribution-430-7548@indico.ipmu.jp
DESCRIPTION:Speakers: Yuki Hirano (Tokyo U. Agri & Tech)\nFor a generic qu
asi-symmetric representation X of a reductive group G\, Halpern-Leistner a
nd Sam show that the derived category of coherent sheaves on a GIT (stacky
) quotient of X is equivalent to magic windows\, which are certain triangu
lated subcategories of the derived categories of coherent sheaves on the q
uotient stack [X/G]. In this talk\, we explain that the equivalences of ma
gic windows\, which correspond to wall-crossings in a hyperplane arrangeme
nt\, correspond to derived equivalences of noncommutative crepant resoluti
ons induced by tilting modules\, and these tilting modules are obtained by
certain operations of modules\, which we call exchanges of modules. This
talk is based on joint work with Wahei Hara.\n\nhttps://indico.ipmu.jp/eve
nt/430/contributions/7548/
LOCATION:Kavli IPMU\, Kashiwa\, Japan Lecture Hall
URL:https://indico.ipmu.jp/event/430/contributions/7548/
END:VEVENT
BEGIN:VEVENT
SUMMARY:On recent developments in quasi-hereditary structures
DTSTART;VALUE=DATE-TIME:20231222T010000Z
DTEND;VALUE=DATE-TIME:20231222T015000Z
DTSTAMP;VALUE=DATE-TIME:20240907T180522Z
UID:indico-contribution-430-7541@indico.ipmu.jp
DESCRIPTION:Speakers: Aaron Chan (Nagoya)\nThe notion of quasi-hereditary
algebras were introduced by Cline-Parshall-Scott\, and there is an abundan
ce of examples arising in algebraic Lie theory and non-commutative resolut
ion of singularities. This notion is defined with respect to a poset struc
ture on the set of simple modules. In this talk\, we will survey some rece
nt developments in enumerating these structures\, and in particular\, thei
r relation with the (po)set of tilting modules. This talk contains joint w
orks with Takahide Adachi\, Yuta Kimura\, and Mayu Tsukamoto.\n\nhttps://i
ndico.ipmu.jp/event/430/contributions/7541/
LOCATION:Kavli IPMU\, Kashiwa\, Japan Lecture Hall
URL:https://indico.ipmu.jp/event/430/contributions/7541/
END:VEVENT
BEGIN:VEVENT
SUMMARY:An example of crepant resolution in characteristic 2 and its duali
ty
DTSTART;VALUE=DATE-TIME:20231218T081000Z
DTEND;VALUE=DATE-TIME:20231218T084000Z
DTSTAMP;VALUE=DATE-TIME:20240907T180522Z
UID:indico-contribution-430-7544@indico.ipmu.jp
DESCRIPTION:Speakers: Linghu Fan (Tokyo)\nIn positive characteristic\, few
examples of crepant resolutions of modular quotient singularities are kno
wn. In this talk\, I will introduce a crepant resolution of the quotient s
ingularity given by the permutation action of the alternating group of deg
ree 4 in characteristic 2. In addition\, I will present some special prope
rties of this resolution by considering its algebraic and geometric struct
ure.\n\nhttps://indico.ipmu.jp/event/430/contributions/7544/
LOCATION:Kavli IPMU\, Kashiwa\, Japan Lecture Hall
URL:https://indico.ipmu.jp/event/430/contributions/7544/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Reflexive modules and Auslander-Gorenstein rings
DTSTART;VALUE=DATE-TIME:20231222T073000Z
DTEND;VALUE=DATE-TIME:20231222T080000Z
DTSTAMP;VALUE=DATE-TIME:20240907T180522Z
UID:indico-contribution-430-7545@indico.ipmu.jp
DESCRIPTION:Speakers: Norihiro Hanihara (Tokyo)\nMotivated by the theory o
f non-commutative resolutions and the results on Auslander correspondence\
, we study the category of reflexive modules over (commutative or non-comm
utative) Noetherian rings. One well-established sufficient condition for t
his category to behave well is that the ring should be (commutative) norma
l. We will explain that these nice behaviors are governed by the Auslander
-type conditions which are some requirements on the minimal injective reso
lution of the ring.\n\nhttps://indico.ipmu.jp/event/430/contributions/7545
/
LOCATION:Kavli IPMU\, Kashiwa\, Japan Lecture Hall
URL:https://indico.ipmu.jp/event/430/contributions/7545/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Spherical objects in dimension two and three
DTSTART;VALUE=DATE-TIME:20231220T020000Z
DTEND;VALUE=DATE-TIME:20231220T023000Z
DTSTAMP;VALUE=DATE-TIME:20240907T180522Z
UID:indico-contribution-430-7546@indico.ipmu.jp
DESCRIPTION:Speakers: Wahei Hara (Tokyo)\nDuring this talk we discuss the
classification problem of spherical “like” objects in various geometri
c settings including the minimal resolution of an ADE surface singularity
and a 3-fold flopping contraction. The classification of spherical objects
is related to questions about the autoequivalence groups or Bridgeland st
ability conditions\, but in 3-fold settings this is not always a correct p
roblem to ask. During the talk\, we discuss what kind of objects should be
classified\, and then\, a sketch of the proof will be explained. Our new
technique also can be applied to the heart of a bounded t-structure\, and
classifies all t-structures of the associated null category. As a corollar
y\, the connectedness of the space of stability conditions follows. This i
s all joint work with Michael Wemyss.\n\nhttps://indico.ipmu.jp/event/430/
contributions/7546/
LOCATION:Kavli IPMU\, Kashiwa\, Japan Lecture Hall
URL:https://indico.ipmu.jp/event/430/contributions/7546/
END:VEVENT
BEGIN:VEVENT
SUMMARY:The invariant Hilbert scheme of the Cox realization
DTSTART;VALUE=DATE-TIME:20231218T020000Z
DTEND;VALUE=DATE-TIME:20231218T023000Z
DTSTAMP;VALUE=DATE-TIME:20240907T180522Z
UID:indico-contribution-430-7552@indico.ipmu.jp
DESCRIPTION:Speakers: Ayako Kubota (Waseda)\nThe invariant Hilbert scheme
is a moduli space of schemes which are stable under an action of a reducti
ve algebraic group. By a suitable choice of the parameter\, it becomes a c
andidate for a resolution of singularities of an affine quotient variety v
ia the so-called Hilbert-Chow morphism. In this talk\, we will focus on th
e Cox realization as a way to represent an affine singularity as a quotien
t variety and consider the associated invariant Hilbert scheme.\n\nhttps:/
/indico.ipmu.jp/event/430/contributions/7552/
LOCATION:Kavli IPMU\, Kashiwa\, Japan Lecture Hall
URL:https://indico.ipmu.jp/event/430/contributions/7552/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hilbert schemes and the Le Bruyn-Procesi theorem
DTSTART;VALUE=DATE-TIME:20231218T063000Z
DTEND;VALUE=DATE-TIME:20231218T072000Z
DTSTAMP;VALUE=DATE-TIME:20240907T180522Z
UID:indico-contribution-430-7542@indico.ipmu.jp
DESCRIPTION:Speakers: Alastair Craw (Bath)\nFor a positive integer n and a
finite subgroup \\Gamma in SL(2\,C)\, I’ll describe work in preparation
with Ryo Yamagishi which shows that the Hilbert scheme of n-points on C^2
/\\Gamma is reduced. In fact\, it’s isomorphic to a Nakajima quiver vari
ety\, so it has symplectic singularities and it admits a unique crepant re
solution. This strengthens previous joint work of mine with Gammelgaard\,
Gyenge and Szendroi. The main tool is a generalisation of the Le Bruyn-Pro
cesi theorem which describes the invariant algebra for the natural action
of the product of general linear groups on the space of representations of
a quiver for a given dimension vector.\n\nhttps://indico.ipmu.jp/event/43
0/contributions/7542/
LOCATION:Kavli IPMU\, Kashiwa\, Japan Lecture Hall
URL:https://indico.ipmu.jp/event/430/contributions/7542/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Towards derived Reid’s recipe for dimer models
DTSTART;VALUE=DATE-TIME:20231221T024000Z
DTEND;VALUE=DATE-TIME:20231221T033000Z
DTSTAMP;VALUE=DATE-TIME:20240907T180522Z
UID:indico-contribution-430-7547@indico.ipmu.jp
DESCRIPTION:Speakers: Liana Heuberger (Bath)\nReid's recipe is an equivale
nt of the McKay correspondence in dimension three. It marks interior line
segments and lattice points in the fan of the G-Hilbert scheme with charac
ters of irreducible representations of G. In joint work with Craw and Tapi
a Amador\, we generalise this by marking the toric fan of a crepant resolu
tion of any affine Gorenstein singularity\, in a way that is compatible wi
th both the G-Hilbert case and its categorical counterpart known as Derive
d Reid's Recipe. To achieve this\, we foray into the combinatorial land of
quiver moduli spaces and dimer models. In this talk I will discuss connec
tions between combinatorial and derived Reid's recipe and recent progress
concerning low-valency vertices in the quiver. This is joint work with Ala
stair Craw.\n\nhttps://indico.ipmu.jp/event/430/contributions/7547/
LOCATION:Kavli IPMU\, Kashiwa\, Japan Lecture Hall
URL:https://indico.ipmu.jp/event/430/contributions/7547/
END:VEVENT
BEGIN:VEVENT
SUMMARY:The E10 diagram\, symmetric polytopes and Enriques surfaces
DTSTART;VALUE=DATE-TIME:20231219T010000Z
DTEND;VALUE=DATE-TIME:20231219T015000Z
DTSTAMP;VALUE=DATE-TIME:20240907T180522Z
UID:indico-contribution-430-7557@indico.ipmu.jp
DESCRIPTION:Speakers: Shigeru Mukai (Kyoto)\nThe affine E8 diagram paramet
rizes the irreducible representations of the binary icosahedral groups by
McKay. The next diagram E10\, or T237\, parametrizes a set of symmetric
polyhedra consisting of octa\, dodeca\, icosa and several zonohedra. This
was observed in studying polarization types of Enriques surfaces. In thi
s talk I will present type III degenerations of Enriques surfaces correspo
nding to such symmetric polytopes as many as possible.\n\nhttps://indico.i
pmu.jp/event/430/contributions/7557/
LOCATION:Kavli IPMU\, Kashiwa\, Japan Lecture Hall
URL:https://indico.ipmu.jp/event/430/contributions/7557/
END:VEVENT
BEGIN:VEVENT
SUMMARY:McKay correspondence and perverse schobers
DTSTART;VALUE=DATE-TIME:20231220T073000Z
DTEND;VALUE=DATE-TIME:20231220T080000Z
DTSTAMP;VALUE=DATE-TIME:20240907T180522Z
UID:indico-contribution-430-7553@indico.ipmu.jp
DESCRIPTION:Speakers: Thimothy Logvinenko (Cardiff)\nI will explain how mo
st of the results we know so far about the McKay correspondence in dim = 2
and 3 can be conjecturally packaged up into a single mathematical object
known as a perverse schober. These were proposed by Kapranov and Schechtma
n in 2014 as a categorification of an earlier notion of a perverse sheaf b
y Beilinson\, Bernstein\, and Deligne.\n\nhttps://indico.ipmu.jp/event/430
/contributions/7553/
LOCATION:Kavli IPMU\, Kashiwa\, Japan Lecture Hall
URL:https://indico.ipmu.jp/event/430/contributions/7553/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Distribution of bricks and one-parameter families of stable module
s
DTSTART;VALUE=DATE-TIME:20231220T024000Z
DTEND;VALUE=DATE-TIME:20231220T033000Z
DTSTAMP;VALUE=DATE-TIME:20240907T180522Z
UID:indico-contribution-430-7556@indico.ipmu.jp
DESCRIPTION:Speakers: Kaveh Mousavand (OIST)\nLet A be a finite dimensiona
l associative algebra A over an algebraically closed field k. A (left) A-m
odule M is called a brick if the endomorphism algebra of M over A is isomo
rphic to k. Bricks (also known as Schur representations) play decisive rol
es in the algebraic and geometric aspects of representation theory of alge
bras\, including in the stability conditions\, wall-and-chamber structures
\, (tau-)tilting theory and wide subcategories. In this talk\, I will focu
s on the behavior of the 1-parameter families of stable modules (in the se
nse of King) and discuss some new results on a (still open) conjecture tha
t I first posed in 2019. When restricted to the setting of tame algebras\,
the aforementioned conjecture states that A admits infinitely many non-is
omorphic bricks if and only if there exists a 1-parameter family of stable
modules under a fixed stability condition. I will discuss the conjecture
over arbitrary algebras\, present a reduction theorem in the general case\
, and then prove it for some important families of tame algebras. This tal
k is partially based on my joint work with Charles Paquette.\n\nhttps://in
dico.ipmu.jp/event/430/contributions/7556/
LOCATION:Kavli IPMU\, Kashiwa\, Japan Lecture Hall
URL:https://indico.ipmu.jp/event/430/contributions/7556/
END:VEVENT
BEGIN:VEVENT
SUMMARY:F-blowups of quotient singularities and toric singularities
DTSTART;VALUE=DATE-TIME:20231218T050000Z
DTEND;VALUE=DATE-TIME:20231218T055000Z
DTSTAMP;VALUE=DATE-TIME:20240907T180522Z
UID:indico-contribution-430-7570@indico.ipmu.jp
DESCRIPTION:Speakers: Takehiko Yasuda (Osaka)\nThe F-blowup gives a caonic
al way to construct a birational transform of a singular variety in positi
ve characteristic. There is also a non-commutative counterpart of this con
struction. There are several natural questions concering the F-blowup. Doe
s this blowup give resolution of singularities? If not\, does it improve s
ingularities? Is it close to be a resolution of singularities in a certain
sense? In this talk\, I would like to present some recent results for quo
tient singularities by finite group scheme actions and for toric singulari
ties in this direction\, which were obtained in my joint works with C. Lie
dtke\, E. Chavez-Martinez and D. Duarte.\n\nhttps://indico.ipmu.jp/event/4
30/contributions/7570/
LOCATION:Kavli IPMU\, Kashiwa\, Japan Lecture Hall
URL:https://indico.ipmu.jp/event/430/contributions/7570/
END:VEVENT
BEGIN:VEVENT
SUMMARY:(Derived) Deformations of Crepant Curves
DTSTART;VALUE=DATE-TIME:20231221T010000Z
DTEND;VALUE=DATE-TIME:20231221T015000Z
DTSTAMP;VALUE=DATE-TIME:20240907T180522Z
UID:indico-contribution-430-7568@indico.ipmu.jp
DESCRIPTION:Speakers: Michael Wemyss (Glasgow)\nMotivated by various contr
action conjectures\, I will describe the full A_infty structure associated
to a general (-3\,1)-curve C inside a smooth CY 3-fold. As a corollary\,
the noncommutative deformation theory of C can be described as a superpote
ntial algebra derived from what we call free necklace polynomials\, establ
ishing a suitably interpreted string theory prediction due to Ferrari\, As
pinwall-Katz and Curto-Morrison. This is joint work with Gavin Brown.\n\nh
ttps://indico.ipmu.jp/event/430/contributions/7568/
LOCATION:Kavli IPMU\, Kashiwa\, Japan Lecture Hall
URL:https://indico.ipmu.jp/event/430/contributions/7568/
END:VEVENT
BEGIN:VEVENT
SUMMARY:3d McKay correspondence and 5d SCFTs
DTSTART;VALUE=DATE-TIME:20231220T050000Z
DTEND;VALUE=DATE-TIME:20231220T055000Z
DTSTAMP;VALUE=DATE-TIME:20240907T180522Z
UID:indico-contribution-430-7567@indico.ipmu.jp
DESCRIPTION:Speakers: Yi-Nan Wang (Peking)\nIn theoretical physics\, a lar
ge class of superconformal field theories (SCFTs) can be constructed by pu
tting superstring/M-theory on canonical singularities. In this talk\, I'm
going to mainly discuss the cases of M-theory on C3 orbifold singularities
\, which lead to a large class of 5d SCFTs. Many physical properties of th
e SCFT\, such as rank\, flavor rank and 1-form symmetry can be read off fr
om 3d McKay correspondence. We have also studied new crepant resolutions o
f non-abelian C3 orbifolds. The cases of C4 orbifolds will also be shortly
mentioned in the end.\n\nhttps://indico.ipmu.jp/event/430/contributions/7
567/
LOCATION:Kavli IPMU\, Kashiwa\, Japan Lecture Hall
URL:https://indico.ipmu.jp/event/430/contributions/7567/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Invariant theory of skew polynomial algebras
DTSTART;VALUE=DATE-TIME:20231219T024000Z
DTEND;VALUE=DATE-TIME:20231219T033000Z
DTSTAMP;VALUE=DATE-TIME:20240907T180522Z
UID:indico-contribution-430-7566@indico.ipmu.jp
DESCRIPTION:Speakers: Kenta Ueyama (Shinshu)\nTraces are a classical tool
in (commutative) invariant theory. When studying invariant subalgebras of
noncommutative algebras\, traces also play an essential role. In this talk
\, for skew polynomial algebras\, we provide a generalization of the class
ical formula that expresses the trace series of an automorphism as the rec
iprocal of the reverse characteristic polynomial of it. We then use this g
eneralization to study 'good' automorphisms and 'good' invariant subalgebr
as of skew polynomial algebras. This talk is based on joint work with W. F
rank Moore.\n\nhttps://indico.ipmu.jp/event/430/contributions/7566/
LOCATION:Kavli IPMU\, Kashiwa\, Japan Lecture Hall
URL:https://indico.ipmu.jp/event/430/contributions/7566/
END:VEVENT
BEGIN:VEVENT
SUMMARY:McKay correspondence for Hilb^n(C^3)\, categorical DT theory and g
eometric Langlands
DTSTART;VALUE=DATE-TIME:20231218T010000Z
DTEND;VALUE=DATE-TIME:20231218T015000Z
DTSTAMP;VALUE=DATE-TIME:20240907T180522Z
UID:indico-contribution-430-7565@indico.ipmu.jp
DESCRIPTION:Speakers: Yukinobu Toda (Tokyo)\nThe McKay correspondence for
Hilb^n(C^2) is its derived equivalence with C^{2n}/S_n\, proven by Bridgel
and-King-Reid and Haiman. In this talk\, I will explan how to give its ver
sion for Hilb^n(C^3) using categorical DT theory and its categorical wall-
crossing formula. It involves semiorthogonal decomposition with factors ca
tegorical Hall products of quasi-BPS categories\, which we conjecture to b
e equivalent to the category of matrix factorizations over C^{3n}/S_n with
zero potential. I explain that how (a variant of ) the above conjecture i
s implied by Betti geometric Langlands conjecture. This is a part of my se
ries of joint works with Tudor Padurariu.\n\nhttps://indico.ipmu.jp/event/
430/contributions/7565/
LOCATION:Kavli IPMU\, Kashiwa\, Japan Lecture Hall
URL:https://indico.ipmu.jp/event/430/contributions/7565/
END:VEVENT
BEGIN:VEVENT
SUMMARY:The Euler characteristic of the Fujiki-Oka resolution via continue
d fractions
DTSTART;VALUE=DATE-TIME:20231219T020000Z
DTEND;VALUE=DATE-TIME:20231219T023000Z
DTSTAMP;VALUE=DATE-TIME:20240907T180522Z
UID:indico-contribution-430-7564@indico.ipmu.jp
DESCRIPTION:Speakers: Yusuke Sato (Kogakuin)\nLet G be a finite subgroup o
f SL(n\, C). If a quotient variety C n/G has a crepant resolution\, then i
ts Euler characteristic is equal to the number of conjugacy classes of G\,
which is a weak version of the McKay correspondence. In this talk\, we ge
neralize this correspondence to a finite cyclic group of GL(n\, C). We con
struct this correspondence using certain toric resolutions obtained throug
h continued fractions.\n\nhttps://indico.ipmu.jp/event/430/contributions/7
564/
LOCATION:Kavli IPMU\, Kashiwa\, Japan Lecture Hall
URL:https://indico.ipmu.jp/event/430/contributions/7564/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Classifying torsionfree classes of the category of coherent sheave
s and their Serre subcategories
DTSTART;VALUE=DATE-TIME:20231222T020000Z
DTEND;VALUE=DATE-TIME:20231222T023000Z
DTSTAMP;VALUE=DATE-TIME:20240907T180522Z
UID:indico-contribution-430-7563@indico.ipmu.jp
DESCRIPTION:Speakers: Shunya Saito (Nagoya)\nThe classification of subcate
gories is one of the long-studied topics in the representation theory of a
lgebras. The most classical result is Gabriel's classification of Serre su
bcategories (i.e.\, subcategories closed under taking subobjects\, quotien
ts\, and extensions). He classified the Serre subcategories of the categor
y of coherent sheaves on a noetherian scheme by using specialization-close
d subsets of the scheme. In the case of the module category over a commuta
tive noetherian ring\, various subcategories such as torsion classes (= su
bcategories closed under taking quotients and extensions) and torsion-free
classes (= subcategories closed under subobjects and extensions) are clas
sified. \nIn this talk\, we will talk about an extension of these classifi
cation results to the category of coherent sheaves. A naive extension does
not hold even in the case of projective lines. Therefore\, we consider su
bcategories closed under tensoring with line bundles and show that by impo
sing this condition\, various subcategories of the category of coherent sh
eaves can be classified in the same way as in the case of the module categ
ory. Using these classifications\, we also classify the Serre subcategori
es of the category of torsion-free sheaves over a reduced projective curve
.\n\nhttps://indico.ipmu.jp/event/430/contributions/7563/
LOCATION:Kavli IPMU\, Kashiwa\, Japan Lecture Hall
URL:https://indico.ipmu.jp/event/430/contributions/7563/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Non-commutative crepant resolutions of a special family of stable
set rings
DTSTART;VALUE=DATE-TIME:20231221T073000Z
DTEND;VALUE=DATE-TIME:20231221T080000Z
DTSTAMP;VALUE=DATE-TIME:20240907T180522Z
UID:indico-contribution-430-7554@indico.ipmu.jp
DESCRIPTION:Speakers: Koji Matsushita (Osaka)\nThe existence of non-commut
ative crepant resolutions (NCCRs) for certain classes is one of the most w
ell-studied problems. In this talk\, we discuss the construction of NCCRs
of toric rings using their conic divisorial ideals and we give an NCCR of
a special family of stable set rings\, which are toric rings arising from
graphs.\n\nhttps://indico.ipmu.jp/event/430/contributions/7554/
LOCATION:Kavli IPMU\, Kashiwa\, Japan Lecture Hall
URL:https://indico.ipmu.jp/event/430/contributions/7554/
END:VEVENT
BEGIN:VEVENT
SUMMARY:On derived McKay correspondence between non-commutative deformatio
ns
DTSTART;VALUE=DATE-TIME:20231219T063000Z
DTEND;VALUE=DATE-TIME:20231219T072000Z
DTSTAMP;VALUE=DATE-TIME:20240907T180522Z
UID:indico-contribution-430-7551@indico.ipmu.jp
DESCRIPTION:Speakers: Yujiro Kawamata (Tokyo)\nWe consider an example of d
erived McKay correspondence between non-commutative deformations in the ca
se of surface singularities of type An. \nWe construct a versal NC deforma
tion of the commutative crepant resolution and compare it with the versal
NC deformation of the non-commutative crepant resolution. We show the der
ived McKay correspondence in the case n=1.\n\nhttps://indico.ipmu.jp/event
/430/contributions/7551/
LOCATION:Kavli IPMU\, Kashiwa\, Japan Lecture Hall
URL:https://indico.ipmu.jp/event/430/contributions/7551/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hyperpolygon spaces and their crepant resolutions
DTSTART;VALUE=DATE-TIME:20231221T020000Z
DTEND;VALUE=DATE-TIME:20231221T023000Z
DTSTAMP;VALUE=DATE-TIME:20240907T180522Z
UID:indico-contribution-430-7549@indico.ipmu.jp
DESCRIPTION:Speakers: Austin Hubbard (Bath)\nHyperpolygon spaces are a fam
ily of symplectic singularities in all even dimensions generalising the D4
surface singularity. We present a work in which we describe the Cox rings
of crepants resolutions of hyperpolygon spaces and give a method for enum
erating ALL such crepant resolutions (including non-projective resolutions
).\n\nhttps://indico.ipmu.jp/event/430/contributions/7549/
LOCATION:Kavli IPMU\, Kashiwa\, Japan Lecture Hall
URL:https://indico.ipmu.jp/event/430/contributions/7549/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nc resolutions of finite dimensional commutative algebras via smoo
th surface blow-ups
DTSTART;VALUE=DATE-TIME:20231221T063000Z
DTEND;VALUE=DATE-TIME:20231221T072000Z
DTSTAMP;VALUE=DATE-TIME:20240907T180522Z
UID:indico-contribution-430-7540@indico.ipmu.jp
DESCRIPTION:Speakers: Alexey Bondal (Steklov/Tokyo)\nI will explain how to
get noncommutative resolutions of some finite dimensional commutative alg
ebras via birational morphisms of smooth surfaces. The resolution is given
by the null category which happens to be highest weight category\, whose
projective generator is the discrepancy sheaf.\n\nhttps://indico.ipmu.jp/e
vent/430/contributions/7540/
LOCATION:Kavli IPMU\, Kashiwa\, Japan Lecture Hall
URL:https://indico.ipmu.jp/event/430/contributions/7540/
END:VEVENT
END:VCALENDAR