1 May  2 May  3 May 
Room 309  309(AM)/509(PM)  Room 509 
10:3011:00 Yukari Ito (Nagoya) 
9:3010:30 Takehiko Yasuda (Osaka) 
9:3010:30 Kazushi Ueda (Osaka) 
11:1012:00 Alastair Craw 1 (Glasgow) 
10:4511:45 Michael Wemyss (Edinburgh) 
10:4511:45 Hokuto Uehara (TMU) 
13:0014:00 Timothy Logvinenko (Warwick) 
13:3014:15 Martin Herschend (Nagoya) 
13:3014:15 Laurent Demonet (Nagoya) 
14:1515:00 Yuhi Sekiya (Nagoya) 
14:3015:30 Osamu Iyama (Nagoya) 
14:3015:30 Hiroyuki Minamoto (Nagoya) 
15:3016:30 Alastair Craw 2 (Glasgow) 
16:0016:45 Alvaro Nolla de Celis (UNIR) 

16:4517:45 Akira Ishii (Hiroshima) 
17:0018:00 Miles Reid (Warwick/Sogang) 
<Titles and Abstracts>
Yukari Ito (Nagoya) Introduction to the McKay correspondence
I will talk on existence of crepant resolutions and the McKay correspondence
in dimension three and higher.
Alasatair Craw 1 (Glasgow) Reid's recipe: the past
In his well known (though somewhat speculative) Kinosaki preprint from
1996, Miles Reid introduced a combinatorial cookery with characters of
certain finite abelian subgroups G of SL(3,C) to construct a basis of the
integral cohomology of the GHilbert scheme in each of his examples. I
will give an introductory and opinionated talk about this recipe and its
proof, with the intention of giving the audience several views on this
classical version of Reid's recipe.
Timothy Logvinenko (Warwick) Derived Reid's recipe for abelian subgroups
of SL3(C)
Derived Reid's recipe is a correspodence where we use BKR derived category
equivalence to assign to every irreducible representation of a finite subgroup
of SL_3(C) a subvariety of the exceptional set of the crepant resolution
GHilb C^3 of the quotient singularity C^3/G. This generalises the classical
McKay correspondence for subgroups of SL_2(C) which assigns to each representation
an irreducible exceptional divisor. I discuss a recent work with Alastair
Craw and Sabin Cautis in which we compute derived Reid's recipe for all
abelian subgroups of SL3(C). A new notion of a "CTsubdivision"
allows for a concise demonstration of the ideas at the heart of our main
theorem."
Yuhi Sekiya (Nagoya) McKay correspondence and essential representations
Special McKay correspondence says that, in the two dimensional case, there
is an onetoone correspondence between exceptional curves and special
representations. First I show examples that the minimal resolution is constructed
as a moduli space by using only special representation. In this viewpoint,
I try to extend this result to higher dimensional case.
Alastair Craw 2 (Glasgow) Reid's recipe: the future
I will discuss work in progress on a generalisation of Reid's recipe that
goes well beyond the original context envisaged by Reid. The categorical
viewpoint taken here is inspired by work of CautisLogvinenko and subsequent
work of Logvinenko.
Akira Ishii (Hiroshima) Dimer models and crepant resolutions
We consider variation of moduli spaces of the quiver representations associated
with dimer models and apply it to a problem on derived equivalences.
* * * * *
Takehiko Yasuda (Osaka) Motivic integration and wild group actions
The cohomological McKay correspondence proved by Batyrev is the equality
of an orbifold invariant and a stringy invariant. The former is an invariant
of a smooth variety with a finite group action and the latter is an invariant
of its quotient variety. Denef and Loeser gave an alternative proof of
it which uses the motivic integration theory developped by themselves.
Then I pushed forward with their study by generalizing the motivic integration
to DeligneMumford stacks and reformulating the cohomological McKay correspondence
from the viewpoint of the birational geometry of stacks. However all of
these are about tame group actions (the order of a group is not divisible
by the characteristic of the base field), and the wild (= not tame) case
has remained unexplored.
In this talk, I will explain my attempt to examine the simplest situation
of the wild case. Namely linear actions of a cyclic group of order equal
to the characteristic of the base field are treated. A remarkable new phenomenon
is that the space of generalized arcs is a fibration over an infinite dimensional
space with infinite dimensional fibers, where the base space is the space
of ArtinSchreier extensions of $k((t))$, the field of Laurent series.
Michael Wemyss (Edinburgh) Simultaneous resolution of nonADE surfaces,
and relationship to 3folds.
In ADE surface singularities, it is wellknown that the versal deformation
space admits a simultaneous resolution after base change. For nonADE surfaces,
there are now many components in the versal space, and only one (namely
the Artin component) admits a simultaneous resolution. I will explain how
to achieve this, at least in Type A, using reconstruction algebra techniques.
This has applications in higher dimensional birational geometry, which
I will also explain.
Martin Herschend (Nagoya) nrepresentation infinite algebras constructed
from skewgroup algebras
This talk is based on joint work with Osamu Iyama and Steffen Oppermann.
I will introduce the class of nrepresentation infinite algebras, which
are an analogue of hereditary representation infinite algebras from the
viewpoint of higher dimensional AuslanderReiten theory. These algebras
can be characterized by the fact that their higher preprojective algebras
are (n+1)CalabiYau. Skewgroup algebras of the polynomial algebra by
finite subgroups H of SL_{n+1} are a source of (n+1)CalabiYau algebras.
I will explain how we can realize such skewgroup algebras as preprojective
algebras of nrepresentation infinite algebras for the case when H is abelian.
Osamu Iyama (Nagoya) Algebraic McKay correspondence for nrepresentation
infinite algebras
nrepresentation infinite algebras A give a distinguished class of finite
dimensional algebras of global dimension n. They bijectively correspond
to bimodule (n+1)CalabiYau algebras B of Gorenstein parameter 1 (AmiotIReiten,
Keller, MinamotoMori). For a nice idempotent e, the algebra C:=eBe is
a (noncommutative) Gorenstein algebra, and the derived/cluster category
of A/e is triangle equivalent to the stable category of (graded) CohenMacaulay
Cmodules. This gives a higher dimensional generalization of Auslander's
algebraic McKay correpondence. This talk is based on joint works with AmiotReiten
and HerschendOppermann.
Alvaro Nolla de Celis (UNIR) On quotients by nonAbelian intransitive groups
in SL(3,C) and their resolutions
Intransitive subgroups in SL(3,C) are groups isomorphic to finite subgroups
of GL(2,C), and they constitute a nice family to test several aspects of
the McKay correspondence with nonAbelian groups. I will introduce this
class of subgroups and give the ingredients to calculate GHilb in this
cases.
Miles Reid (Warwick/Sogang) Crepant resolutions and AHilb for 1/r(a,b,1,1,..,1)
An easy ndimensional result says (in the coprime case) that 1/r(a,b,1,1,..,1)
has a crepant resolution resolution if and only if the point nearest the
(x1=0) face is (1,r(n2)c1,c,.. c) (c repeated n2 times) with (n2)c
 1 < r, and every entry of the HirzebruchJung continued fraction of
r/(r(n2)c1) is == 2 mod n2. The calculation of AHilb in these cases
by an algorithm in the style of Nakamura and CrawReid is also interesting,
although it gets somewhat trickier as n gets larger.
* * * * *
Kazushi Ueda (Osaka) On orbifold projective lines and their higerdimensional generalizations
We first recall the theory of weighted projective lines in the sense of
Geigle and Lenzing, and its application to McKay correspondence.
Then we discuss generalizations to higher dimensions.
Hokuto Uehara (TMU) Frobenius morphisms and derived categories on
two dimensional toric DeligneMumford stacks
For toric DeligneMumford stacks X, we can consider a cerrtain generalization
of Frobenius endomorphism. For such an endomorphism on 2dimensional toric
DeligneMumford stacks X, we show that the pushforward of the structure
sheaf generates the bounded derived category of coherent sheaves on X.
My talk is based on a joint work with Ryo Ohkawa.
Laurent Demonet (Nagoya) Quiver of skewgroup algebras. Application to
hereditary and preprojective algebras
In this talk, we shall present a formula to compute the quiver of a skewgroup
algebra of an algebra given by a quiver and relations by the action of
a semisimple finite group. As an application, we compute the skewgroup
algebras of hereditary and preprojective algebras (in good cases), the
later one generalizing the usual formula of McKay correspondence. We also
explain how to generalize these kind of result to a more abstract setting
(mainly the case of $d$CalabiYau dgalgebras).
Hiroyuki Minamoto (Nagoya) Behavior of Serre functors and skew group rings