===================== Monday ==========================
Speaker:
Title: The geography of symplectic 4-manifolds
with b_2^+=1
One of fundamental problems in symplectic 4-manifolds
is to find a new manifold which was not known before. Even though gauge theory
has been very successful in finding a new family of symplectic
4-manifolds, most known constructions produce symplectic
4-manifolds with b_2^+ large. In the case of b_2^+ small, in particular b_2^+
=1, until now there has been little progress. In this talk I'll review known symplectic 4-manifolds with b_2^+=1 and I'll present a new
family of simply connected symplectic 4-manifolds
with b_2^+=1 which have not been known before. My talk will be based on the
following three articles:
1. D. McDuff and D. Salamon, A survey of symplectic 4-manifolds with b_2^+ =1, Turkish Jour. Math. 20 (1996), 47--61
2. J. Park, Non-complex
symplectic 4-manifolds with b_2^+ =1, Bull.
3. J. Park, Simply connected symplectic
4-manifolds with b_2^+=1 and c_1^2 =2, To appear in
Invent. Math. (2004)
Speaker: Shinobu Hosono
Title: Central charges and period integrals in
local mirror symmetry
I introduce a cohomology-valued
hypergeometric series which naturally arises in the
description of local mirror symmetry. I identify it as a central charge formula
for BPS states and study its monodromy property from
the viewpoint of homological mirror symmetry. In case of local mirror symmetry,
I will make an explicit conjecture about an integral and symplectic
monodromy property of the central charges. I will
also present a closed formula of the prepotential at
genus zero. This talk is based on the preprint hep-th/0404043.
=================== Tuesday
==========================
Speaker: Kaoru Ono
Title: Floer-Novikov cohomology and the flux conjecture
The flux conjecture states that the group
of Hamiltonian diffeomorphisms is closed in the symplectomorphism group with respect to C^1-topology. This
claim is equivalent to that the flux group is closed in the first de Rham cohomology group. I plan to
speak about a proof based on Floer-Novikov cohomology.
Speaker: Young-Hoon Kiem
Title: Intersection cohomology
of symplectic reductions
The symplectic
reductions of proper Hamiltonian spaces are often singular and naturally
stratified with even dimensional strata. In this talk, I present a way to compute the
middle perverstiy intersection cohomology
of symplectic reductions by embedding it into
the equivariant
cohomology of the zero level set of the moment map which is computable by
the Atiyah-Bott-Kirwan
theory. This talk is based on the following articles:
1. Y.-H. Kiem, Intersection cohomology of quotients of
nonsingular varieties, Inv. Math. 155 (2004),
pp163--202.
2. Y.-H. Kiem and J.M. Woolf, Intersection cohomology of symplectic
quotients by circle actions, to appear in Jour. Lond.
Math. Soc.
3. Y.-H. Kiem and J.M. Woolf,
The Kirwan map for singular symplectic
quotients, Preprint.
Speaker: Martin Guest
Title: Quantum differential equations
We shall discuss "abstract quantum cohomology D-modules", that is,
D-modules which have similar properties to the D-modules associated to (small)
quantum cohomology. Various examples will be
presented.
Spearker: Kyungho
Oh
Title: On conectedness
of the space of maps to the moduli spaces of curves.
We would like to discuss connectedness of the
spaces of maps from P^1 to the moduli spcae of stable curves
Speaker: Atsushi Takahashi
Title: Categories of D-branes in
Landau-Ginzburg Orbifolds.
We will give a
mathematical definition of the category of D-branes in Landau-Ginzburg
Orbifold. We will show that the category for the A_n singularity orbifoldized
by Z_{n+1} is equivalent as a triangulated cateory to the derived category of representations of the A_n quiver.
============== Wednesday =================================
Speaker: Hiroaki Kanno
Title: Nekrasov's partition function and (generalized) Gopakumar-Vafa invariants
Speaker: Hoil Kim
Title: Symmetry for quantum torus
We describe the symmetry for quantum tori comparing with the case of classical one. This is a
slight extension of the works by Rieffel, Schwarz, Manin etc.
Spearker:
Michi-aki Inaba
Title:
Moduli of parabolic connections on a curve and
Riemann-Hilbert correspondence
We will introduce a moduli space of stable parabolic
connections on a curve and will show that the Riemann-Hilbert correspondence
gives an analytic resolution of singularities of the moduli
space of representations of a fundamental group.
Speaker: Masao Jinzenji
Title: Quantum Cohomology
of General Type Hypersurfaces : Mirror Computation
and Interpretation
Speaker: Masa-Hiko Saito
Geometry of equations of Painleve type
Differential
equations of Painleve type are endowed with rich
geometric structure and related to many integrable
systems. Based on joint works with Inaba and Iwasaki
on the moduli space of stable parabolic connections
and Riemann-Hilbert correspondence, we will try to give a clear and complete pitcture of the geometric structure of these equations,
such as isomonodrmic deformations of connections, Backlund transformations, tau
functions as well as its relation to the moduli space
of Higgs bundles.
=========================== Thursday
========================
Speaker: Hirosh Ohta
Title: Rigidity and flexibility of symplectic fillings and normal surface singularities
The topology of symplectic
filling 4-manifold of the link of a normal surface singularity is deeply
related to the property of the singularity. I will present rigidity or
semi-rigidity of the topology for the cases of simple singularities and simple
elliptic singularities. I will also report some flexible aspect for the case of
certain singularities of genera type. This is based on joint works with Kaoru
Ono.
Speaker: Seungsu Hwang
Title: The critical point equation on a compact
manifold
On a compact n-dimensional manifold M^n, a critical point of the total scalar curvature
functional, restricted to the space of metrics with constant scalar curvature
of volume 1, satifies the critical point equation
(CPE), given by s^*_g(f)=z_g.
It has been conjectured that a solution (g,f)
of CPE is Einstein. We survey and list some of the recent partial results of
the conjecture.
Speaker:
Title: Instanton counting
Nekrasov defined a partition function by using the equivariant intersection theory of the framed moduli spaces of coherent sheaves on P^2. I want to talk
about joint works with H. Nakajima and L. Goettsche
on Nekrasov's partition function.
Speaker: Urs Frauenfelder
Title: Finite dimensional approximations for the symplectic vortex equations
We study Furuta's
finite dimensional approximations for the symplectic
vortex equations for toric symplectic
orbifolds. These are the analogon
of the finite dimensional approximations for the Seiberg-Witten
equations studied by Kronheimer and Manolescu. We prove that the Conley indices of the flow on
the finite dimensional approximations are well defined and their pointed homotopy type is given by the Thom space of the normal
bundle of Givental's toric
map space.
Speaker: Jinhong Kim
Title: Periodic diffeomorphisms
of homotopy K3 surfaces
Every holomorphic
cyclic action of prime order on a K3 surface is known to be homologically
trivial in a certain sense. One can ask the same question for periodic diffeomorphisms of prime order on a K3 surface, as in the
Problem 4.124 of the Kirby's problem list. In this talk we address some recent
progress on the question using the stable homotopic
interpretation of the
Seiberg-Witten
invariants.
==================== Friday ==========================================
Speaker: Yong Seung Cho
Title: Symplectic
Cut and its Applications
Suppose that M
is a symplectic manifold with a Hamiltonian circle
action and a moment map m: M à R .
We introduce Lerman's symplectic
cut which is a generalization of the blow-up construction. We may apply the symplectic cut to Riemann surfaces to calculate the Hurwitz
number which is the number of ramified covering of Riemann surface by Riemann
surface. Also the symplectic cut allows us to reprove
the Kalkman's localization theorem from the Berline-Vergue localization theorem.
Speaker: Kyoji Saito
Title: The
semi-algebraic geometry of the braid groups and Artin groups
It is well known that the fundamental group of the
regular orbit space of a finite reflection group (so called the configuration
space) is a generalized braid group or an Artin
group. In this talk, I'll explain how the flat structure on the orbit space is
used to determine the fundamental group.