Date

2014年11月18日 （火）15:00-16:30

Room

Room 206, RIMS, Kyoto University

Speaker

Manabu Akaho (Tokyo Metropolitan University)

Title

**
Symplectic displacement energy for exact Lagrangian immersions
**

Summary
We give an inequality of the displacement energy for exact Lagrangian
immersions and the symplectic area of punctured holomorphic discs. Our
approach is based on Floer homology for Lagrangian immersions and
Chekanov's homotopy technique of continuations. Moreover, we discuss our
inequality and the Hofer--Zehnder capacity.

Organizer
Kaoru Ono

Date

2014年11月18日 （火）13:00-14:30

Room

Room 206, RIMS, Kyoto University

Speaker

Dingyu Yang (Institut de Mathématiques de Jussieu)

Title

**
Deriving maximality and 4 applications of level-1 structures from
FOOO Kuranishi structures
**

Summary
In this talk, I will sketch elements of polyfold--Kuranishi
correspondence
which perfectly identifies Fukaya-Oh-Ohta-Ono's Kuranishi structures with
Hofer-Wysocki-Zehnder's polyfold Fredholm structures up to germs in two
geometric
ways intertwining associated perturbation theories. These two
aforementioned
structures are abstract geometric structures appearing in the foundational
theory of
moduli spaces in Lagrangian Floer theory and symplectic field theory
respectively.
Polyfold Fredholm theory generalizes the notion of smoothness, and
underpins the
ideal of making domain reparametrization smooth and equipping smooth
structures to
general moduli spaces in symplectic geometry while making almost no extra
choice. As
a finite dimensional approach, a Kuranishi structure is a global way to
consistently
fit together finite dimensional reductions constructed from local
neighborhoods of
moduli spaces, and provides a framework to globally perturb moduli spaces
in spite
of possible dimension jumps when switching to nearby local models. I
defined a
notion of Kuranishi structures by adding maximality and topological
matching
conditions to FOOO's Kuranishi structures; from this, one naturally
obtains a
Hausdorff level-1 good coordinate system, which is a coherent system of
structured
tubular neighborhoods built upon an ordered finite cover and serves as a
device to
overcome dimension jumps (in 4 applications below). I also defined a
notion of a
(global) germ via common refinements possibly increasing local dimensions,
which is
applicable to any version of Kuranishi structures. I will show how to
functorially
obtain these two conditions from any representative (and thus all of its
shrinkings)
within each germ of FOOO's Kuranishi structures, and thus level-1
structures become
available to use to show the following: (i) A germ of FOOO's Kuranishi
structures is
an equivalence class. (ii) We can define and compose maps between germs
(where
level-1 structures define left inverses to chart embeddings), and obtain a
category
of FOOO Kuranishi structure germs. (iii) We can lift local perturbations
using
level-1 structures to globally perturb a Kuranishi structure, and can lift
small
such global perturbation through level-1 refinement to show that
perturbation theory
descends to germs; and combining (i) to (iii), we do not need to compare
different
perturbations constructed using choices for truncated moduli space of
different
finite energy levels and can do a single perturbation for the entire
moduli space,
just as in polyfold theory. (iv) Level-1 structures provide sc-smooth
retract models
for gluing across dimension-jumping coordinate changes and thus convert
FOOO
Kuranishi structures to polyfold Fredholm structures, and a further
polyfold--Kuranishi correspondence for analysis involved in constructing
these
geometric structures would merge methods and results from these two fields
and make
construction of Legendrian symplectic field theory easier and as a common
extension.

Organizer
Kaoru Ono

Date

2014年11月17日 (月) 10:30-12:00

Room

Room 110, RIMS, Kyoto University

Speaker

Naichung Conan Leung (Chinese University of Hong Kong)

Title

**
Witten deformation, A_infinity Morse category and
scattering
**

Date

2014年11月17日 (月) 13:30-15:00

Room

Room 110, RIMS, Kyoto University

Speaker

Naichung Conan Leung (Chinese University of Hong Kong)

Title

**
Donaldson-Thomas invariants for Calabi-Yau fourfolds
**

Organizer
Kaoru Ono

Date

2013年7月18日 (木) 15:00-16:30

Room

Room 006, RIMS, Kyoto University

Speaker

Sheel Ganatra (Stanford University)

Title

**
Symplectic cohomology and duality for the wrapped Fukaya category
**

Abstract
To an exact symplectic manifold M, one can two important
Floer-theoretic invariants: symplectic cohomology SH^*(M) and the
wrapped Fukaya category W(M). We will explain how, when M contains
enough Lagrangians, the natural geometric open-closed string maps
between the Hochschild homology of W(M), symplectic cohomology, and
the Hochschild cohomology of W(M) are all isomorphisms. The induced
isomorphism between Hochschild homology and cohomology is an instance
of a new self-duality for the wrapped Fukaya category, a non-compact
version of a Calabi-Yau structure.

Organizer
Kaoru Ono

Date

2013年7月11日（木）15:00--16:30

Room

Room 006, RIMS, Kyoto University

Speaker

Bai-Ling Wang (Australian National University)

微分トポロジーセミナーと共同開催

Title

**
K-theory virtual fundamental classes for moduli spaces of
stable maps
**

Abstract
In this talk, I will propose K-theory virtual fundamental
classes for moduli spaces of stable map, based on joint work in
progress with Bohui Chen and Jianxun Hu in an attempt to define
quantum K-theory for general symplectic manifolds.

Organizer
K. Ono

Date

2013年5月30日（木）15:30−17:00

Room

Room 006, RIMS, Kyoto University

Speaker

Andrei Pajitnov (Universite Nantes)

Title

**
Twisted Novikov homology, jump loci and non-abelian Hodge theory
**

Abstract
We begin with a brief introduction
to the Novikov homology and circle-valued Morse theory.
Then I will explain our joint work with Toshitake
Kohno about the applications of the Novikov homology
to the jump loci in the homology
with local coefficients, in particular
on compact Kaehler manifolds.

Organizer
K. Ono

Date

April 2 (Tue), 2013, 11:00−12:00,
13:30−14:30, 15:00-16:00

Room

Room 204, RIMS, Kyoto University

Speaker

Naichung Conan Leung (Chinese University of Hong Kong)

Title

**
SYZ mirror transformation**

Organizer
K. Ono

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