## Geometry and related topics セミナー

Date

3月29日 14:00-15:30, 2016

Room

Room 006 → 111, RIMS, Kyoto University

Speaker

Emmy Murphy 氏 (MIT)

Title

**
Weinstein manifolds and flexibility of loose Legendrians
**

Abstract

Weinstein manifolds are a class of open symplectic manifolds, including all smooth affine varieties. By definition they admit a Morse decomposition compatible with the symplectic geometry, which allows us to completely describe their geometry by a collection of Legendrian spheres. For example, the Legendrian contact homology of these spheres gives a computation of the wrapped Fukaya category. On the other hand, the flexibility phenomenon of loose Legendrians gives a partial classification of Weinstein manifolds up to symplectomorphism. We will discuss this flexibility, which is proven using a resolution of certain Legendrian singularities.

Date

3月30日 10:30-12:00, 2016

Room

Room 006 → 111, RIMS, Kyoto University

Speaker

Emmy Murphy 氏 (MIT)

Title

**
Applications of flexibility to constructions of exotic Lagrangian embeddings and immersions
**

Abstract

The h-principle for loose Legendrians tells us that we have far more freedom to isotope loose Legendrians than what one would expect for non-loose Legendrians. For example, a loose Legendrian can be isotoped to become disjoint from any given subset, as long as it is possible topologically. Since the graph of a Legendrian isotopy is a Lagrangian embedding, this gives new methods for constructing Lagrangians which unusual properties. For example, we build compact Lagrangian embeddings in $C^n$ which are not uniruled, and have infinite relative Gromov width. We also show that the number of self-intersections of exact Lagrangian immersions fail to conform to the Arnol'd conjecture philosophy, for example every 3-manifold admits an exact Lagrangian immersion in $C^3$ with a single self-intersection, regardless of total homological rank.

Date

3月31日 10:30-12:00, 2016

Room

Room 111, RIMS, Kyoto University

Speaker

Emmy Murphy 氏 (MIT)

Title

**
Lefschetz fibrations from the perspective of Legendrian Kirby diagrams
**

Abstract

Many Weinstein manifolds are naturally presented as the total space of a Lefschetz fibration. We give an explicit algorithm to translate the Lefschetz fibration picture into a presentation of a Legendrian Kirby diagram. This in turn gives an efficient method to visualize and study the total space of Lefschetz fibrations. On the flexibility side this can be used to demonstrate a number of surprising symplectomorphisms, for example the affine hypersurfaces ${xy^k + z^2 + w^2 = 1}$ are all symplectomorphic, independent of k. On the rigidity side this gives an efficient combinatorial method to compute wrapped Fukaya categories, which can then be applied to homological mirror symmetry. The main advantage of this perspective is that the contact geometry picture has more geometric freedom, which allows us to make a number a geometric simplifications before making pseudo-holomorphic computations.

Date

2月25日 14:00-15:30, 2016

Room

Room 110, RIMS, Kyoto University

Speaker

Ailsa Keating氏 (Columbia University)

Title

**
Homological mirror symmetry for $T_{pqr}$ singularities
**

Date

11月20日 15:00-16:30, 2015

Room

Room 110, RIMS, Kyoto University

Speaker

Yakov Eliashberg 氏 (Stanford University)

Title

**
TBA
**

Date

10月9日 15:00-16:30, 2015

Room

Room 111, RIMS, Kyoto University

Speaker

Patrick Bernard 氏 (ENS, Paris)

Title

**
Variational and viscosity solutions of the Hamilton-Jacobi equation
**

Date

7月16日, July 16, 2015

Room

Room 006, RIMS, Kyoto University

Speaker

13:30-15:00 石田裕昭氏 (京大数理研)

Hiroaki Ishida (RIMS, Kyoto University)

Title

**
Equivariant basic cohomology (in progress)
**

Speaker

15:30-17:00 江孟蓉 (River Chiang) 氏 (国立成功大学, 台湾)

River Chiang (National Cheng Kung University, Taiwan)

Title

**
TBA
**

Date

6月11日 15:00-16:30, 2015

Room

Room 420, RIMS, Kyoto University

Speaker

Garrett Alston 氏 (University of Oklahoma)

Title

**
Legendrian DGA as Immersed Floer Theory
**

Abstract

An embedded Legendrian in a contact manifold of the form P x R can be interpreted as an immersed Lagrangian in P. I will explain how the Floer theory of the immersed Lagrangian contains the information of the Legendrian dga. I will also give some conjectural SFT-type applications to non-compact Lagrangians.

Date

4月1日 15:00-16:30 2015

Room

Room 006, RIMS, Kyoto University

Speaker

Sobhan Seyfaddini (MIT)

Title

**
Toward a dynamical interpretation of Hamiltonian spectral invariants on surfaces**

Date & Place

March 12, RIMS Room 206, 2015

Time & Speaker

15:00-16:30 Thomas Schick (Gottingen)

Title

**
Differential K-theory
**

Date & Place

March 25, RIMS Room 110

Time & Speaker

10:30-11:30 Sobhan Seyfaddini (MIT)

Title

**
Coisotropic submanifolds and $C^0$-symplectic geometry
**

Time & Speaker

13:30-14:30 Otto van Koert (Seoul National University)

Title

**
Contact homology and some of its problem
**

Time & Speaker

16:30-17:30 Erkao Bao (UCLA)

Title

**
Definition of contact homology in dimension three (I)
**

Date & Place

March 26, RIMS Room 110

Time & Speaker

10:30-11:30 Otto van Koert (Seoul National University)

Title

**
Nonfillable contact manifolds
**

Time & Speaker

13:30-14:30 Erkao Bao (UCLA)

Title

**
Definition of contact homology in dimension three (II)
**

Date & Place

March 27, RIMS Room 110

Time & Speaker

10:30-11:30 Otto van Koert (Seoul National University)

Title

**
Symplectic and equivariant symplectic homology
**

Time & Speaker

13:30-14:30 Erkao Bao (UCLA)

Title

**
Definition of contact homology in dimension three (III)
**

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
**

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
**

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
**

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
**

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
**

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
**

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**