Geometry and related topics セミナー

Date

7月19日 14:00-16:00, 2016

Room

Room 402, RIMS, Kyoto University

Speaker

Jake Solomon氏 (Hebrew University)

Title

TBA

Organizer K. Ono

Date

5月20日 16:00-17:00, 2016

Room

Room 204, RIMS, Kyoto University

Speaker

Viktor Ginzbrug氏 (UC Santa Cruz)

Title

Random chain complexes

Organizer K. Ono

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.

Organizer K. Ono

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

Organizer K. Ono

Date

11月20日 15:00-16:30, 2015

Room

Room 110, RIMS, Kyoto University

Speaker

Yakov Eliashberg 氏 (Stanford University)

Title

TBA

Organizer K. Ono

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

Organizer K. Ono

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

Organizer K. Ono

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.

Organizer K. Ono

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

Organizer K. Ono

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)

Organizer Kaoru Ono

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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