## Seminar on Geometry and Related Topics

Date

June 27(Thu) 15:00-17:00, 2024

Place

Room 201 in Building No.15, RIMS, Kyoto University

Speaker

Emmy Murphy (University of Toronto)

Title

**
Obstructions to Lagrangian surgery
**

Abstract

Given a Lagrangian immersion with a transverse double point, we can surger this point to obtain an embedded Lagrangian with more complicated topology. As a classical example, both the Clifford and Chekanov tori in C^2 are obtained via Lagrangian surgery on a immersed sphere called the Whitney sphere. In the talk we'll discuss a Floer-theoretic obstruction to this: that is, showing that a Lagrangian cannot be realized as a surgery. An interesting dilemma is that PH invariants of an immersed Lagrangian itself cannot detect the fact that it is immersed. Instead, we have to consider families of Floer invariants coming from all possible surgeries, and use properties specific to SFT Lagrangian cobordism maps.

Date

April 7(Fri) 10:00-12:00, 2023

Place

Room 201 in Building No.15, RIMS, Kyoto University

Speaker

Laura Escobar (Washington University in St.Louis)

Title

**
Wall-crossing phenomenon for Newton--Okounkov bodies
**

Abstract

The interplay between combinatorics and algebraic geometry has immensely enriched both areas. In this context, the theory of Newton--Okounkov bodies has led to the extension of the geometry-combinatorics dictionary from toric varieties to certain varieties which admit a toric degeneration. A Newton--Okounkov body is a convex set associated to a projective variety, equipped with a valuation. Work of Kaveh--Manon gives an explicit link between tropical geometry and Newton--Okounkov bodies. We use this link to describe a wall-crossing phenomenon for Newton--Okounkov bodies. As an example, we describe wall-crossing formula in the case of the Grassmannian Gr(2,m). This is joint work with Megumi Harada.

Date

April 5(Tue) 10:30-12:00, 2023

Place

Room 206, RIMS, Kyoto University

Speaker

Naichung Conan Leung (Chinese University of Hong Kong)

Title

**
Quantizations of Kähler manifolds
**

Date

August 1--5, 2022

Place

Maskawa Hall, North Comprehensive Education and Research Building, Kyoto University

Date and Time

February 21, 2020 15:00-16:30

Room

Room 111, RIMS, Kyoto University

Speaker

Cheol-Hyun Cho (Seoul National University)

Title

**
Homological mirror symmetry for invertible curve singularities
**

Abstract

Given an invertible curve singularity, namely one of $x^p+y^q, x^p+xy^q, x^py+xy^q$, we introduce a constructive method to describe its homological mirror symmetry ( to its Berglund-Hubsch mirror). For the case of ADE singularites, we find interesting relationship between Auslander-Reiten quiver of the mirror singularity and Lagrangian surgery. This is a work in progress with Dongwook Choa and Wonbo Jung.

Date

December 2 -- 4, 2019

Room

Room 110, RIMS, Kyoto University

Date

October 8 (Tuesday) 15:00-16:30, 2019

Room

Room 110, RIMS, Kyoto University

Speaker

Pengfei Guan (McGill University)

Title

**
The Weyl problem and isometric embedding of surfaces in 3-manifolds
**

Abstract

The classical Weyl problem concerns isometric embedding of positively curved compact surface in to $R^3$. The solution by Nirenberg (in 1950s) and Pogorelov's subsequent solution for hyperbolic space $H^3$ play important roles in the definition of quasi-local masses in general relativity, e.g., the Brown-York mass. The recent works of Liu-Yau and Wang-Yau generated some renewed interests on this classical problem: isometric embedding of a given surface $S^2,g)$ to general $3$-manifolds. Of particular interest is the anti de sitter-Schwarzchild space. We will discuss some progress in this direction. When the ambient space is replaced by a general $3$-manifold, local solvablity ( Li-Wang) and a priori estimates (Guan-Lu) can be established from recent works. The existence of such isometric embeddings can be obtained if the topology of the ambient space is trivial. We will discuss some applications and open problems.

Date

February 15, 10:30-12:00, 2019

Room

Room 110, RIMS, Kyoto University

Speaker

Xiaobo Liu (BICMR, Beijing University)

Title

**
Connecting Hodge integrals to Gromov-Witten invariants by Virasoro operators
**

Abstract

Kontsevich-Witten tau function and Hodge tau functions are important tau functions for KP hierarchy which arise in geometry of moduli space of curves. Alexandrov conjectured that these two functions can be connected by Virasoro operators. In a joint work with Gehao Wang, we have proved Alexandrov's conjecture. In a joint work with Haijiang Yu, we show that this conjecture can also be generalized to Gromov-Witten invariants and Hodge integrals over moduli spaces of stable maps to smooth projective varieties.

Date

March 15, 15:00-16:30, 2018

Room

Room 111, RIMS, Kyoto University

Speaker

小川 竜 氏 (東海大学)

Title

**
Levi-flat CR manifolds and the embedding problems
**

Abstract

A Levi-flat CR manifold is an odd dimensional real manifold foliated by complex hypersurfaces. In this talk, we consider the embedding problem of Levi-flat CR manifolds into complex manifolds. Also we focus on the Barrett's non-embeddability theorem and its higher dimensional analogue. This is based on a joint work with Takayuki Koike.

Date

February 16, 15:00-16:30, 2018

Room

Room 110, RIMS, Kyoto University

Speaker

Jack Smith氏 (University College of London)

Title

**
A monotone Lagrangian menagerie
**

Abstract

Apart from a few striking rigidity results, relatively little is known in general about the possible topologies of monotone Lagrangian submanifolds. I will survey some interesting examples, and a selection of techniques for computing or constraining their self-Floer cohomology, some old and some new. A common theme is subtle dependence of the Floer theory on the characteristic of the coefficient ring.

Date

December 20, 14:00-16:00, 2017

Room

Room 111, RIMS, Kyoto University

Speaker

Vivek Shende氏 (UC Berkeley)

Title

**
The conormal torus is a complete knot invariant.
**

Date

December 19, 10:30-12:00, 14:30-16:30, 2017

December 20, 10:00-12:00

Room

Room 111, RIMS, Kyoto University

Speaker

Vivek Shende氏 (UC Berkeley)

Title

**
Localization of Fukaya category
**

Date

June 2, 15:00-16:30, 2017

Room

Room 006, RIMS, Kyoto University

Speaker

Tian-Jun Li氏 (University of Minnesota)

Title

**
The symplectomorphism group of rational surfaces
**

Abstract

I will talk about the joint work with Jun Li and Weiwei Wu on
the topology ofthe symplectomorphism group of a symplectic rational
surface.

We will illustrate our approach with the 5 point blowup of the
projective plane. For an arbitrary symplectic form on this rational
surface, we are able to determine the
symplectic mapping class group and describe the answer in terms of
the Dykin diagram of Lagrangian sphere classes. In this case, we are
also able to compute the fundamental group for an open region of the
symplectic cone.

Date

April 3, 15:00-16:30, 2017

Room

Room 110, RIMS, Kyoto University

Speaker

Tobias Ekholm 氏 (Uppsala University)

Title

**
Legendrian surgery formulas and duality between Lagrangian and Legendrian invariants
**

Abstract

We give a Legendrian surgery formula for partially wrapped Floer cohomology and study (Koszul) duality between wrapped Floer cohomology and ordinary Floer cohomology using the surgery isomorphism. The talk reports on joint work with Y. Lekili.

Date

April 3, 13:00-16:30, 2017

Room

Room 110, RIMS, Kyoto University

Speaker

Naichung Conan Leung氏 (Chinese University of Hong Kong)

Title

**
SYZ for coisotropic A-branes
**

Date

March 21, 15:00-16:30, 2017, Room 110

March 22, 10:30-12:00, 2017, Room 402

Room

Room 110, 402, RIMS, Kyoto University

Speaker

大場貴裕氏 (東京工業大学)

Title

**
Higher-dimensional contact manifolds with infinitely many Stein fillings
**

Date

March 6,7, 13:30-15:00, 2017

Room

Room 110, RIMS, Kyoto University

Speaker

池 祐一氏 (東大数理)

Title

**
Sheaf-theoretic approaches to symplectic geometry
in cotangent bundles
**

Date

February 21, 10:30-12:00, 2017

Room

Room 111, RIMS, Kyoto University

Speaker

Georgios Dimitroglou-Rizell 氏 (Uppsala University)

Title

**
The wrapped Fukaya category of a Weinstein manifold is generated by the Lagrangian cocore discs
**

Abstract

In a joint work with B. Chantraine, P. Ghiggini, and R. Golovko we decompose any object in the wrapped Fukaya category as a twisted complex built from the cocores of the critical (i.e. half-dimensional) handles in a Weinstein handle decomposition. The main tools used are the Floer homology theories of exact Lagrangian immersions, of exact Lagrangian cobordisms in the SFT sense (i.e. between Legendrians), and relations between them. Note that exact Lagrangians admit Legendrian lifts, and that appropriate Lagrange surgeries can be seen to give rise to an exact Lagrangian cobordisms of this type.

Date & Room

2017年2月15日 15:00-16:30, Room 402

2017年2月16日 10:30-12:00, Room 110

Speaker

Georgios Dimitroglou-Rizell 氏 (Uppsala University)

Title

**
Classification of two-dimensional Lagrangian embeddings using pseudoholomorphic foliations
**

Abstract

We describe how the techniques of pseudoholomorphic foliations and neck stretching can be used to derive several strong classification results for Lagrangian embeddings in the four-dimensional setting. Notably, in a joint work with E. Goodman and A. Ivrii, we establish the nearby Lagrangian conjecture in the cotangent bundle of the two-torus. In an ongoing work we also provide a classification up to Hamiltonian isotopy of Maslov-0 Lagrangian tori, as well as spheres with one transverse double point, in the complement of a binodal cubic in the projective plane.

Date

7月29日 15:00-16:30, 2016

Room

Room 111, RIMS, Kyoto University

Speaker

Egor Shelukhin氏 (IAS)

Title

**
Lagrangian cobordisms and measurements
**

Abstract

We describe a natural way of measuring the distance between two (possibly non-isotopic!) Lagrangian submanifolds based on the notion of a Lagrangian cobordism, and study the non-degeneracy or degeneracy properties of the resulting pseudo-metrics, reflecting the rigidity or flexibility of the class of cobordisms considered. This is a joint work with Octav Cornea.

Date

7月19日 14:00-16:00, 2016

Room

Room 402, RIMS, Kyoto University

Speaker

Jake Solomon氏 (Hebrew University)

Title

**
TBA
**

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
**

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**