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
