2024 RIMS-IBSCGP
Conference on Recent Developments in Symplectic Topology
November 4–8, 2024
IBS POSTECH Campus
Organizers
- Dongwook Choa (IBS Center for Geometry and Physics)
- Yong-Geun Oh (IBS Center for Geometry and Physics & POSTECH)
- Kaoru Ono (RIMS, Kyoto University)
Invited Lecturers
- Mohammed Abouzaid (Stanford University)
- Cheol-Hyun Cho (Seoul National University)
- Egor Shelukhin (Université de Montréal)
Invited Speakers
- Jongmyeong Kim (Seoul National University)
- Yoosik Kim (Pusan National University)
- Takahiro Oba (Osaka University)
- Yukihiro Okamoto (RIMS, Kyoto University)
- Semon Rezchikov (Princeton University)
- Taisuke Shibata (RIMS, Kyoto University )
- Yoshihiro Sugimoto (Nagasaki University)
- Toru Yoshiyasu (Kyoto University of Education)
- Jun Zhang (University of Science and Technology of China)
- Zhengyi Zhou (Chinese Academy of Science)
Venue
IBS POSTECH Campus Bldg. #301
*For the location of the conference site, click here for google map.
Registration
Online registration is not available.
Program
| Nov 4 (Mon) | Nov 5 (Tue) | Nov 6 (Wed) | Nov 7 (Thu) | Nov 8 (Fri) | |
|---|---|---|---|---|---|
| 09:30 – 10:00 | Welcome and Registration |
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| 10:00 – 11:00 | Takahiro Oba | Zhengyi Zhou | Toru Yoshiyasu | [Lecture Series-B] Mohammed Abouzaid |
[Lecture Series-C] Cheol-Hyun Cho |
| 11:00 – 11:20 | Break / Teatime | ||||
| 11:20 – 12:20 | Jongmyeong Kim | Yukihiro Okamoto | Semon Rezchikov | [Lecture Series-C] Cheol-Hyun Cho |
[Lecture Series-B] Mohammed Abouzaid |
| 12:20 – 14:00 | Lunch | ||||
| 14:00 – 15:00 | Jun Zhang | [Lecture Series-A] Egor Shelukhin |
Free Afternoon | [Lecture Series-C] Cheol-Hyun Cho |
Free Discussion & Closing |
| 15:00 – 15:15 | Break / Teatime | Break / Teatime | |||
| 15:15 – 16:15 | [Lecture Series-A] Egor Shelukhin |
Yoosik Kim | [Lecture Series-A] Egor Shelukhin |
||
| 16:15 – 16:30 | Break / Teatime | Break / Teatime | |||
| 16:30 – 17:30 | Yoshihiro Sugimoto | Taisuke Shibata | [Lecture Series-B] Mohammed Abouzaid |
||
| 17:30 – 20:00 | Photo Session & Banquet |
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Abstract
Monday, November 4
| Time | Speaker | Title & Abstract |
|---|---|---|
| 10:00 – 11:00 | Takahiro Oba (Osaka University) |
Symplectic fillings of unit cotangent bundles of spheres This talk is concerned with symplectic fillings of contact manifolds. After briefly giving an overview of results on the topology of symplectic fillings, I will present joint work with Myeonggi Kwon, where we give some topological restrictions on symplectic fillings of unit cotangent bundles of spheres. In particular, we show a uniqueness result on diffeomorphism types of them, under certain condition, for the case where the base manifold is a 3-sphere. Additionally, I will explain an application of our result to exact symplectic cobordisms. |
| 11:20 – 12:20 | Jongmyeong Kim (Seoul National University) |
Cluster categories from Fukaya categories A cluster category can be obtained as the quotient of a certain (non-proper) triangulated category by a proper subcategory satisfying a relative Calabi-Yau property. In this talk, I will explain this construction can be applied to the wrapped and compact Fukaya categories of a Liouville manifold with a nice generator. This is based on a joint work with Hanwool Bae and Wonbo Jeong. |
| 14:00 – 15:00 | Jun Zhang (University of Science and Technology of China) |
Spectral capacities of submanifolds In this talk, we will discuss how to measure the size of submanifolds in a symplectic manifold. This is based on symplectic invariants that are constructed from spectra extracted from (Hamiltonian) Floer theory. Moreover, these invariants are concrete examples of spectral capacities. We will use these capacities to demonstrate the fundamental differences between Lagrangian submanifolds and symplectic submanifolds (or more generally nowhere coisotropic submanifolds). Meanwhile, we will also prove a quantitative Lagrangian control estimate that intriguingly relates these invariants. This talk is based on joint work with Dylan Cant. |
| 15:15 – 16:15 | Egor Shelukhin (Université de Montréal) |
Power operations and Hamiltonian dynamics Power operations in Floer cohomology have recently seen fruitful applications to Hamiltonian dynamics. We will describe this emerging subfield along with a few recent developments. Some of the results we will mention are based on joint works with Jingyu Zhao, Marcelo Atallah, and Nicholas Wilkins. |
| 16:30 – 17:30 | Yoshihiro Sugimoto (Nagasaki University) |
Homological Lagrangian monodromy Given a Lagrangian submanifold and a Hamiltonian diffeomorphism which preserves the Lagrangian submanifold, we have a monodromy of the singular homology of the Lagrangian submanifold. In this talk, I explain that the monodromy is trivial if the Hofer norm of the Hamiltonian isotopy is sufficiently small. I also treat the monodromy of Lagrangian quantum homology (Floer homology). |
Tuesday, November 5
| Time | Speaker | Title & Abstract |
|---|---|---|
| 10:00 – 11:00 | Zhengyi Zhou (Chinese Academy of Science) |
Kahler compactification of C^n and Reeb dynamics. I will present two results in complex geometry: (1) A Kahler compactification of C^n with a smooth divisor complement must be P^n, which confirms a conjecture of Brenton and Morrow under the Kahler assumption; (2) Any complete asymptotically conical Calabi-Yau metric on C^3 with a smooth link must be flat, confirming a modified version of Tian's conjecture regarding the recognition of the flat metric among Calabi-Yau metrics in dimension 3. Both proofs rely on relating the minimal discrepancy number of a Fano cone singularity to its Reeb dynamics of the conic contact form. This is a joint work with Chi Li. |
| 11:20 – 12:20 | Yukihiro Okamoto (RIMS, Kyoto University) |
Legendrian non-isotopic unit conormal bundles in higher dimensions For any compact submanifold of R^n, its unit conormal bundle is a compact Legendrian submanifold of the unit conormal bundle of R^n. In this talk, I will give examples of pairs of compact connected submanifolds of R^n of codimension greater than 3 such that their unit conormal bundles are not Legendrian isotopic, although these two Legendrian submanifolds cannot be distinguished by classical invariants. The main tools to distinguish them are the strip Legendrian contact homology and a coproduct on it, which are defined under certain conditions on Legendrian submanifolds. I will show that, in a special case including the main examples, the coproduct can be computed by using the idea of string topology. |
| 14:00 – 15:00 | Egor Shelukhin (Université de Montréal) |
Power operations and Hamiltonian dynamics Power operations in Floer cohomology have recently seen fruitful applications to Hamiltonian dynamics. We will describe this emerging subfield along with a few recent developments. Some of the results we will mention are based on joint works with Jingyu Zhao, Marcelo Atallah, and Nicholas Wilkins. |
| 15:15 – 16:15 | Yoosik Kim (Pusan National University) |
Cluster algebras and monotone Lagrangian tori Cluster algebras, introduced by Fomin and Zelevinsky as a combinatorial framework for understanding the dual canonical basis, are powerful tools in symplectic topology. In this talk, I will explain how cluster algebras can be used to construct and distinguish monotone Lagrangian tori in a smooth Fano variety that is a compactification of a cluster variety. Using the framework, I will construct distinct infinitely many monotone Lagrangian tori in most partial flag varieties. This talk is based on ongoing joint work with Yunhyung Cho, Myungho Kim, and Euiyong Park. |
| 16:30 – 17:30 | Taisuke Shibata (RIMS, Kyoto University) |
Existence of infinitely many simple positive hyperbolic orbits in convex Reeb flows A closed 3-dimensional Reeb orbit can be classified into three types: positive hyperbolic, negative hyperbolic, and elliptic. Cristofaro-Gardiner, Hutchings, and Pomerleano proved that if a contact 3-manifold has a positive first Betti number, then there exists at least one simple positive hyperbolic orbit. They also conjectured that every contact 3-manifold (with limited exceptions) contains such an orbit. In this talk, we will show that certain Reeb flows on lens spaces with convexity have infinitely many simple positive hyperbolic orbits. |
Wednesday, November 6
| Time | Speaker | Title & Abstract |
|---|---|---|
| 10:00 – 11:00 | Toru Yoshiyasu (Kyoto University of Education) |
Contact contractions and Liouville domains Recently, Yang Huang gave a new construction of Liouville domains. It is a suspension of a compact contact manifold by a contactly contracting map, called a contact contraction. In this talk, I will give a necessary condition for the existence of such maps and some examples of Liouville domains via Huang's construction. This is a joint work in progress with Noboru Ogawa. |
| 11:20 – 12:20 | Semon Rezchikov (Princeton University) |
Applications of Symmetries in Symplectic Floer Homology Often, geometric situations have symmetries, and these symmetries enhance the invariants of the geometric situation at hand. This talk will explain how symmetry enhances Floer theoretic invariants to objects of the genuine equivariant stable homotopy category, and will explain various applications of this technique to concrete problems in enumerative geometry (namely, to the quantum Steenrod operations) and to symplectic and low-dimensional topology. |
Thursday, November 7
| Time | Speaker | Title & Abstract |
|---|---|---|
| 10:00 – 11:00 16:30 – 17:30 |
Mohammed Abouzaid (Stanford University) |
Floer homotopy via flow modules I will describe joint work with Blumberg, starting with the results appearing in arXiv:2404.03193, whose goal is to build a foundation for the study of the interaction between generalised homology and Floer theory. The key idea is to interpret flow categories, due to Cohen-Jones-Segal, as objects of a category whose morphisms we call flow bimodules. While Morse and Floer complexes give rise to flow categories, continuation maps between them give rise to flow bimodules. These constructions have many flavours, as one can consider flow categories whose morphisms spaces are manifolds, equipped with various tangential structures, or more generally orbifolds or derived orbifolds. These variants are designed to accommodate specific Floer-theoretic applications, such as studying Floer theory on Liouville manifolds, or on general closed symplectic manifolds, as I will illustrate by discussing Hamiltonian Floer cohomology. |
| 11:20 – 12:20 14:00 – 15:00 |
Cheol-Hyun Cho (Seoul National University) |
Floer theory for singularities I,II,III Lecture 1. We give an introduction for singularity theory and an overview on some of the recent symplectic developments. Lecture 2. We consider popsicle maps with insertions and their compactifications. This leads to a construction of Fukaya category of Landau-Ginzburg orbifolds of log Fano and Calabi-Yau Type (joint work with Choa and Jeong) Lecture 3. Variation operator associated with an isolated singularity is an isomorphism between the relative homology and the absolute homology of the Milnor fiber. We study a Lagrangian Floer theoretic version of this operator. We will examine the case of plane curve singularities. (joint works with Bae, Choa,Jeong and Portilla) |
| 15:15 – 16:15 | Egor Shelukhin (Université de Montréal) |
Power operations and Hamiltonian dynamics Power operations in Floer cohomology have recently seen fruitful applications to Hamiltonian dynamics. We will describe this emerging subfield along with a few recent developments. Some of the results we will mention are based on joint works with Jingyu Zhao, Marcelo Atallah, and Nicholas Wilkins. |
Friday, November 8
| Time | Speaker | Title & Abstract |
|---|---|---|
| 10:00 – 11:00 | Cheol-Hyun Cho (Seoul National University) |
Floer theory for singularities I,II,III Lecture 1. We give an introduction for singularity theory and an overview on some of the recent symplectic developments. Lecture 2. We consider popsicle maps with insertions and their compactifications. This leads to a construction of Fukaya category of Landau-Ginzburg orbifolds of log Fano and Calabi-Yau Type (joint work with Choa and Jeong) Lecture 3. Variation operator associated with an isolated singularity is an isomorphism between the relative homology and the absolute homology of the Milnor fiber. We study a Lagrangian Floer theoretic version of this operator. We will examine the case of plane curve singularities. (joint works with Bae, Choa,Jeong and Portilla) |
| 11:20 – 12:20 | Mohammed Abouzaid (Stanford University) |
Floer homotopy via flow modules I will describe joint work with Blumberg, starting with the results appearing in arXiv:2404.03193, whose goal is to build a foundation for the study of the interaction between generalised homology and Floer theory. The key idea is to interpret flow categories, due to Cohen-Jones-Segal, as objects of a category whose morphisms we call flow bimodules. While Morse and Floer complexes give rise to flow categories, continuation maps between them give rise to flow bimodules. These constructions have many flavours, as one can consider flow categories whose morphisms spaces are manifolds, equipped with various tangential structures, or more generally orbifolds or derived orbifolds. These variants are designed to accommodate specific Floer-theoretic applications, such as studying Floer theory on Liouville manifolds, or on general closed symplectic manifolds, as I will illustrate by discussing Hamiltonian Floer cohomology. |
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Accommodation
We regret to say that we cannot support your travel and local expenses unless the conference promised to pay.
For booking accommodation in Pohang, please contact the hotel directly referring the list below.
There is a limited number of rooms available, so please make a reservation as soon as you can.
| Room Type | POSCO Int'l Center | Hotel Yeongildae | Apple Tree Hotel | Tour de Pohang (Woman's Safety Sohotel) |
|---|---|---|---|---|
| Double Room | 90,200 KRW | 110,000 KRW | 45,000 KRW | 43,000 ~ 48,000 KRW (1 person) |
| Twin Room | 90,200 KRW | 132,000 KRW | - | 58,000 ~ 63,000 KRW (2 persons) |
| Breakfast (1 person) |
13,200 KRW | Free | Free | Free |
| Distance from Venue | 5 min. drive | 15 min. drive | 15 min. drive | 15 min. drive |
| Contact | +82-54-279-8500 | +82-54-280-8900 | +82-54-241-1234 | +82-0507-1397-1234 |
* The above rate and condition may vary.
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Contact
Soon Ok Jung (sojung@ibs.re.kr)
