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Conference on Fukaya Category and
Homological Mirror Symmetry
August 15– 20 , 2019
Peking University
Scientific Committee
Mohammed Abouzaid (Columbia University) Kenji Fukaya(Simons Center)
Chiu-Chu Melissa Liu (Columbia University) Kaoru Ono (RIMS)
Organizing Committee
Bohui Chen (Sichuan University),
Huijun Fan (SMS, Peking University),
Bohan Fang (BICMR, Peking University)
Sponsored by
School of Mathematical Scicence, Peking University
Beijing International Center for Mathematical Research, PekingUniversity
NSFC PKU
CONTENTS
01
Timetable
04
Talk
09
List of participants
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Conference Information
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General Information
Conference on Fukaya Category and Homological Mirror Symmetry is
sponsored by the School of Mathematical Sciences and BICMR at Peking
University. The aim of this conference is to bring the active researchers
together to exchange ideas and report their latest progress in Fukaya
category and the related topics. We commemorate the name “Fukaya
category” which has already been known for more than 20 years, and
celebrate Professor Kenji Fukaya's 60th birth.
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Lecture room: 107 Room, Natural Science Classroom Building (理科教学楼 107 教室)
Timetable
Wednesday, August 14
14:00-20:00 Registration（Yanshan Hotel 燕山大酒店）
Thursday, August 15
9:00-9:30 Opening Remark
Chair: Huijun Fan
9:30-10:30 Kenji Fukaya
10:30-11:00 Group Photo / Coffee Break
11:00-12:00 Cheol-hyun Cho
12:30 Lunch
Chair: Bohui Chen
14:00-15:00 Yusuf Baris Kartal
15:00-15:30 Coffee Break
15:30-16:30 Guangbo Xu
16:30-16:45 Coffee Break
16:45-17:45 Hansol Hong
18:00 Dinner
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Friday, August 16
Chair: Kenji Fukaya
10:00-11:00 Tobias Ekholm
11:00-11:15 Coffee Break
11:15-12:15 Kazushi Ueda
12:30 Lunch
Chair: Jianxun Hu
14:00-15:00 Bai-ling Wang
15:00-15:30 Coffee Break
15:30-16:30 Dingyu Yang
16:30-16:45 Coffee Break
16:45-17:45 Mohammad Tehrani
18:00 Dinner
Saturday, August 17
Chair: Tobias Ekholm
10:00-11:00 Vivek Shende
11:00-11:15 Coffee Break
11:15-12:15 Yanki Lekili
12:30 Lunch
Chair: Cheol-hyun Cho
14:00-15:00 Penka Georgieva
15:00-15:30 Coffee Break
15:30-16:30 Rui Wang
17:30 Dinner
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Sunday, August 18
10:00-18:00
Free Discussion
18:00 Banquet (Yajing Room,Yanshan Hotel)
Monday, August 19
Chair: Kaoro Ono
10:00-11:00 David Nadler
11:00-11:15 Coffee Break
11:15-12:15 Emanuel Scheidegger
12:30 Lunch
Chair: Mohammed Abouzaid
14:00-15:00 Andrew Hanlon
15:00-15:30 Coffee Break
15:30-16:30 Suguru Ishikawa
17:30 Dinner
Tuesday, August 20
Chair: Bohan Fang
10:00-11:00 Siu-Cheong Lau
11:00-11:15 Coffee Break
11:15-12:15 Mohammed Abouzaid
12:30 Lunch
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Talks
Local Fukaya categories (Mohammed Abouzaid) Abstract: I will explain joint work with Yoel Groman and Umut Varolgunes whose purpose is to define a Fukaya category associated to each compact subset of a closed symplectic manifold. Much of the difficulty has to do with curvature, and I will explain how to build the necessary algebraic toolkit to resolve them. Auslander-Reiten quivers of ADE curve singularities and Lagrangian Floer theory (Cheol-Hyun Cho)
Abstract: For ADE singularity, indecomposable Cohen-Macaulay modules (or equivalently $\Z/2$-graded matrix factorizations) are classified and described by Auslander-Reiten quivers. For ADE curve singularity $f(x,y)$, we consider Berglund-H\"ubsch dual singularity $f^t(x,y)$ and their Milnor fiber together with diagonal symmetry group $G$. We consider $G$-equivariant Lagrangian Floer theory of the Milnor fiber to construct a full functor to matrix factorization category of $f$, And discuss the relationship of AR quiver and Lagrangian Floer theory. This is a joint work with Dongwook Choa and Wonbo Jung. Augmentation, Alexander polynomial, and Annuli (Tobias Ekholm) Abstract: We give a formula for the Alexander polynomial of a knot in terms of its Augmentation polynomial. The formula gives a certain deformation of the Alexander polynomial. Lagrangian Floer theory of Divisor complement (Kenji Fukaya) Abstract: I report a work in progress on the Lagrangian Floer theory of divisor complement.I will explain how the `Myer Vietoris type sequence' of Lagrangian Floer homology is expected to be obtained when family of symplectic manifolds degenerates to a union of two symplectic manifolds which intersect transversally on the smooth divisor. A Klein TQFT : the local real Gromov-Witten theory of curves（Penka Georgieva）
Abstract: The local Gromov-Witten theory of curves studied by Bryan and Pandharipande revealed strong structural results for the local GW invariants, which were later used by Ionel and Parker in the proof of the Gopakumar-Vafa conjecture.
In this talk I will report on a joint work with Eleny Ionel on the extension of these results to the real setting. We show that the local real GW theory gives rise to a 2-dimensional Klein TQFT defined on an extension of the category of unorientable surfaces.
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We use this structure to completely solve the theory by providing a closed formula for the local real GW invariants in terms of representation theoretic data. As a corollary we obtain the local version of the real Gopakumar-Vafa formula. In the case of the resolved conifold the partition function of the real GW invariants agrees with that of the SO/Sp Chern-Simons theory on S^3. Monomial admissibility and monodromy (Andrew Hanlon)
Abstract: We will discuss monomial admissibility conditions for Laurent polynomials and their corresponding Fukaya-Seidel categories. This discussion will include the relationship of this definition of the Fukaya-Seidel category with more traditional definitions. We will use this framework to compute certain monodromy functors and natural transformations in the mirror to a smooth compact toric variety and their relationship with homological mirror symmetry. Noncommutative resolutions of singularities from Lagrangian deformation (Hansol Hong)
Abstract: Given a Lagrangian in a symplectic manifold, one can consider its Maurer-Cartan deformation which produces a local chart of the mirror that encodes mirror geometry near this Lagrangian. Construction applies to the union of Lagrangian spheres in a certain open symplectic manifold, and produces noncommutative resolutions of well-known algebraic singularities, which are in the form of quivers with potentials. In this talk, I will examine such a construction in different dimensions, and explain how quivers can be used to effectively compare mirror geometries. Construction of symplectic field theory and smoothness of Kuranishi structure (Suguru Ishikawa)
Abstract: Symplectic field theory (SFT) is a generalization of Gromov-Witten invariant and Floer homology for contact manifolds and symplectic cobordisms between them, which was introduced by Eliashberg, Givental and Hofer around 2000. Its algebraic structure was well studied by them, but its construction was a difficult problem. Recently, I succeeded in its construction by usign Kuranishi theory. Kuranishi theory is a theory developed by Fukaya and Ono for the construction of Gromov-Witten invariant and Floer homology for general symplectic manifolds. To use this theory for the construction of SFT, we need to construct smooth Kuranishi structures of moduli spaces. In this talk, I will talk about my work on the construction of SFT and smoothness of Kuranishi structure. Distinguishing symplectic manifolds via the continuous dynamics on wrapped Fukaya categories (Yusuf Baris Kartal)
Abstract: This talk is about distinguishing symplectic manifolds by using the differences in amounts of ``vector fields on Fukaya categories that integrate to periodic flows''. More precisely, we use an algebraic incarnation of the classical symplectic invariant- called Flux- on
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deformations of wrapped Fukaya categories to partially classify open symplectic mapping tori. As an application, we obtain pairs of diffeomorphic Weinstein fillings of a contact manifold that cannot be distinguished by their symplectic cohomology groups, but that are different as Liouville domains. T-equivariant disc potentials (Siu-Cheong Lau) Abstract: Lagrangian Floer theory developed by Fukaya-Oh-Ohta-Ono has played a central role in symplectic geometry and mirror symmetry. In particular, we have a well-defined disc potential for weakly unobstructed Lagrangians. In this talk, we will study and compute a torus-equivariant version of the disc potential for Lagrangian tori and certain Lagrangian immersions which are important for the SYZ construction. This is a joint work with Yoosik Kim and Xiao Zheng. Title: A symplectic look at the Fargues-Fontaine curve (Yanki Lekili) Abstract: I will explain how to introduce a Frobenius twist in the construction of Fukaya category. This new construction applied to a symplectic 2-torus gives a symplectic mirror to the Fargues-Fontaine curve of p-adic Hodge theory. This is joint work in progress with David Treumann. Arboreal skeleta (David Nadler)
Abstract: I will discuss progress in understanding Weinstein manifolds via skeleta with simple singularities. Joint work with Y. Eliashberg and D. Alvarez-Gavela.
TBA (Emanuel Scheidegger) Skeins on branes (Vivek Shende)
Abstract: I will describe how to count open higher genus curves in Calabi-Yau 3-folds, and give an enumerative interpretation of the coefficients of the HOMFLYPT polynomial. This is joint work with Tobias Ekholm. Time permitting, I will speculate on categorification.
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Deformation theory of pseudoholomorphic curves relative to an SNC divisor (Mohammad Farajzadeh Tehrani)
Abstract: Moduli spaces of pseudoholomorphic curves in the presence of an SNC (simple normal crossings) divisor appear naturally in Gromov-Witten theory, Mirror Symmetry, and various other applications. In this talk, we introduce an analytical setup for studying the deformation theory of such curves. In particular, we derive an analog of Ruan-Tian perturbations of the Cauchy-Riemann operator for these moduli spaces. Such perturbations, together with a new compactification that was introduced recently, enable a geometric construction of Gromov-Witten type invariants for certain semi- positive pairs in arbitrary genera. Mirror symmetry for Grassmannians and cluster transformations (Kazushi Ueda)
Abstract: We will discuss a construction of Rietsch's mirror for Grassmannians from the point of view of cluster structures, and the description of the Fukaya categories in terms of matrix factorizations. If the time permits, we will also discuss the other direction of homological mirror symmetry. This is a joint work in progress with Yuichi Nohara. Chen’s proof of the Kotshchick-Morgan conjecture and (equivaraint) K-theoretical Donaldson invariants (Bai-Ling Wang) Abstract: In this talk, I will first briefly review two important results in Bohui Chen’s PhD thesis: Bubble tree compactification of instanton moduli spaces and his proof of the Kotshchick-Morgan conjecture. As a new application, we will define the K-theoretical Donaldson invariant and establish its wall crossing formula for b^+ =1 manifolds. In the presence of compact Lie group (such as U(1)) action, there is an equivariant version of these results. This is work in progress with Bohui Chen. On the Hamiltonian Gromov—Witten invariants for compact symplectic manifolds (Rui Wang)
Abstract: Based on joint work with Bohui Chen and Bai-Ling Wang, we explain the construction of Hamiltonian Gromov—Witten invariants for a compact symplectic manifold which admits compact Lie group Hamiltonian action. The invariants are constructed through moduli spaces of symplectic vortices with cylindrical-ended metrics. Analytic setup for the moduli spaces will be explained. Applications, including a version of quantization for Kirwan morphism (under the assumption that the Lie group is abelian) will be introduced. A Compactness Theorem for translation invariant ASD equation and Atiyah--Floer conjecture（Guangbo Xu）
Abstract: In this talk we will consider the anti-self-dual equation over the product of the real line and a three-manifold with cylindrical end for gauge group SO(3). I will explain the proof
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of a Gromov--Uhlenbeck type compactness result for this equation. This is the first step towards constructing a natural bounding cochain for the symplectic side of the SO(3) Atiyah--Floer conjecture. Fukaya category of Landau-Ginzburg model and the algebra of the infrared (Dingyu Yang) Abstract: In the first part of the talk, I will go over my joint work with Huijun Fan and Wenfeng Jiang on how to define a Fukaya category from a tame holomorphic Morse function on a Kähler manifold, where some of the key points are the use of Witten equation and a highly non-trivial C^0 compactness argument. Then, I will explain how to use Witten equation to construct moduli spaces underlying the algebra of infrared of Gaiotto-Moore-Witten, which incorporates our construction as a natural sub-picture. Here, the space of all pointed subdivisions of the convex hull of the critical values of the holomorphic Morse function provides the setting of coherent families of Witten equation solutions. Mathematically, the algebra structure is formulated by Kapranov-Kontsevich-Soibelman as L infinity structure of secondary polytope and its restriction to A infinity structure, and I will outline how to approach some of their conjectures. If time permits, I will touch upon the wall-crossing aspect and mirror symmetry.
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List of Participants Mohammed Abouzaid Columbia University
Zhuo Chen Beijing Normal University
Xiaojun Chen Sichuan University
Bohui Chen Sichuan University
Cheol-hyun Cho Seoul National University
Dongwook Choa Seoul National University
Jiajun Dai Sichuan University
Hao Ding Southwest Jiaotong University
Chengyong Du Sichuan Normal University
Tobias Ekholm Uppsala
Huijun Fan Peking University
Bohan Fang Peking University
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Kenji Fukaya Simons Center
Penka Georgieva IMJ-PRG
Wenmin Gong Beijing Normal University
Andrew Hanlon Berkeley
Xingbang Hao
[email protected] Sun Yat-sen University
Hailong He Nanjing Normal University
Yue He Nanjing Normal University
Weiqiang He Sun Yat-sen University
Hansol Hong Yonsei University
Wenchuan Hu Sichuan University
Jianxun Hu Sun Yat-sen University
Jin Huang Peking University Shenzhen Graduate School
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Kei Irie University of Tokyo
Suguru Ishikawa Kyoto University
Wenfeng Jiang Sun Yat-sen University
Rongrong Jin Civil Aviation University of China
Yusuf Baris Kartal MIT
HuaZhong Ke Sun Yat-sen University
Siu-Cheong Lau Boston University
Yanki Lekili King's College
Xiaobin Li Southwest Jiaotong University
Aijin Lin National University of Defence Technology
Yijie Lin Sun Yat-sen University
David Nadler Berkeley
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Kaoru Ono RIMS
Emanuel Scheidegger Peking University
Vivek Shende Berkeley
Li Sheng Sichuan University
Kun Shi Beijing Normal University
Tao Su ENS-CNRS
Shanzhong Sun Capital Normal University
Yuhan Sun Stony Brook University
Mohammad Tehrani University of Iowa
Kazushi Ueda University of Tokyo
Bai-ling BRYAN Wang ANU
Rui Wang UC-Berkeley
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Yi Wang Stony Brook University
Gehao Wang Sun Yat-sen University
Yunfeng Wang Science and Technology of China
Maosong Xiang Huazhong University of Science and Technology
Guangbo Xu Texas A&M University
Dingyu Yang Humboldt-Universität zu Berlin
Chenglang Yang Peking University
Mingzhi Yang Sun Yat-sen University
Futoshi Yagi Southwest Jiaotong University
Sirui Yu Sichuan University
Jinheng Zeng Sichuan University
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Bingyu Zhang Institut Fourier, Universite Grenoble Alpes
Rui Zhang Huazhong University of Science and Technology
Shuo Zhang Berkeley
Shuji Zhao Tongji University
Jian Zhou Tsinghua University
Zhengyi Zhou Institute for Advanced Study
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Conference Information
1. Conference Venue
107 Room, Natural Science Classroom Building (理科教学楼 107 教室)
2. Hotel
Beijing Yanshan Hotel （北京燕山大酒店）
Address: A38 Zhong Guan Cun Street,Hai Dian District,Beijing
Check-in Time From 14:00
Check-out Time To 14:00
Tel.: +86 10 62563388
Convenient stores and Coffee Shops are near Yanshan Hotel with 50 meters.
Please check in directly with your passport.
3. Registration Time: 14:00-20:00, August 14th
Venue: Beijing Yanshan Hotel （北京燕山大酒店）
4. Meals
Breakfast
August 15th-20th（6:30-10:00): Beijing Yanshan Hotel
Lunch August 15th-17th, August 19th-20th (12:00-14:00)
Venue: Time Western Restaurant, 2nd Floor, Building No. 2, Zhongguanyuan Global
Village, Peking University（中关新园 2 号楼二层时光西餐厅）
Dinner August 15th-17th, August 19th (17:30-20:00)
Venue: Time Western Restaurant, 2nd Floor, Building No. 2, Zhongguanyuan Global
Village, Peking University（中关新园 2 号楼二层时光西餐厅）
Banquet Time: 18:00-20:00, August 18th
Venue: Yajing Room, Yanshan Hotel
All registered participants are provided with lunch and dinner coupons for 6 days,
Please submit the coupon to the staff of Time Western Restaurant when taking meals.
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5.Traffic information
Transportation from airport to Yanshan Hotel
The most convenient way is to take a taxi at the Beijing International Airport and go directly
the hotel. The taxi fee is about RMB100 to RMB130 depending on the traffic situation. You can
show the map and the Chinese hotel name (燕山大酒店，海淀) to the driver.
If you take the subway, please first take the airport fast line to Sanyuan Bridge Station (三
元桥) . The single way ticket is about RMB 25. Then buy a single way subway ticket and transfer
to line 10 (direction to Sun Palacet 太阳宫) to Haidian Huangzhuang Station （海淀黄庄）and
transfer to line 4 (direction toTian gongyuan 天宫院 ) and get off at Renming University
Station(人民大学) , then walk out from Exit A2 to the ground. Finally it takes 8-10 minute walk
to Yanshan Hotel.
Transportation between Peking University and Yanshan Hotel
Please take the subway line 4 at Renming University Station (direction to Anhe Bridge
North 安河桥北) and get off at Peking University Station (北京大学东门). The Exit gate is A
Yanshan Hotel
Peking University
Renming University Station
East Gate of Peking University Station
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Place of Natural Science Classroom Building and Building No. 2, Zhongguanyuan
Global Village from Exit A of East Gate of Peking University Station
6. Map of Zhongguanyuan Global Village, Peking University
The entrance of Zhongguanyuan Global Village, Peking University, is on the Zhongguancun North Street.
East Gate of Peking University Station
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General Information
1. Emergency Contacts
Dr. FAN Huijun +86-135-5268-6981
Dr. FANG Bohan +86-185-1833-1563
Ms. Chen Pingping +86-184-0162-1500
Ambulance: 120 Police:110
2. Name Badge
For identification purpose, badges are expected to be worn at all times during
the conference.
3. Internet
If you have an eduroam account, you will be able to get internet access in PKU.
Free cable network is available in your room at Beijing Yanshan Hotel
4. Taxi
The minimum charge is RMB13. After 3 kilometers, RMB2.3 is added every
kilometer. The charge will be 20% higher after 15 kilometers or during the
night time (11pm–5am). Please request a receipt from the taxi driver in case
you leave belongings in the taxi.
5. Currency Exchange
Most banks provide exchange service for foreign currency and traveler’s
checks. Credit cards such as Mastercard, Visa, JCB, Diners are accepted in most
hotels, shopping centers and restaurants. However, they may not be accepted at
small shops or restaurants.
6. Tips & Tax
Tip is not expected or commonly practiced in Beijing. Taxes are already
included in the stated prices.
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Map of PKU Main Campus
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