Conference Schedule
Monday, 1 December 2025
09:00–09:30 Registration
Morning Session Chair: Peter Bouwknegt
09:30–10:15 Ezra Getzler (Northwestern University) The Gauss-Manin connection in noncommutative geometry
Recording: https://anu.zoom.us/rec/share/XAKvcDoasKIVtg-kq6PvH_Bn0LKiQeeyF9vEbTkdf6ohg5Rrsmvn1brNsmOxIeEy.RH9ZCkov8WNkiuRD
Passcode: jG5#7cgZ
10:15–10:40 Tea Break
10:40–11:25 Ruben Minasian (CEA-Saclay, France) D-type holography: gauge theories from geometry with ... a touch of topology
Recording: https://anu.zoom.us/rec/share/eClT_wyAcIECKneJAuc7Cmv1zpGP8bNOadHqkXmuvrOJkvpWYNr2iRuzqWtLLxMd.o1EnLv7rRUXF0kJH?startTime=1764546153000
Passcode: jG5#7cgZ
11:30–12:15 Ctirad Klimcik (Universitate Aix-Marseille, France) Euclidean E-models
Recording: https://anu.zoom.us/rec/share/eClT_wyAcIECKneJAuc7Cmv1zpGP8bNOadHqkXmuvrOJkvpWYNr2iRuzqWtLLxMd.o1EnLv7rRUXF0kJH?startTime=1764549488000
Passcode: jG5#7cgZ
12:20–14:00 Lunch Break
Afternoon Session Chair: Johanna Knapp
14:00–14:45 Emanuel Scheidegger (BICMR, Peking University) Gauged linear sigma models and Calabi-Yau orbifolds
Recording: https://anu.zoom.us/rec/share/BVKF9zugiiXg9VwcensbVoc74oj2T8VYALhmNeK8lNzRLrWksHXKzab5k5iG6N1A.Eerjgi1G78oBo3jW?startTime=1764558080000
Passcode: jG5#7cgZ
14:45–15:10 Tea Break
15:10–15:55 Siye Wu (National Tsing Hua University, Hsinchu) D-branes and mirror symmetry from Kapustin-Witten theory
Passcode: jG5#7cgZ
16:00–18:00 Reception (Wine and Cheese)
Tuesday, 2 December 2025
Morning Session Chair: Brett Parker
09:00–09:45 Meng-Chwan Tan (National University of Singapore) Topological 5d N = 2 Gauge Theories: Mirror Symmetry and Langlands Duality of A∞-categories of Floer Homologies
Recording: https://anu.zoom.us/rec/share/lFhovNk8N_wcYoVJOshHx8I8cupf3wn2uNSUIZSdbSk5MoR4gdK_jVEKsIGsDpI.VX0eV9zVzjbh-ZQa?startTime=1764626697000
Passcode: vjkJ#0%+
09:50–10:35 Fei Han (National University of Singapore) Differential Models for Anderson Dual to Twisted Spin^c Bordism and Twisted Anomaly Map
Recording: https://anu.zoom.us/rec/share/XPjbU8Kfb6ow8htoZmKx-cX28bqrcGX1yT62FbRkNexwaReLLQooHkMsYJnEkPIa.s8m5P8aAZY7bCLk_?startTime=1764636546000
Passcode: .fj7RyJ1
10:35–10:50 Tea Break
10:50–11:35 Thorsten Hertl (University of Melbourne) G2 Moduli Spaces May Have Holes
Recording: https://anu.zoom.us/rec/share/s1w3Qhe2iKERg1ZlYYAbv3S4URnmerq1yXg6SQ4lNa6aJDGpl8QLZwSz8It_Iqla.GZSLddBN_CPb3dfA
Passcode: iVBW0!Vu
11:40–12:25 Minchun Hong (University of Queensland) The Yang-Mills flow over higher dimensional Riemannian manifolds
Recording: https://anu.zoom.us/rec/share/lFhovNk8N_wcYoVJOshHx8I8cupf3wn2uNSUIZSdbSk5MoR4gdK_jVEKsIGsDpI.VX0eV9zVzjbh-ZQa?startTime=1764629645000
Passcode: vjkJ#0%+
12:30–14:00 Lunch Break
Afternoon Session Chair: Hiroshi Ohta
14:00–14:45 Hai-Long Her (Jinan University) The sum of Hamiltonian manifolds
Recording: https://anu.zoom.us/rec/share/FDI1dXvcHlGIuSuJGwCx9cnnoU1k4SMuHg_cNYiFITtG08FA9NhzN24_6WkpUdQ.p62Pj0qiWtYylfOi
Passcode: jG5#7cgZ
14:45–15:10 Tea Break
15:10–15:55 Weiqiang He (Sun Yat-sen University) Landau-Ginzburg mirror symmetry for x^p + y^q
Recording: https://anu.zoom.us/rec/share/W0JyFZf8d-Zni1BJLcFdJKA1H2reQV3Z5QWeWFMO9JHI42yYMxIydEUsVs4LPSrN.Zd2EA8BN32_VIswD
Passcode: hn?c6PjG
16:00–16:45 Or Kedar (The Hebrew University of Jerusalem) A_∞ Algebra of a Non-Orientable Lagrangian
Recording: https://anu.zoom.us/rec/share/biBNYWt9Awlgn5AZ1qiRUsOEi5Irw_Jwqxnkvszh88D6FihvGfxrHPLcmOmfB0du.NiJ2SwT84MgZDjpK
Passcode: 1+#LHcLr
18:00–20:00 Conference Dinner @ Little Steamer
Wednesday, 3 December 2025
Morning Session Chair: Jianxun Hu
09:00–09:45 Xiaobo Liu (Peking University) Quantum Volume Elements
Passcode: RXj5EQ%S
09:50–10:35 Cheol-Hyun Cho (POSTECH) Geometric models of simple Lie algebras via singularity theory
Passcode: 04ys@EU2
10:35–10:45 Tea Break
10:45–11:30 Yingchun Zhang (Shanghai Jiao Tong University) Seiberg duality conjecture, cluster algebra and quantum cohomology
Passcode: 1g@i3Jca
11:35–12:10 Arif Er (National University of Singapore) Topological 8d N = 1 Gauge Theory: Novel Floer Homologies, and A∞-categories of Six, Five, and Four-manifolds
Passcode: 1g@i3Jca
12:20–13:40 Lunch Break
Afternoon Session Chair: Chengyong Du
13:45–14:30 Yong-Geun Oh (IBS-CGP & POSTECH) Contact Hamiltonian dynamics and geometric analysis
Recording: https://anu.zoom.us/rec/share/gwUOh4Vo0s01PAhkjAcMjuTfytVllYXhfle1KsIWJOQLkr-rpVT0-Iih0MNmW5SF.oRycbyCav6Wwthac
Passcode: aV+0&Y7@
14:35–15:20 Hiroshi Ohta (Nagoya University) Stokes curves in WKB analysis and Lagrangian Floer theory
Passcode: Y%0DJ#2k
15:20–15:35 Tea Break
15:35–16:20 Aliakbar Daemi (Washington University in St. Louis) The mapping class group action on the odd character variety
16:25–17:10 Yaoxiong Wen (Korea Institute for Advanced Study, Seoul) Mirror Symmetries for Parabolic Hitchin Systems
Thursday, 4 December 2025
Morning Session Chair: Yong-Geun Oh
09:00–09:45 Jongil Park (Seoul National University) Algebraic Montgomery-Yang problem via smooth obstructions
09:50–10:35 Hirofumi Sasahira (Kyushu University) Exact triangles in Seiberg-Witten Floer spectra
10:35–11:00 Tea Break
10:50–11:35 Jun Zhang (University of Science and Technology of China) Strong Arnold chord conjecture
11:40–12:25 Longting Wu (Southern University of Science and Technology, China) Poincare polynomials of moduli spaces of 1-dimensional sheaves on the projective plane
12:30– 13:45 Lunch Break
Afternoon Session Chair: Kaoru Ono
13:50–14:45 Hang Wang (East China Normal University) Euler Characteristics and Higher Kazhdan Projections
14:50–15:35 Tsuyoshi Kato (Kyoto University) First step to a combinatorial Gamma-Bauer-Furuta theory
15:35–16:00 Colloquium Tea
16:00–17:00 MSI Colloquium
Kenji Fukaya (Tsinghua University, Beijing) Q structure in open closed Gromov Witten theory
Friday, 5 December 2025
Morning Session Chair: Xiaobo Liu
09:00–09:45 Gabriele Tartaglino-Mazzucchelli (University of Queensland) On TTbar, 4d duality invariance, and deformations of 2d integrable field theories
09:50–10:35 Michele Galli (University of Queensland)
10:35–11:05 Tea Break
11:05–11:50 Jock McOrist (University of New England)
11:50–12:00 Conclusion of the conference
Abstracts
Bohui Chen (Sichuan University)
Automorphisms of (higher) Lie groupoids
Abstract: It is known that an orbifold is a proper etale Lie groupoid. In order to consider the group action
on orbifolds, it is natural to ask what is an automorphism of an orbifold and what is the group structure on
the total collection of automorphisms. In this talk, I will focus on the case of Lie 1-groupoids and answer these
questions. In particular, I will explain what an action on Lie 1-groupoids (including orbifolds) means and also
give some applications. If time permits, I will report some progresses on higher groupoids. The talk is based on
joint works with Chengyong Du, Fengyu Jiang and etc.
Cheol-Hyun Cho (Postech)
Geometric models of simple Lie algebras via singularity theory
Abstract: It is well-known that ADE Dynkin diagrams classify both the simply-laced simple Lie algebras
and simple singularities. We introduce a polygonal wheel in a plane for each case of ADE, called the Coxeter
wheel. We show that equivalence classes of edges and spokes of a Coxeter wheel form a geometric root system
isomorphic to the classical root system of the corresponding type. This wheel is in fact derived from the Milnor
fiber of corresponding simple singularities of two variables, and the bilinear form on the geometric root system is
the negative of its symmetrized Seifert form. Furthermore, we give a completely geometric definition of simple Lie
algebras using arcs, Seifert form and variation operator of the singularity theory. It is a joint work with Wonbo
Jeong and Beom-Seok Kim.
Aliakbar Daemi (Washington University in St. Louis)
The mapping class group action on the odd character variety is faithful
Abstract: The odd character variety of a Riemann surface is a moduli space of SO(3) representations of
the fundamental group which can be interpreted as the moduli space of stable holomorphic rank 2 bundles of
odd degree and fixed determinant. This is a symplectic manifold, and there is a homomorphism from a finite
extension of the mapping class group of the surface to the symplectic mapping class group of this moduli space.
When the genus is at least 2, it is shown that this homomomorphism is injective. This answers a question posed
by Dostoglou and Salamon and generalizes a theorem of Smith from the genus 2 case to arbitrary genus. A
corresponding result on the faithfulness of the action on the Fukaya category of the odd character variety is also
proved. The proofs use instanton Floer homology, a version of the Atiyah-Floer Conjecture, and aspects of a
strategy used by Clarkson in the Heegaard Floer setting.
Arif Er (National University of Singapore)
Topological 8d N = 1 Gauge Theory: Novel Floer Homologies, and A∞-categories of Six, Five, and Four- manifolds
Abstract: In this talk, we show how one can define novel gauge-theoretic Floer homologies of seven, six, and five-manifolds, from the physics of a topologically-twisted 8d N = 1 gauge theory via its supersymmetric quantum mechanics interpretation. We will then derive Atiyah-Floer-type correspondences between these gauge-theoretic Floer homologies and symplectic intersection Floer homologies of instanton moduli spaces. Via a 2d gauged A-twisted Landau-Ginzburg model interpretation of the 8d theory, we will also obtain novel Fukaya-Seidel-type A∞-categories that categorify the aforementioned gauge-theoretic Floer homologies of six and five-manifolds, and that of four-manifolds in a previous work. These results of novel Floer homologies and A∞-categories therefore furnish puerly physical proofs and generalizations of the conjectures by Donaldson-Thomas, Donalson-Segal, Cherkis, Hohloch-Noetzel-Salamon, Haydys, and Bousseau, and more.
Michele Galli (University of Queensland)
Ezra Getzler (Northwestern University)
The Gauss-Manin connection in noncommutative geometry
Abstract: The Gauss-Manin connection in noncommutative geometry is a flat connection on the periodic
cyclic homology of a family of differential graded algebras (or, more generally,A∞ categories). It appears, for
example, in the study of mirror symmetry. Recently, it has been understood that it is more easily understood by
introducing a modified product on the differential forms on the base, called the Fedosov product.
Kenji Fukaya (Tsinghua University, Beijing)
Title: Q-structure in open closed Gromov Witten theory
Abstract: Q (rational number) is used as a ground field to study virtual fundamental chain of the moduli
space of pseudo-holomorphic curve, because it is basically fundamental class of an orbifold. In our work with
Oh-Ohta-Ono and etc. we use real number R in many cases since we use de Rham cohomology. Using de Rham
cohomology makes it easier to keep more symmetry. In this talk I will explain some example where working
over Q- (or its finite extension) is interesting and explain an idea how we can work over Q- to study open closed
Gromov Witten invariant. (The latter part is mostly work in progress.)
Fei Han (National University of Singapore)
Differential Models for Anderson Dual to Twisted Spinc Bordism and Twisted Anomaly Map
Abstract: Spinc bordism is an important bordism theory with many connections and applications in topology, geometry and physics. Our talk will explain the constructions of models for twisted Spinc bordism and its Anderson dual, in homotopy, geometric and differential flavours. The talk is based on our joint work with Yuanchu Li.
Weiqiang He (Sun Yat-sen University)
Landau-Ginzburg mirror symmetry for xp + yq
Abstract: Suppose W is a quasi-homogenous invertible polynomial and G is some admissible symmetry
groups of W. The Landau-Ginzburg (LG) mirror symmetry conjecture states the equivalence between LG A
model on the pair (W,G) and LG B model on the mirror pair (WT ,Gˇ). Here LG A model is induced by curve
counting and LG B model is induced by variation of Hodge structure. This talk includes an introduction on LG
A B model and a recent progress for the proof of the above conjecture in the case xp + yq.
Hai-Long Her (Jinan University)
Thorsten Hertl (University of Melbourne)
G2 Moduli Spaces May Have Holes
Abstract: In his two seminal articles, Dominic Joyce not only constructed the first examples of closed
manifolds with G2-holonomy metrics, but also proved that the moduli space of all G2-metrics on a closed manifold
is itself a finite-dimensional manifold. The statement is, however, only a local one, and global topological properties
of these moduli spaces have remained quite mysterious ever since. Indeed, up to now, we only know that they
may be disconnected by the work of Crowley, Goette, and NordstrÅNom; the question whether all path components
are contractible or not has not been answered yet. In this talk, I will outline a construction of an element in the
second homotopy group of the moduli space of G2 metrics on Joyce’s first example and present along the way
a homotopy-theoretical result that guarantees its non-triviality. This talk is based on joint work with Diarmuid
Crowley and Sebastian Goette.
Minchun Hong (University of Queensland)
The Yang-Mills flow over higher dimensional Riemannian manifolds
Abstract: We develop a parabolic formulation of the Uhlenbeck gauge fixing theorem and use it to prove the
maximal existence of the Yang-Mills flow over compact n-dimensional Riemannian manifolds for n ≥ 4. Using an
idea of Hamilton’s on the Ricci flow, we provide new proofs for uniform estimates of higher covariant derivatives
of curvature by improving Moser’s iteration technique. Furthermore, we investigate the blow-up of the Yang-Mills
flow at the maximal existence time and improve an asymptotical result of Hong-Tian.
Tsuyoshi Kato (Kyoto University)
First step to a combinatorial Γ-Bauer-Furuta theory
Abstract: In this talk, I propose a combinatorial approach for constructing Bauer-Furuta theory on infinite
covering spaces. First, I will explain a motivation for constructing Bauer-Furuta theory on covering spaces. There
is an analytic construction which is currently difficult to compute. Recently, a discretization of the index theorem
has been given using lattice gauge theory. I will use this to aim for constructing something more computable, and
explain the first step to that goal.
Or Kedar (The Hebrew University of Jerusalem)
A∞-Algebra of a Non-Orientable Lagrangian
Abstract: We construct a family of cyclic unital curved A-infty structures on differential forms on a
Lagrangian submanifold L in a sympletic manifold with values in the local system of graded non-commutative
rings, given by the tensor algebra of the orientation local system of L. The algebra satisfies Gromov-Witten like
axioms. On account of the non-orientability of L, the evaluation maps on moduli spaces of J-holomorphic disks
with boundary in L may not be relatively orientable. To deal with this problem, we introduce orientor calculus
and prove analogous relations for orientors on the moduli spaces.
Ctirad Klimcik (Universitate Aix-Marseille, France)
Euclidean E-models
Abstract: We review the concept of integrability in non-linear ?-models in the context of string theory. In particular, we focus on models defined on the Euclidean world-sheet and develop an E-model approach for generating them. We also study the renormalizability of such models. These concepts are illustrated using the example of the eta-deformed hyperbolic WZW model.
Xiaobo Liu (Peking University)
Quantum Volume Elements
Abstract: For a compact symplectic manifold, the quantum volume element is defined by quantum products
of dual basis elements of the cohomology space. In this talk I will describe application of this element to Virasoro
conjecture for Gromov-Witten invariants and complexity of topological field theory.
Jock McOrist (University of New England)
Ruben Minasian (CEA-Saclay, France)
D-type holography: gauge theories from geometry with ... a touch of topology
Abstract: AdS-CFT correspondence is one of the prime examples of the interplay between the gauge theories
and string geometry. In this talk I will describe some subtleties and surprises in constructing smooth geometries
that are dual to superconformal field theories of type D, and discuss new examples of such geometries.
Yong-Geun Oh (POSTECH)
Contact Hamiltonian dynamics and geometric analysis
Abstract: In this talk, I will introduce a new elliptic system of Hamiltonian-perturbed contact instanton
equation with the Legendrian boundary condition in the study of contact dynamics and topology. As an application,
I will explain how one can use the interplay between contact Hamiltonian dynamics and geometric
analysis of the equation to give an optimal result for Shelukhin’s conjecture concerning the translated points of a
contactomorphism and their periods in terms of Hofer-Shelukhin energy.
Hiroshi Ohta (Nagoya University)
Stokes curves in WKB analysis and Lagrangian Floer theory
Abstract: The WKB analysis is asymptotic analysis for solutions to certain ODE on a Riemann surface with a parameter. The Stokes curves on the Riemann surface play important roles in the WKB analysis. In this talk, I will discuss some aspect of the Stokes curves in the WKB analysis from the point of view of Lagrangian Floer theory. This is based on a joint work with Tatsuki Kuwagaki.
Jongil Park (Seoul National University)
Algebraic Montgomery-Yang problem via smooth obstructions
Abstract: A normal projective surface with the same Betti numbers of the projective plane CP2 is called a
rational homology projective plane or a Q-homology CP2. People working in algebraic geometry and topology
have long studied a Q-homology CP2 with possibly quotient singularities. It is now known that it has at most five
such singular points, but it is so mysterious that there are still many unsolved problems left. Among them, the
(algebraic) Montgomery-Yang problem is one of the most famous conjectures in this field. In this talk, I’ll review
some known results and recent developments on the algebraic Montgomery-Yang problem obtained by utilizing
gauge theoretic results such as Donaldson diagonalisation theorem, Heegaard Floer correction terms and so on.
This is a joint work with Woohyeok Jo and Kyungbae Park.
Hirofumi Sasahira (Kyushu university, Japan)
Exact triangles in Seiberg-Witten Floer spectra
Abstract: The Seiberg-Witten Floer spectrum is a stable homotopy refinement of the Seiberg-Witten Floer
homology. In this talk, I will explain there are exact triangles for Seiberg-Witten Floer spectra associated with
surgery triples of 3-manifolds. (joint work with Matt Stoffregen) I will also show that the Seiberg-Witten Floer
spectrum for AR plumbed 3-manifolds can be computed by using these exact triangles. (joint work with Irving
Dai and Matt Stoffregen)
Emanuel Scheidegger (BICMR, Peking University)
Gauged linear sigma models and Calabi-Yau orbifolds
Abstract: We consider orbifold phases of gauged linear sigma models. By using the universal properties of the hemisphere partition function in gauged linear sigma models we show how to compute orbifold Gromov-Witten invariants for Calabi-Yau orbifolds of dimension 3.
Shanzhong Sun (Capital Normal University, Beijing, China)
Around Witten’s Asymptotic Expansion Conjecture
Abstract: Gukov-Pei-Putrov-Vafa (GPPV) invariant is a refinement of the well-known Witten-Reshetikhin-
Turaev (WRT) invariant in quantum topology. I will talk about our recent progress on the quantum modularity
of GPPV invariants for Seifert fibered integral homology spheres (SFIHS) using resurgence theory, and its applications
to the asymptotic expansion conjecture through the non-tangential limit to the WRT invariants. Its
relation to Habiro invariant will also be addressed if time permitted. Based on joint works with J. Andersen, L.
Han, Y. Li, W. Mistergard and D. Sauzin.
Meng-Chwan Tan (National University of Singapore)
Abstract: Topological 5d N = 2 Gauge Theories: Mirror Symmetry and Langlands Duality of A∞-categories of Floer
Homologies
Abstract: This talk is based on our recent work in [arXiv:2511.15953]. We explain how topological 5d
N = 2 gauge theory of Haydys-Witten twist with gauge group G, can be dual to that of Geyer-MÅNulsch twist
with gauge group LG, where G is a real, compact Lie group with Langlands dual LG. Proceeding via their 2d
and 3d gauged A/B-twisted Landau-Ginzburg model interpretations, we will show that (i) a Fukaya-Seidel-type
A∞-1-category of an HW4-instanton Floer homology of three-manifolds and (ii) a Fueter-type A∞-2-category
of an HW3-instanton Floer homology of two-manifolds, are dual to (i) an Orlov-type A∞-1-category of a novel
LGH-flat Floer homology of three-manifolds and (ii) a Rozansky-Witten-type A∞-2-category of a novel LGO-flat
Floer homology of two-manifolds, respectively. Finally, we will derive their Atiyah-Floer-type correspondences to
symplectic categories. This demonstration of a mirror symmetry and Langlands duality of (higher) A∞-categories
of symplectic and gauge-theoretic Floer homologies, therefore furnishes one with purely physical proofs and gaugetheoretic
generalizations of the mathematical conjectures by Bousseau [1] and Doan-Rezchikov [2], and more.
Gabriele Tartaglino-Mazzucchelli (University of Queensland)
Hang Wang (East China Normal University, China)
Euler Characteristics and Higher Kazhdan Projections
Abstract: This joint work with Sanaz Pooya and Baiying Ren uncovers a new link between combinatorial
invariants and K-theoretic charge classes arising from higher Kazhdan projections. For non-amenable virtually
free groups, we show that the Emerson-Meyer Euler characteristic is exactly the preimage of the higher Kazhdan
projection under the Baum-Connes assembly map, giving a finite alternating-sum formula built from averaging
projections over finite stabilisers in the Bass-Serre tree. This identification leads to explicit non-vanishing results
for delocalised l2-Betti numbers.
Yaoxiong Wen (Korea Institute for Advanced Study, Seoul)
Mirror Symmetries for Parabolic Hitchin Systems
Abstract:. he Hitchin system plays a pivotal role in modern mathematics, forming a bridge between integrable
systems, gauge theory and mirror/Langlands dualities. In this talk I will review the mirror symmetry phenomenon
for the Langlands dual pair of Hitchin systems, as initiated by Hausel-Thaddeus, including both the SYZ dual
abelian fibration story and the topological mirror symmetry predictions. Then I will mention more recent advances.
Finally I will outline our recent joint work (with B. Wang and X. Wen) extending some of those ideas to parabolic
Hitchin systems.
Longting Wu (Southern University of Science and Technology, China)
PoincarÅLe polynomials of moduli spaces of 1-dimensional sheaves on the projective plane
Abstract: The geometry of moduli spaces of one-dimensional sheaves on the projective plane has attracted
a lot of study recently. In this talk, I will give a new calculation of the Betti numbers of the moduli spaces of
one-dimensional sheaves on the projective plane using Gromov-Witten invariants of local P2 and local curves.
The new calculation is based on the refined sheaves/GW correspondence established by Bousseau and all genus
local/relative correspondence given by Bousseau-Fan-Guo-Wu. It can be used to prove the divisibility property
of PoincarÅLe polynomials of moduli spaces of one-dimensional sheaves on projective plane conjectured by Choivan
Garrel-Katz-Takahashi, and can also be used to determine the leading Betti numbers. Some conjectures
concerning the higher range Betti numbers will be proposed if time permits. This is based on a joint work with
Shuai Guo and Miguel Moreira.
Siye Wu (National Tsing Hua University, Hsinchu)
D-branes and mirror symmetry from Kapustin-Witten theory
Abstract: We consider reduction of the Kapustin-Witten gauge theory on a four
dimensional orientable manifold which is not a global product of two
surfaces but contains embedded non-orientable surfaces. The resulting
theory is a sigma-model on a two dimensional worldsheet with boundary
with D-branes naturally coming from four dimensions. We compare the
topological sectors in four and two dimensions and verify the mirror
symmetry predicted by S-duality in gauge theory.
Jun Zhang (University of Science and Technology of China)
Strong Arnold chord conjecture
Abstract: In this talk, we will show how to prove the strong Arnold chord conjecture for a large family of star-shaped domains in R4, which says that for any Legendrian knot on their contact boundaries, there exists a Reeb chord on the Legendrian knot with distinct endpoints. The proof heavily relies on the recent advances in various equivalences of symplectic capacities on monotone toric domains. A higher-dimensional version for star-shaped domains in R2n also holds under a technical condition. This talk is based on joint work with Jungsoo Kang.
Yingchun Zhang (Shanghai Jiaotong University)
Seiberg duality conjecture, cluster algebra and quantum cohomology
Abstract: In the first part, I will introduce our in progress work on the Seiberg duality conjecture in geometric
level. Consider a quiver with potential. It has been proved by many people that its quasimap I function is
preserved under quiver mutation in some sense. In this work, we further prove that the underlying scheme is
preserved under quiver mutations. In the second part, I will talk about an expected application of the Seiberg
duality conjecture to the relation between cluster algebra and quantum cohomology ring. Considering the given
quiver, one can construct a cluster algebra. One the other hand, one can consider the quantum cohomology ring
of the quiver variety when it is smooth. We claim an algebra homomorphism from the cluster algebra to the
quantum cohomology ring. This talk is based on joint works with Yaoxiong Wen and Zijun Zhou.