About
The Greater Bay Area Geometry and Mathematical Physics Seminar, abbreviated as Lambda Seminar because of the similarity between the shape of Pearl River Estuary and the Greek letter λ , is jointly hosted by Southern University of Science and Technology (SUSTech), The Chinese University of Hong Kong (CUHK) and Sun Yat-Sen University (SYSU) to increase access to mathematical research and enhance the communication between Mathematicians working in the area of Geometry and Mathematical Physics.
This seminar will usually take place on Wednesday 9:00-11:30 or Thursday 16:00-18:30. The schedule below will be updated as talks are confirmed. For those interested in subscribing to our updates, please contact Ms. Ruimin Yin (yinrm@mail.sustech.edu.cn).
We are grateful for the financial support from the SUSTech International Center for Mathematics and NSFC (National Natural Science Foundation of China).
Events shown in time zone: Asia/Shanghai (UTC/GMT+8)
Next Talk(s)
Relative mirror symmetry and the proper Landau—Ginzburg potential
Time:13 April 2023 (17:15-18:15)
Abstract:I will talk about mirror symmetry for smooth log Calabi–Yau pairs. I will explain how to use the intrinsic mirror symmetry construction from the Gross—Siebert program to define the proper Landau–Ginzburg potential and show that it is the inverse of the relative mirror map in a relative version of Givental mirror theorem proved by Fan-Tseng-You.
Upcoming Talks
Past Talks
A generalization mixed-spin-P fields
Time:06 December 2022 (17:15-18:15)
Speaker:
Yang Zhou (Fudan University)
Venue:
Zoom ID: 920 7313 5240 Password: 973824
Abstract:The theory of Mixed-Spin-P fields was introduced by Chang-Li-Li-Liu for the quintic threefold. Chang-Guo-Li has successfully applied it to prove important conjectures on the higher-genus Gromov-Witten invariants. In this talk I will explain a generalization of the construction to more spaces. The key is the stability condition which guarantees the separatedness and properness of certain moduli spaces. It also generalizes the construction of the mathematical Gauged Linear Sigma Model by Fan-Jarvis-Ruan, removing their technical assumption about "good liftings".
This is a joint work with Huai-Liang Chang, Shuai Guo, Jun Li and Wei-Ping Li.
BCOV Feynman Structure of high genus GW invariants of quintic Calabi Yau threefold
Time:06 December 2022 (16:00-17:00)
Venue:
Zoom ID: 920 7313 5240 Password: 973824
Abstract:Gromov Witten invariants Fg encodes the numbers of genus g curves in Calabi Yau threefolds and play an important role in enumerative geometry. In 1993, Bershadsky, Cecotti, Ooguri, Vafa exhibited a hidden "Feynman structure" governing all Fg’s at once, using path integral methods. The counterpart in mathematics has been missing for many years.
After a decades of search, in 2018, a mathematical approach: Mixed Spin P field (MSP) moduli, is finally developed to provide the wanted “Feynman structure”, for quintic CY 3-fold. Instead of enumerating curves in the quintic 3-fold, MSP enumerate curves in a large N dimensional singular space with quintic-3-fold boundary. The “P fields” and “cosections” are used to formulate counting in the singular space via a Landau Ginzburg type construction.
In this talk, I shall focus on geometric ideas behind the MSP moduli. Some update will be provided. The results follow from a decade of joint works with Jun Li, Shuai Guo, Young Hoon Kiem, Weiping Li, Melissa C.C. Liu, Jie Zhou, and Yang Zhou.
Moduli of algebraic varieties
Time:29 November 2022 (16:00-17:00)
Abstract:In this talk I will define stable varieties of non-negative Kodaira dimension and then describe results on existence of moduli spaces and their compactifications for such varieties in any dimension.
Mirror symmetry for special nilpotent orbit closures
Time:09 November 2022 (10:15-11:15)
Venue:
Zoom ID: 971 1062 5774 Password: 474205
Abstract:Motivated by geometric Langlands, we initiate a program to study the mirror symmetry between nilpotent orbit closures of a semisimple Lie algebra and those of its Langlands dual.
The most interesting case is Bn via Cn. Classically, there is a famous Springer duality between special orbits. Therefore, it is natural to speculate that the mirror symmetry we seek may coincide with Springer duality in the context of special orbits. Unfortunately, such a naive statement fails. To remedy the situation, we propose a conjecture which asserts the mirror symmetry for certain parabolic/induced covers of special orbits. Then, we prove the conjecture for Richardson orbits and obtain certain partial results in general. In the process, we reveal some very interesting and yet subtle structures of these finite covers, which are related to Lusztig’s canonical quotients of special nilpotent orbits. For example, there is a mysterious asymmetry in the footprint or range of degrees of these finite covers. Finally, we provide two examples to show that the mirror symmetry fails outside the footprint.
This is a joint work with Yongbin Ruan and Yaoxiong Wen.
Moduli Space of ALH^*-Gravitational Instantons
Time:09 November 2022 (09:00-10:00)
Venue:
Zoom ID: 971 1062 5774 Password: 474205
Abstract:Gravitational instantons are the building blocks of Hawking's quantum gravity theory. They are non-compact hyperK\"ahler 4-manifolds with L^2 curvature and can be viewed as the local pieces of K3 surfaces. Similar to K3 surfaces, the cohomology classes of the hyperK\"ahler triples of gravitational instantons induce a period map. In this talk, we will restrict to a particular type of gravitational instanton of type ALH^*. As a side product of studying SYZ mirror symmetry of log Calabi-Yau surfaces, we will prove that the period map is both injective and surjective. As a consequence, the period domain is the moduli space of ALH^*-gravitational instantons. The talk is based on joint works with T. Collins, A. Jacob and the joint work with T.-J. Lee.
Elliptic chiral homology and quantum master equation
Time:02 November 2022 (10:15-11:15)
Abstract:We present an effective BV quantization theory for chiral deformation of two dimensional conformal field theories. We explain a connection between the quantum master equation and the chiral homology for vertex operator algebras. As an application, we construct correlation functions of the curved beta-gamma/b-c system and establish a coupled equation relating to chiral homology groups of chiral differential operators. This can be viewed as the vertex algebra analogue of the trace map in algebraic index theory. The talk is based on the recent work arXiv:2112.14572 [math.QA].
Topology of Hitchin systems: old and new
Time:02 November 2022 (09:00-10:00)
Abstract:Hitchin’s integrable systems lie in the crossroads of geometry, representation theory, and mathematical physics. I will discuss two central conjectures raised in the last two decades which greatly influenced the development for the algebraic geometry of Hitchin moduli spaces. The first is the P=W conjecture, which concerns the interaction of the topology of the Hitchin system and the non-abelian Hodge correspondence. The second is the topological mirror symmetry conjecture which connects the Langlands duality of groups and the mirror symmetry for Hitchin systems. I will explain that both conjectures can be proved in a uniform way, via vanishing cycles techniques and support theorem. Based on joint work with Davesh Maulik.
Oscillatory integrals on mirror Lagrangian cycles
Time:26 October 2022 (10:15-11:15)
Abstract:I will discuss the oscillatory integrals on the mirror Landau-Ginzburg models for toric mirrors. They are related to genus zero Gromov-Witten invariants and are compatible with homological mirror symmetry. The asymptotic expansion of such integrals leads to the Gamma II conjecture for toric varieties. I will also report some recent progress in some non-toric situation inspired by the Gross-Siebert program.
The Chromatic Lagrangian: Wavefunctions and Open Gromov-Witten Conjectures
Time:26 October 2022 (09:00-10:00)
Abstract:Inside a symplectic leaf of the cluster Poisson variety of Borel-decorated $PGL_2$ local systems on a punctured surface is an isotropic subvariety we will call the “chromatic Lagrangian.” Local charts for the quantized cluster variety are quantum tori defined by cubic planar graphs, and can be put in standard form after some additional markings giving the notion of a “framed seed.”
The mutation structure is encoded as a groupoid. The local description of the chromatic Lagrangian defines a “wavefunction” which, we conjecture, encodes open Gromov-Witten invariants of a Lagrangian threefold in threespace defined by the cubic graph and the other data of the framed seed.
We also find a relationship we call “framing duality”: for a family of “canoe” graphs, wavefunctions for different framings encode DT invariants of symmetric quivers.
This talk is based on joint work with Gus Schrader and Linhui Shen.
Log intersection theory of the moduli space of curves_copy
Time:18 October 2022 (16:00-17:00)
Abstract:I will explain some developments in the study of the log Chow ring of the moduli space of curves: tautological classes, piecewis polynomials, and the log DR cycle.