GRASP seminar, Spring 2024


This is the website for the GRASP (Geometry, Representations, And Some Physics) seminar, organized by:

  • Pengfei Huang (黄鹏飞), pfhwangmath@gmail.com, Max Planck Institute for Mathematics in Sciences

  • Tao Su (苏桃), sutao08@gmail.com, BIMSA

  • Hao Sun (孙浩), hsun71275@outlook.com, Dept. of mathematics, South China University of Technology

    • See also here for the seminar webpage at BIMSA. The seminar borrows its name from similar seminars at Berkeley and UT Austin (without formal permission).

    Schedule


    The seminar typically takes place from 15:30 to 16:30 on Wednesdays, with occasional adjustments ranging from 10:00 to 21:30 (Beijing time).


    Upcoming talks


  • Title: On the hbar-Riemann-Hilbert program

  • Speaker: Tatsuki Kuwagaki (Kyoto University)

  • Abstract: The classical Riemann-Hilbert correspondence is about an equivalence between D-modules and constructible sheaves. D-modules can be considered as a specialization of D_hbar-modules, the latter is a deformation quantization of T^*M. Can we upgrade Riemann-Hilbert correspondence to D_hbar-setting? An expected answer has a very rich structure involving sheaf quantization, Fukaya category, exact WKB/resurgent analysis, and etc. In this talk, I’d like to explain these things.

  • Date: May 22, 2024 (Wednesday)

  • Time: 4:00-5:00 pm (Beijing)/10:00-11:00 am (Bonn)

  • Venue: A3-2-303, BIMSA

  • Zoom meeting ID: 242 742 6089

  • Zoom passcode: BIMSA

  • Date: May 29, 2024 (Wednesday)

  • No seminar

  • Title: TBA

  • Speaker: TBA

  • Abstract: TBA

  • Date: Jun. 05, 2024 (Wednesday)

  • Time: TBA

  • Venue: A3-2-303, BIMSA

  • Zoom meeting ID: 242 742 6089

  • Zoom passcode: BIMSA

  • Title: TBA

  • Speaker: TBA

  • Abstract: TBA

  • Date: Jun. 12, 2024 (Wednesday)

  • Time: TBA

  • Venue: A3-2-303, BIMSA

  • Zoom meeting ID: 242 742 6089

  • Zoom passcode: BIMSA

  • Title: TBA

  • Speaker: TBA

  • Abstract: TBA

  • Date: Jun. 19, 2024 (Wednesday)

  • Time: TBA

  • Venue: A3-2-303, BIMSA

  • Zoom meeting ID: 242 742 6089

  • Zoom passcode: BIMSA

  • Title: TBA

  • Speaker: TBA

  • Abstract: TBA

  • Date: Jun. 26, 2024 (Wednesday)

  • Time: TBA

  • Venue: A3-2-303, BIMSA

  • Zoom meeting ID: 242 742 6089

  • Zoom passcode: BIMSA


    • Past talks


  • May 16, 2024: the BIMSA AG talk Nonabelian Hodge theory for stacks and BPS cohomology by Ben Davison is strongly recommended.

  • Title: Quantum Stokes matrices

  • Speaker: Xiaomeng Xu (徐晓濛) (Peking University)

  • Abstract: This talk gives an introduction to the Stokes phenomenon of the universal quantum linear ordinary differential equations at a k-th order pole. It then proves that the quantum Stokes matrices give rise to an associative algebra, that quantize the Poisson structure on the moduli space of meromorphic connections at a k-th order pole. In the case k=2, the associative algebra involved is the Drinfeld-Jimbo quantum group.

  • Date: May 15, 2024 (Wednesday)

  • Time: 3:00-4:00 pm (Beijing)/9:00-10:00 am (Bonn)

  • Venue: A3-2-303, BIMSA

  • Zoom meeting ID: 242 742 6089

  • Zoom passcode: BIMSA

  • Title: On the geometric P=W conjecture

  • Speaker: Mirko Mauri (École Polytechnique)

  • Abstract: The geometric P = W conjecture is a conjectural description of the asymptotic behaviour of a celebrated correspondence in non-abelian Hodge theory. In a joint work with Enrica Mazzon and Matthew Stevenson, we establish the full geometric conjecture for compact Riemann surfaces of genus one, and obtain partial results in arbitrary genus: this is the first non-trivial evidence of the conjecture for compact Riemann surfaces. To this end, we employ non-Archimedean, birational and degeneration techniques to study the topology of the dual boundary complex of certain character varieties.

  • Date: May 8, 2024 (Wednesday)

  • Time: 3:30-4:30 pm (Beijing)/9:30-10:30 am (Bonn)

  • Venue: A3-2-303, BIMSA (online)

  • Zoom meeting ID: 242 742 6089

  • Zoom passcode: BIMSA

  • Date: May 1, 2024 (Wednesday)

  • No seminar (holiday)

  • Title: Generalized Beauville decompositions

  • Speaker: Qizheng Yin (訚琪峥) (BICMR)

  • Abstract: This serves as a complement to Junliang Shen’s talk. I will begin with the classical theory of the Beauville decomposition, which provides a canonical, multiplicative splitting of the Leray filtration for abelian schemes. Then I will discuss the problem of extending the Beauville decomposition to certain abelian fibrations with singular fibers. I will explain how the extension leads to the multiplicativity of the perverse (Leray) filtration for such fibrations, and eventually to a new proof of the P = W conjecture. Further results and open questions will also be discussed. Joint work with Younghan Bae, Davesh Maulik, and Junliang Shen.

  • Date: Apr. 24, 2024 (Wednesday)

  • Time: 4:00-5:00 pm (Beijng)/10:00-11:00 am (Bonn)

  • Venue: A3-2-303, BIMSA (in person)

  • Zoom meeting ID: 242 742 6089

  • Zoom passcode: BIMSA

  • Title: The P=W conjecture and Fourier transform

  • Speaker: Junliang Shen (沈俊亮) (Yale University)

  • Abstract: Around 2008, de Cataldo, Hausel, and Migliorini proposed the P=W conjecture, which predicts a connection between the topology of the Hitchin system and the Hodge theory of the character variety under the non-abelian Hodge correspondence. Since then, much effort has been devoted to understanding this myterious phenomenon, leading to the discovery of new geometric structures on both the Higgs side and the character variety side. In this talk, I will first review the P=W conjecture, which has been proven as a theorem since 2022 by Maulik-Shen and Hausel-Mellit-Minets-Schiffmann. Then I will discuss a recent attempt, in joint work with Davesh Maulik and Qizheng Yin, to understand this conjecture using Fourier transform. This approach establishes links between derived equivalences and the decomposition theorem, shedding further light on the algebraic cycles/motives associated with the Hitchin system.

  • Date: Apr. 17, 2024 (Wednesday)

  • Time: 10:00-11:00 am (Beijing)

  • Venue: A3-2-303, BIMSA (online)

  • Zoom meeting ID: 242 742 6089

  • Zoom passcode: BIMSA

  • Title: A Deligne-Simpson problem for irregular G-connections over P^1

  • Speaker: Konstantin Jakob (TU Darmstadt)

  • Abstract: The Deligne-Simpson problem asks for the existence of meromorphic G-connections with prescribed local behavior at the poles. I will explain joint work with Zhiwei Yun in which we give a solution to this problem for G-connections on P^1 with two poles, one of which is regular singular with residue in a fixed nilpotent orbit, the other of which is irregular and satisfies a condition that we call isoclinic (all slopes are equal). Perhaps surprisingly, our solution is related to the representation theory of the rational Cherednik algebra. If time permits, I will discuss joint work with Andreas Hohl regarding uniqueness (rigidity) of the solution for two famous families of such G-connections, the Kloosterman (aka Frenkel-Gross) G-connection and the Airy G-connection. Our approach is based on the Stokes phenomenon for irregular connections.

  • Date: Apr. 10, 2024 (Wednesday)

  • Time: 3:00-4:00 pm (Beijing)/9:00-10:00 am (Bonn)

  • Venue: A3-4-312, BIMSA (online)

  • Zoom meeting ID: 242 742 6089

  • Zoom passcode: BIMSA

  • Date: Apr. 3, 2024 (Wednesday)

  • No seminar due to Arbeitsgemeinschaft: Geometry and Representation Theory around the P=W Conjecture

  • Mar. 28, 2024: the BIMSA AG talk 3d cohomological Hall algebras for local surfaces by Adeel Khan is strongly recommended.

  • (Joint with Seminar on "Moduli Spaces and Related Topics" at YMSC)

  • Title: Hodge properties of confluent hypergeometric connections

  • Speaker: Yichen Qin (秦翊宸) (Humboldt-Universität zu Berlin)

  • Abstract: Sabbah and Yu computed the irregular Hodge numbers associated with hypergeometric connections. In this talk, we introduce a new approach for hypergeometric connections whose defining parameters are rational numbers. Our method relies on a geometric interpretation of hypergeometric connections, which enables us to describe the irregular Hodge filtrations explicitly and derive several arithmetic applications on hypergeometric sums. This research is conducted in collaboration with Daxin Xu.

  • Date: Mar. 27, 2024 (Wednesday)

  • Time: 2:00-3:00 pm (Beijing)/7:00-8:00 am (Bonn)

  • Venue: C654, Shuangqing Complex Building, YMSC (in person)

  • Zoom meeting ID: 242 742 6089

  • Zoom passcode: BIMSA

  • Title: The spectral base of Hitchin maps

  • Speaker: Jie Liu (刘杰) (Academy of Mathematics and Systems Science, Chinese Academy of Sciences)

  • Abstract: Let X be a projective manifold. The Hitchin morphism is a map from the moduli stack of Higgs bundles over X to the Hitchin base, which sends a Higgs bundle to its characteristic polynomial. If X is a curve, it is well-known that the Hitchin morphism is surjective and it plays an important role in the study of the moduli space of Higgs bundles. However, if X has dimension at least two, the Hitchin morphism in general is not surjective. Thus a closed subset of the Hitchin base, called the spectral base, is introduced by Tsao-Hsien Chen and Bao Chau Ng{\^o} and it is conjectured that the Hitchin morphism is onto the spectral base. This conjecture is confirmed when X is a surface by the works of Tsao-Hsien Chen & Bao Chau Ng{\^o} and Lei Song & Hao Sun. In this talk, I will present our solution to this conjecture for rank two Higgs bundles and also show the vanishing of the spectral base for Hermitian locally symmetric spaces with higher rank. This is joint work with Siqi He and Ngaiming Mok.

  • Date: Mar. 20, 2024 (Wednesday)

  • Time: 10:00-11:00 am (Beijing)

  • Venue: A3-2-303, BIMSA (online)

  • Zoom meeting ID: 518 868 7656

  • Zoom passcode: BIMSA

  • Title: On quantization of Coulomb branches II

  • Speaker: Du Pei (裴度) (Centre for Quantum Mathematics, University of Southern Denmark)

  • Abstract: In this talk, we will study the geometry of Coulomb branches of 4d quantum field theories and identify hidden algebraic structures within them.

  • Date: Mar. 13, 2024 (Wednesday)

  • Time: 4:00-5:00 pm (Beijing)/9:00-10:00 am (Bonn)

  • Venue: A3-2-303, BIMSA (online)

  • Zoom meeting ID: 242 742 6089

  • Zoom passcode: BIMSA

  • Title: Deformation quantization and perverse sheaves

  • Speaker: Sam Gunningham (Montana State University)

  • Abstract: Given a holomorphic symplectic manifold and a pair of oriented holomorphic lagrangian submanifolds, the lagrangian intersection carries a canonical perverse sheaf known as the DT sheaf. On the other hand, the theory of deformation quantization provides another, seemingly quite different, construction of a perverse sheaf. I will explain some recent results with Pavel Safronov in which we identify these two constructions, shedding new light on Joyce's conjectural description of the holomorphic Fukaya category. Time permitting, I will outline a potential application of these results, in which we related the skein module of a 3-manifold to the sheaf-theoretic Floer homology of Abouzaid and Manolescu.

  • Date: Mar. 13, 2024 (Wednesday)

  • Time: 10:00-11:00 am (Beijing)

  • Venue: A3-2-303, BIMSA (online)

  • Zoom meeting ID: 518 868 7656

  • Zoom passcode: BIMSA

  • Title: Skein algebras and quantized Coulomb branches

  • Speaker: Dylan Allegretti (YMSC)

  • Abstract: It is believed that character varieties of surfaces arise in quantum field theory as Coulomb branches of four-dimensional N=2 field theories on R^3xS^1. In this talk, I will explain how this prediction can be proved rigorously in some cases using the notion of a K-theoretic Coulomb branch introduced by Braverman, Finkelberg, and Nakajima. I will describe a relationship between the Kauffman bracket skein algebra, which quantizes the SL2-character variety of a surface, and an associated quantized K-theoretic Coulomb branch. This is joint work with Peng Shan.

  • Date: Mar. 6, 2024 (Wednesday)

  • Time: 3:30-4:30 pm (Beijing)/8:30-9:30 am (Bonn)

  • Venue: A3-2-303, BIMSA (in person)

  • Zoom meeting ID: 242 742 6089

  • Zoom passcode: BIMSA

  • Title: On quantization of Coulomb branches I

  • Speaker: Du Pei (裴度) (Centre for Quantum Mathematics, University of Southern Denmark)

  • Abstract: In this talk, we will study the geometry of Coulomb branches of 4d quantum field theories and identify hidden algebraic structures within them.

  • Date: Feb. 28, 2024 (Wednesday)

  • Time: 4:00-5:00 pm (Beijing)/9:00-10:00 am (Bonn)

  • Venue: A3-2-303, BIMSA (online)

  • Zoom meeting ID: 242 742 6089

  • Zoom passcode: BIMSA