Titles, Abstracts and Slides

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January 7 (Sat)

Takuro Mochizuki (RIMS)

Title: Twistor D-modules and holomorphic Landau-Ginzburg models

Abstract: For a complex manifold X with a holomorphic function f, we obtain the twisted de Rham complex (Ω_X^• [[λ]], λd + d f ). On the one hand, it plays important roles in the study of mirror symmetry as a main object associated with a holomorphic Landau-Ginzburg model. On the other hand, it naturally appears in the context of twistor D-modules. In this talk, we shall briefly review the theory of twistor D-modules, and explain how to apply it in the study of twisted de Rham complexes.

Seok Kim (Seoul National University)

Title: A cohomology problem on the black hole microstates in AdS/CFT

Abstract: I will explain a cohomology problem which is related to the quantum states of black holes in Anti de Sitter (AdS) spacetime via holography. Recent breakthroughs as well as future prospects will be discussed.

Mikhail Bershtein (HSE, IPMU)

Title: Quantum spectral problems and isomonodromic deformations

Abstract: We study the spectral properties of a class of quantummechanical opera- tors by using the knowledge about monodromies of 2 × 2 linear systems (Riemann- Hilbert correspondence). The main examples for the talk will be Mathieu operator and Lame operator. By using the Kyiv formula for the isomonodromic tau functions, we obtain the spectrum of such operators in terms of self-dual Nekrasov functions. Through blowup relations, we also find Nekrasov-Shatashvili type of quantizations. Based on joint work with A. Grassi and P. Gavrylenko.

Takuya Okuda (University of Tokyo) [PDF (18.9MB))]

Title: Conserved charges in the quantum simulation of integrable spin chains

Abstract: With the advancement of quantum computing technologies, quantum sim- ulation of many-body systems such as spin chains and lattice gauge theories will be- come an essential application target. In my talk, I will describe our work where we studied the quantum simulation of the spin-1/2 Heisenberg XXX spin chain. The model admits an integrable Trotterization so that the discretized time evolution pre- serves deformations of the original conserved charges. We implemented the integrable Trotterization on a real quantum computer and classical simulators. We then studied how quantum noise affects the time evolution of several conserved charges, and ob- served the decay of their expectation values. In addition, we examined the early-time behaviors, which can potentially be used to benchmark quantum devices and algorithms in the future. We also provided an efficient method to generate the conserved charges at higher orders.
Based on arXiv:2208.00576 with K. Maruyoshi, J. Pedersen, R. Suzuki, M. Yamazaki, and Y. Yoshida.

January 8 (Sun)

Jae-Hoon Kwon (Seoul National University) [PDF (722KB))]

Title: Representations of quantum affine superalgebra of type A

Abstract: In this talk, we introduce a new approach to finite-dimensional represen- tations of the quantum affine superalgebra of type A. We show that a well-known construction of simple modules of the quantum affine algebra by using the R matrix on the tensor product of fundamental representations can be extended to the case of the quantum affine superalgebra of type A. This is done by introducing an ex- act tensor functor called truncation motivated by the theory of super duality due to Cheng-Lam-Wang.
This talk is based on a joint work with S.M. Lee.

Vyacheslav Lysov (OIST) [PDF (3.5MB))]

Title: Tropical mirror symmetry

Abstract: In my talk I will start with the brief review the tropical geometry, tropical Gromov-Witten invariants and tropical correspondence theorem. I will formulate the tropical mirror correspondence theorem for toric spaces and describe the key steps of its proof. The first step introduces the A-type higher topological quantum mechanics (HTQM) to describe the tropical GW invariants as correlation functions. The second step is the mirror relation between the A-type HTQM and B-type HTQM in the form of deformation by divisor states. The last step is the evaluation of the B-type HTQM correlation functions in terms of Jacobi ring data for mirror superpotential.

Tatsuki Kuwagaki (Kyoto University)

Title: A-branes via sheaves

Abstract: Homological mirror symmetry predicts equivalence between the A-model and B-model brane categories. In mathematics, the A-brane category is classically modeled by Fukaya category defined via Lagrangian intersection Floer theory. In the last 10 years, a sheaf-theoretic approach to the A-brane category has been developed. Namely, there are categories defined via microlocal sheaf theory that are shown or expected to be equivalent to Fukaya categories. In this talk, I will give an introduction to this approach and explain why this approach is connected to various quantizations.

Hosho Katsura (University of Tokyo) [PDF (1.8MB))]

Title: Constructing frustration-free models via Witten’s conjugation

Abstract: Witten’s conjugation is a powerful method to construct a family of in- equivalent Hamiltonians with the same number of zero-energy ground states [1]. This method provides a means to map a complicated Hamiltonian to a simpler one, in which the counting of the ground states is rather trivial. Although the method was originally introduced in the context of supersymmetric quantum mechanics, the same idea applies to frustration-free models, which are not necessarily supersymmetric. In this talk, I will show that this conjugation approach allows us to construct a family of frustration-free models starting from a simple model, e.g., the classical Ising model [2]. The method not only provides a unified framework to treat different models scat- tered in the literature but also allows us to construct new models with exact ground states.
[1] E. Witten, Nucl. Phys. B 202, 253 (1982).
[2] J. Wouters, H. Katsura, and D. Schuricht, SciPost Phys. Core 4, 027 (2021) [arXiv:2005.12825].