This joint workshop will bring together physicists and mathematicians who work with asymptotics and perturbation theory techniques. This includes theorists in cosmology, high energy physics, quantum gravity, solar physics, astrophysics.

Workshop overview
Over three days, there will be approximately 15 invited (1 hour slot) or contributed (20-30 min slot) talks about:
Fundamental asymptotics and perturbation theory techniques used in theoretical physics. Various applications of asymptotics and perturbation theory techniques in (wave transport or oscillation related) astrophysics and cosmology eigenvalue problems.

The workshop will also feature hands-on Mathematica and Python tutorials introducing:
Practical use of WKB methods in applied mathematics for any “Schrodinger-like” wave equations, Resummation methods in high energy theory, Deriving normal modes in stars, and their application to tidal evolution in binary star or planet systems, Eigenvalue problems in core collapse supernova theory.

The RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS) and the Faculty of Science at Nara Women's University are promoting a project to foster female researchers under the auspices of the RIKEN Diversity Promotion Office. As part of the program, 21 undergraduate and graduate students from Nara Women's University will visit several laboratories on the RIKEN Wako campus to ask questions about their research and hold workshops with iTHEMS researchers.

Organizers:
RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS)
Faculty of Science, Nara Women's University

March 2 (Mon)
13:15-14:15
Center for Brain Science (CBS) (C56 Ikenohata Building)
Laboratory for Multi-scale Biological Psychiatry (Team Director: Akiko Hayashi-Takagi)

14:30-15:45
Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS) (C01 Main Research Building, 4th Floor Rooms 435-437)
Introduction to iTHEMS: Tetsuo Hatsuda (iTHEMS Division Director of Applied Mathematical Science)
Lecture and Q&A: Megumi Oya (iTHEMS Medical Science Data-driven Mathematics Team Postdoctoral Researcher)

16:00-17:30
Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS) (C01 Main Research Building, 4th Floor Rooms 435-437)
Lecture and Q&A: Leo Spiedel (iTHEMS ECL Research Unit Leader)

18:00-20:30 Networking Session (C01, Research Main Building 3F East Side (Okochi Hall Side))

March 3 (Tue)
9:00-10:30
RIBF Facility, RIKEN Nishina Center (RNC)

11:15-12:00
Center for Quantum Computing (RQC)
Optical Quantum Control Research Team (Team Director: Hidehiro Yonezawa)

The interplay between black hole interior dynamics and quantum chaos provides a crucial framework for probing quantum effects in quantum gravity. According to the holographic "Complexity=Volume" proposal, we investigated non-perturbative generating function of geodesic length in Jackiw-Teitelboim (JT) gravity to uncover universal signatures of quantum chaos and quantum complexity. We observed that the generating function interpolates between two major probes of quantum chaos - spectral form factor and complexity - highlighting its utility as a probe of chaotic spectrum in quantum gravity. Generalizing the result to general chaotic systems, we demonstrated that time evolution of the complexity is universally governed by a certain pole structure of observables, suggesting a validity of wide class of observables as a probe of quantum chaos in quantum gravity.

The minimal absolute value \sigma_{\ell}(n) of a weight-n sum of \ell-th roots of unity, for all n and a fixed \ell, is an interesting value in the study of maximal determinant matrices. In the cases where \ell=2,3,4, or 6, this minimal absolute value is either 0 or 1. Thus \ell=5 constitutes the smallest non-trivial case. In this talk I will discuss recent results in collaboration with Akihiro Munemasa, where we determined \sigma_5(n) for all n\geq 1. This problem turns out to be related to the Diophantine approximation of the golden ratio, and can be tackled using the theory of continued fractions.

The world is filled with numerous odors that are impossible to experience all in our lifetime. Perhaps to cope with this situation, the brain is equipped with an ability to recognize whether an odor is attractive or aversive even from the first encounter and guide adaptive behavior. However, how information about the innate value of odors (attractiveness/aversiveness) is computed and transformed into appropriate behavioral outputs in the brain remains poorly understood. We are addressing this question in the olfactory circuit of fruit flies by combining behavioral analysis in virtual reality, comprehensive neuronal activity imaging, neuronal connectivity analysis, and computational modeling. In this talk, I will present our latest efforts to decipher how odor value is computed and how this information is transformed into motor-related signals in a tiny brain.

The Mathematical Application Research Team is pleased to welcome Chiyaha Jibiki, who will join the team as an SPDR in April. He will give a talk at this meeting prior to his official start date. Everyone is welcome to join the meeting.

Title: Left-Orders and Dynamics: Applications to Hyperbolic Geometry and Low-Dimensional Topology

Abstract: A left-order on a group is a total order that is invariant under left-multiplication. The concept dates back to the early 20th century, when Dedekind and Hölder characterized the natural order on the real line purely in terms of group actions.
In the 21st century, this theory has evolved significantly through connections with discrete dynamical systems. Currently, there is active research linking geometric structures to left-orders on geometrically significant groups, such as fundamental groups and mapping class groups.
In this talk, I will introduce the framework of left-order theory, starting from the simple perspective of binary operations on infinite sets. I will then provide an overview of the field by presenting, as much as possible, the diverse applications arising from its high versatility. In particular, I will discuss the speaker's recent results concerning the structure of the space of left-orders (comparisons between left-orders) and methods for constructing specific left-orders.
This talk includes joint work with Shuhei Maruyama (Kanazawa University).

The two fundamental questions—“What is quantum?” and “What is spacetime?”—are deeply intertwined. On one hand, the formulation and interpretation of quantum theory depend both implicitly and explicitly on our conceptions of time and space. On the other hand, we believe that fully taking into account the quantum character of nature will force us to revise our understanding of spacetime. These two conceptual problems lie at the heart of the unsolved challenge of how to quantize classical spacetime, and conversely, how (semi-) classical descriptions of spacetime emerge from quantum theory. Furthermore, if the entire matter-spacetime system is a kind of quantum many-body system, thermodynamics—which governs its statistical behaviors—should play a key role in elucidating these problems.

This workshop will discuss the question “How can quantum theory and spacetime be understood in a consistent manner?” from a fundamental and broad perspective. To tackle this challenge, we gather researchers in foundations of quantum theory, quantum gravity, and related fields from around the world, providing a "space and time" to share various ideas with open minds and engage in lively discussions. By exploring new concepts and principles, we hope to uncover directions to guide quantum theory over the next 100 years.

This workshop covers…

Foundations of quantum theory
Quantum gravity and emergence of spacetime
Formulation of semi-classical gravity
Experimental aspects of fundamental properties in nature and quantum gravity
Foundations of quantum many-body systems and thermodynamics
Other related topics are welcome.

We welcome short talk presentations and poster presentations.

This event is a workshop jointly organized by KEK Theory Center and RIKEN iTHEMS.

Living systems operate far from equilibrium under continuous time-varying forcing across multiple temporal and spatial scales. From neural and cardiovascular rhythms to microcirculatory dynamics and circadian cycles, physiological processes are inherently nonautonomous. Classical stability concepts based on autonomous attractors and stationary limit cycles are therefore insufficient to explain how such systems remain robust yet adaptable.
In this talk, I will introduce chronotaxicity as a framework for nonautonomous oscillatory systems possessing time-dependent point attractors and contraction regions. Chronotaxic systems maintain stability under continuous forcing, providing a rigorous theoretical description of dynamic robustness.
To illustrate the generality of this concept, I will show how chronotaxicity can be observed in a controlled physical experiment. I will then present a new order parameter based on angular velocity for quantifying phase dynamics in numerical simulations of coupled nonautonomous oscillators, along with the methods collected in the Multiscale Oscillatory Dynamics Analysis (MODA) toolbox for analysing time-dependent oscillatory behaviour.
This approach provides a unified perspective on dynamic stability in complex systems, highlighting how living systems remain robust yet adaptable and suggesting quantitative signatures of dysfunction in health and disease. While the focus is on physiological and numerical models, it is broadly applicable to complex nonautonomous systems, underscoring its generality as a dynamical principle.

Quantum invariants are invariants of knots and 3-manifolds which relate deeply to mathematical physics and representation theory.
In recent years, it has become increasingly clear that it is also deeply related to number theory, that is, quantum modularity for quantum invariants.
This topic is interesting from a topological viewpoint since this is a refinement of establishing asymptotic expansions of quantum invariants, which is an important problem in quantum topology,
and is interesting from a number-theores[tic viewpoint since this gives examples of quantum modular forms, which are mysterious objects in number theory.

I obtained two linked results on topology and number theory:
Establishing explicit asymptotic expansions of quantum invariants for negative definite plumbed 3-manifolds and establishing quantum modularity of false theta functions in full generality.

In this talk, I will outline previous progress on quantum modularity for quantum invariants and my results.

We investigate the critical behavior of a family of Z2-symmetric scalar field theories on the Bethe lattice (the tree limit of regular hyperbolic tessellations) using both the non-perturbative Functional Renormalization Group and perturbation theory. Due to the hyperbolic nature of Bethe lattices, the Laplacian lacks a zero mode and exhibits a spectral gap. We demonstrate that closing the spectral gap via a modified Laplacian leads to novel critical behavior governed by interacting fixed points. This stands in contrast to the nearest-neighbor Ising model, which exhibits a phase transition with mean-field critical exponents. We further comment on the possible reasons for such a deviation.

PROGRAM:

9h45 - 10h15 Registration & Coffee

10h15 - 10h20 Opening Remarks - Satoshi Iso (RIKEN), Director of iTHEMS

10h20 - 11h20 SESSION 1 - Chair: Tetsuo Hatsuda (RIKEN)

Yoshihiko Susuki (Kyoto University): Koopman resolvents in dynamical systems and control

11h20 -11h40 Free Discussions

11h40 - 13h00 Lunch Break & Discussions

13h00-14h00 SESSION 2 - Chair: Narumi Fujii (Institute of Science Tokyo)

Alexandre Mauroy (University of Namur, Belgium): Analytic EDMD method for spectral analysis of fixed point dynamics

14h00 - 14h30 Coffee Break & Discussions

14h30 - 15h30 SESSION 3 - Chair: Tetsuo Hatsuda (RIKEN)

Hiroya Nakao (Institute of Science Tokyo): Koopman operator analysis of coupled oscillator systems

15h30 - 16h00 Coffee Break & Discussions

16h00 - 17h00 SESSION 4 - Chair: Riccardo Muolo (RIKEN)

Yuzuru Kato (Future University Hakodate): Analysis of quantum nonlinear oscillators on the basis of Koopman operator theory

17h00 - 17h05 Closing Remarks - Tetsuo Hatsuda, Chair of the Workshop

17h05 - 18h00 Free Discussions

Understanding how complex organs reliably form during development remains a key question in biology. In this talk, I discuss how gene regulatory networks may generate skeletal patterns in the vertebrate limb, using Sox9 expression as a proxy, as it marks the earliest stages of cartilage formation. To address this, I developed new computational tools for reconstructing spatiotemporal gene expression and built models ranging from machine learning approaches to mechanistic frameworks. These analyses reveal that limb patterning cannot be explained by a single universal mechanism. Instead, different regions of the limb appear to use distinct regulatory strategies, uncovering an unexpected qualitative modularity in skeletal development. Together, these findings lead to a new hypothesis in which other systems, such as the vasculature may actively shape skeletal spacing in specific limb regions.

Correlation functions of local operators in Quantum Field Theory (QFT) on hyperbolic space can be fully characterized by the set of QFT data. These are the scaling dimensions of boundary operators, the boundary Operator Product Expansion (OPE) coefficients and the Boundary Operator Expansion (BOE) coefficients that characterize how each bulk operator can be expanded in terms of boundary operators. For simplicity, we focus on two dimensional QFTs and derive a universal set of first order Ordinary Differential Equations (ODEs) that encode the variation of the QFT data under an infinitesimal change of a bulk relevant coupling. In principle, our ODEs can be used to follow a renormalization group flow starting from a solvable QFT into a strongly coupled phase and to the flat space limit.

Gravitational-wave detections by the LIGO-Virgo-KAGRA network have turned compact-object mergers into precision probes of strong gravity. The post-merger ringdown is particularly incisive: it is governed by quasinormal modes (QNMs), the damped oscillations that encode the remnant's structure and provide a fingerprint of the final object. While current detectors constrain the dominant mode, next-generation observatories will resolve multiple modes with high precision, placing stringent demands on the accuracy of theoretical predictions. Computing QNMs for rotating black holes is, however, a non-trivial task, as it requires solving highly coupled, complex-valued perturbation equations where standard methods struggle. In this talk, I present SpectralPINN, a hybrid solver combining Pseudo-spectral methods with Physics-Informed Neural Networks, validated at 10⁻⁵ relative accuracy. I will present results for Kerr and Kerr-Newman black holes, demonstrating the method's robustness and accuracy across parameter space, and discuss its potential for extension to more exotic compact objects relevant to next-generation detector science.

Recent advances in X-ray spectroscopic observation have enabled researchers to reveal distinct clumpy structures in the super-Eddington outflows from the supermassive black hole in PDS 456 (XRISM Collaboration 2025), initiating detailed investigation of fine-scale structures in accretion-driven outflows. In this talk, I will introduce our high-resolution, two-dimensional radiation-hydrodynamics simulations with time-varying and anisotropic initial and boundary conditions that reproduce clumpy outflows from super-Eddington accretion flows. The resulting clumpy outflows extend across a wide range of radial distances and polar angles, exhibiting typical properties such as a size of ~10 rg (where rg is the gravitational radius), a velocity of ~0.05–0.2 c (where c is the speed of light), and about five clumps along the line of sight. Although the velocities are slightly smaller, these characteristics reasonably resemble those obtained from the XRISM observation. The gas density of the clumps is on the order of 10^-13–10^-12 g cm^-3, and their optical depth for electron scattering is approximately 1–10. The clumpy winds accelerated by radiation force are considered to originate from the region within <300 rg.