The quest for a quantum description of gravity has been long, diverse, and productive. Yet, despite decades of theoretical progress, there is still no direct experimental evidence for the quantum nature of spacetime. In this talk, I explore an alternative, indirect route to probing quantum gravity by assuming the fundamental classicality of the gravitational field and examining the resulting observational conflicts. In particular, I will discuss a key consistency condition—known as the decoherence–diffusion trade-off—that any theory of fundamentally classical gravity coupled to quantum matter must satisfy. By analysing a toy model of a linearised classical–quantum (CQ) gravity–matter system, I will explicitly show how this trade-off implies unavoidable, measurable effects, such as a fundamental stochastic gravitational-wave background, which cannot be eliminated by fine-tuning the model parameters.

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.

In this talk, I will introduce quantum states over time (QSOT), a formalism for describing quantum systems over space-time. I will begin by reviewing how QSOT has emerged in the literature. While conventional density operator formalism has been effective across many areas of quantum information theory, QSOT was developed to meet more specialized research needs— most notably, as a key ingredient to develop a quantum version of Bayes’ theorem. I will end the first part of my talk by comparing various QSOT that have been proposed.

In the second part, I will discuss the causal compatibility problem as an application of QSOT. I will focus on the temporal compatibility problem, which asks the following: from correlations in measurement outcomes alone, can two otherwise isolated parties establish whether such correlations are atemporal (i.e., temporally incompatible)? That is, can they rule out that they have been given the same system at two different times? I will first explain how characterizing measurement statistics in a causal agnostic scenario is equivalent to characterizing a specific type of QSOT, known as pseudo-density operators. I will then present our recent findings obtained by analyzing pseudo-density operators; In particular, we demonstrate that atemporality is distinct from entanglement, though they appear to be equivalent at first glance. Specifically, we show atemporality implies entanglement, but not vice versa, thus revealing that atemporality is a strictly stronger form of quantum correlations than entanglement. Nevertheless, we also find that sufficiently strong entanglement does imply atemporality.

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.

The microscopic world offers a fascinating diversity of locomotion strategies, relying primarily on the use of flagella and cilia. These slender structures, capable of complex periodic deformations, serve as a major source of inspiration for medical microrobotics.
At this scale, fluid dynamics is governed by the predominance of viscosity over inertia. This low-Reynolds number regime imposes strict physical constraints, summarized by the famous « scallop theorem »: a reciprocal deformation cannot produce any net displacement. Mathematically, this is framed by the Stokes connection, which links changes in body shape to net movement in space.
This presentation proposes a journey through the modeling principles of microscopic swimmers. We will see how to derive analytical solutions to the locomotion problem by simplifying degrees of freedom or by assuming small deformation amplitudes. I will then present the perspective of control theory to address the « controllability » property, i.e. the ability of a locomotor to reach any target position and shape.
Finally, I will question a classic hypothesis in the field: the inextensibility of flagella. Although the literature often assumes these structures are rigid in the longitudinal direction, certain micro-organisms and artificial robots exhibit significant compression variations. I will present recent results, based on classical modeling tools, exploring the influence of compression-curvature coupling on locomotion efficiency at low Reynolds numbers.

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.