Persistent homology is one of the main tools in topological data analysis (TDA), which encodes the topological features of given data into persistence diagrams. It has been successfully applied to various fields such as material science and computer graphics. In this talk, I will provide an overview of persistent homology and its applications. Furthermore, I will also discuss its integration with machine learning, specifically how persistent-homology-based loss functions can be used to regularize the topological structure of parameters.

The Square Peg Problem asks whether every Jordan curve in the plane contains four distinct points that form the vertices of a square. This
problem was proposed by Toeplitz in 1911 and remains unsolved in full generality. It can be generalized to the Rectangular Peg Problem, which concerns the existence of inscribed rectangles with a prescribed aspect ratio. Recently, Greene and Lobb successfully applied techniques in symplectic geometry to the problem and obtained new results. In this talk, I will explain how microlocal sheaf theory allows us to further extend their approach and affirmatively solve the Rectangular Peg Problem for a large class of Jordan curves, including all curves of finite length. This is joint work with Tomohiro Asano.

Data Assimilation (DA) is the backbone of modern weather forecasting. It integrates observational data into computer simulations to synchronize the model with nature. The Duality Principle posits that chaos control is mathematically the "twin" (dual) of DA.

Data Assimilation: Uses observations to synchronize the Model to Nature.
Chaos Control: Uses interventions to synchronize Nature to a desired Model ("target trajectory").

"The butterfly effect has long been a symbol of unpredictability," says Dr. Miyoshi. "But I asked a simple question: If a butterfly's wings can change the future, does that not imply that with the right, tiny push, we could choose a better future?"

Instead of suppressing the chaotic system with massive force, this method acts like mathematical judo—leveraging the system's inherent instability. By applying minute, calculated "interventions" (analogous to the butterfly's flap), the system can be guided toward a "target trajectory"—for instance, shifting real-world conditions just enough to align with a model-simulated scenario where a typhoon causes no damage. Once synchronized, control becomes much easier to maintain.

This study establishes the theoretical foundation for "Control Simulation Experiments" (CSE), a framework previously proposed by Miyoshi’s team. It provides a roadmap for future disaster prevention research, moving beyond passive prediction to active mitigation. Beyond meteorology, this general framework is expected to serve as a universal tool for studying interventions in various chaotic systems, from ecosystems to economics.

Following the seminar, we will hold an informal discussion (brainstorming) on data assimilation with quantum computing in the same room from 2-4 pm.

We will discuss the potential of quantum computing for applications in data assimilation.

14:45-15:00 Teatime discussion

[15:00-16:00 The 31th MACS Colloquium]
Talk by Dr. Yujiro Eto (Associate Professor, Center for Science Adventure and Collaborative Research Advancement (SACRA), Graduate School of Science, Kyoto University)

[16:10-18:30 2025 MACS Achievement Report Meeting]
16:10-17:10 Flash Talks to report results
17:10-18:00 Poster Session by SG participating students

In this talk, I will discuss the problem of inferring an evolutionary tree from DNA sequence data. The main focus will be on the sample complexity of this problem---i.e., the question of how much data is required to achieve high probability of correct inference. After introducing a standard stochastic model of gene and DNA evolution, I will highlight some surprising features of DNA sequence data that complicate inference. Finally, I will present an impossibility result which takes the form of an information-theoretic lower bound on the minimum amount of data needed for accurate inference when genes exhibit variation in mutation rates. No prior knowledge of phylogenetics or information theory is assumed. Based on joint work with Sebastien Roch.

This seminar is a joint seminar between GWX-EOS and the iTHEMS-ABBL Joint Astro SG.

The recent rise of multi-messenger astronomy—including radius measurements from NICER, tidal deformability constraints from gravitational-wave events GW170817, and first-principles calculations from chiral effective field theory (χEFT) and perturbative QCD—has significantly tightened constraints on the neutron star equation of state. These advances consistently point to a non-monotonic sound speed in dense matter, suggesting that the cores of massive neutron stars may host exotic phases such as quark matter. However, the masquerade effect in static neutron stars makes it difficult to directly probe the nature of the transition (e.g., a smooth crossover or a sharp phase transition) near the core through observation alone.

In this talk, I will introduce a novel geometric framework for quantum error correction based on spectral triples in noncommutative geometry. In this formulation, quantum error-correcting codes are described as spectral projections onto the low-energy eigenspaces of Dirac-type operators, where the separation between logical information and local errors is captured geometrically. This approach provides a unified spectral and geometric understanding of key properties such as code distance and error thresholds. Moreover, it accommodates various existing codes, including classical linear codes, stabilizer codes, GKP codes, and topological codes. This geometric perspective also suggests intriguing connections to deformation quantization and holographic quantum error correction, offering promising directions for future research.

In this talk we discuss some of the most basic conceptual and mathematical difficulties that arise in the standard physics analysis of QFT. In particular we shall discuss the origin of UV divergences in QFT—pointing out that there is both a kinematic and a dynamic aspect to this problem, and that the standard physics explanation (’new physics’) only considers the latter—and suggest that despite the notoriety of the problem, UV divergences are essentially under control. Secondly we discuss Haag’s theorem—which ensures the nonexistence of the interaction picture and the triviality of the perturbative S-Matrix—and indicate how this is the most elementary manifestation of a series of infrared problems in QFT. Finally we will outline why the rigorous construction of path-integral measures is difficult. If we have time, we may discuss some difficulties associated with gauge theories such as the infraparticle problem of QED and the mass-gap problem of Yang-Mills theory.

Quantum gravity remains one of the major challenges in modern physics. Even at the most fundamental level, there is no experimental confirmation of whether a mass placed in a spatial superposition generates a corresponding superposition of gravitational fields. In recent years, experiments aiming to create gravity-induced quantum entanglement have attracted significant attention as a way to probe the quantum nature of non-relativistic gravity. In particular, optomechanical systems, which exploit the interaction between light and mechanical oscillators, provide a promising platform for such studies. We are pursuing experiments at the milligram scale, which lies between the smallest mass scale at which classical gravity has been tested and the largest mass scale at which quantum states of mechanical oscillators have been realized [1]. In this seminar, I will discuss experimental approaches to testing the quantum nature of gravity using suspended and levitated mirrors. I will also discuss our recent proposal to use inverted oscillators to enhance gravity-induced entanglement exponentially [2].

While my career began in a linear way, it gradually opened into a non-traditional path through unexpected mergings, where theoretical nuclear physics, filmmaking, and creative public and academic engagement intertwined. I will share how scientific inquiry, artistic practice, and storytelling began shaping one another, opening new ways to explore complexity, emotion, and connection. Drawing on work from my physics research to cinema projects like Rare Connections, I will reflect on how curiosity and creative thinking move freely across science and art, deepening each and expanding how we understand the human experience. My aim is to offer a perspective on the possibilities that emerge when we allow our multitudes to meet and transform one another.

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 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.

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

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.

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.