Coffee Meeting Log

2026-06-12

But how many baskets should you put your eggs in?

Brian Mintz (iTHEMS)

“Don’t put all your eggs in one basket” is old advice against investing too much in any single area, but it does not tell us how many baskets to use, or how many eggs to place in each one. This everyday question contains a deep mathematical problem: how should we choose between different ways of distributing risk? Depending on the precise formulation, the “best” strategy can change completely; or in some cases, not exist at all. We will trace the history of answers to this simple yet profound question, connecting the work of Nobel prize winners across a variety of disciplines including biology, mathematics and economics. Understanding this topic even made one mathematician a multi-millionaire!

2026-06-05

Spontaneous symmetry breaking

Masazumi Honda (Senior Research Scientist, Division of Fundamental Mathematical Science, RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS) / Visiting Professor, Graduate School of Science and Engineering, Saitama University)

Why is iron strongly attracted to magnets? Why do elementary particles such as electrons have mass? The answers to these questions are closely related to a common idea called spontaneous symmetry breaking. In my talk, I will introduce the idea of spontaneous symmetry breaking starting with a demonstration experiment. I am also going to mention speculative examples of spontaneous symmetry breaking in various areas beyond physics.

2026-05-29

Current "virus trends": hanta, ebola, et cetera

Catherine Beauchemin (Deputy Director, RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS) / Associate Division Director, Division of Fundamental Mathematical Science, RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS) / Professor, Department of Physics, Toronto Metropolitan University, Canada)

I will discuss some viruses that have been in the news lately, what they are, where they come from, and explain whether and to what extent you should be worried about them. I'll also tell you about some cool and weird stuff I found out as part of preparing this short talk.

2026-05-22

The Origami Classification of Cosmic Structures

Derek Beattie Inman (Research Scientist, Division of Fundamental Mathematical Science, RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS))

The cosmic web forms from the gravitational collapse of a nearly uniform density field. I will discuss how this process proceeds starting from the first light objects to the present massive ones. Along the way, I will show an analogy between phase-space folding and origami which can be used to classify different types of structures.

2026-05-15

Exploring the Minimal Scale and Complexity of Networks that Generate Intelligence

Hokto Kazama (Team Director, Laboratory for Circuit Mechanisms of Sensory Perception, RIKEN Center for Brain Science (CBS))

When individual elements interact within a system, there exists a transition point where qualitatively new phenomena arise—properties that cannot be reduced to a single component. For example, in inorganic systems, this transition can manifest as a phase transition, while in organic systems, it can give rise to life-specific functions. However, a fundamental question remains: what is the minimum cellular scale and network complexity required to generate higher brain functions? Moving beyond anthropocentric viewpoints, we will investigate the structural and functional principles of intelligence within the broader context of life. By cross-examining gene regulatory networks, neural connectivity, and functional dynamics, we aim to uncover the essential architectural motifs that define the origins of biological intelligence.

2026-04-24

GW ringdowns and echoes

Che-Yu Chen (Special Postdoctoral Researcher, Division of Fundamental Mathematical Science, RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS))

Typical gravitational wave (GW) waveforms emitted by binary black hole mergers contain three phases, including inspiral, merger, and ringdown. Beyond the standard picture of classical black holes, there could be series of GW echoes following the standard ringdown signals, whose existence could be an indicator of horizon-scale new physics. In this talk, I will briefly introduce the physics of ringdown and GW echoes.

2026-04-10

The transition to synchronization: from phase reduction to the Kuramoto model

Riccardo Muolo (Special Postdoctoral Researcher, Division of Fundamental Mathematical Science, RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS))

Synchronization is one of the most studied phenomena in the field of complex systems and a paradigmatic example of self-organizing behavior. The synchronization of coupled oscillators was first observed by Christiaan Huygens, who in the 17th century noticed that pendula hanging on the same wall tend to synchronize in anti-phase. Later research highlighted the occurrence and relevance of synchronization in many natural and artificial systems, ranging from fireflies’ blinking and frogs’ croaking to rhythmic contractions in cardiac cells and neuronal activity, and from bridge oscillations to power angles in electrical power grids. The key factor enabling this collective behavior is the interaction among oscillators, which can be, for example, mechanical (bridges, pendulum clocks), electrical (heart, power grids), visual (fireflies), or acoustic (frogs). Until about sixty years ago, it was unclear how synchronization emerges. A major step forward came from Winfree, who proposed describing oscillators using only their phases and conjectured that a transition to synchronization would occur above a critical coupling strength. This idea inspired Kuramoto, who introduced his celebrated model and provided a solution to this longstanding problem. In this short talk, I will introduce the phase reduction approach and retrace the path that led Winfree and Kuramoto to these results. I will then discuss the Kuramoto model and illustrate the transition to synchronization.

2026-03-27

Condensation Tensor Network

Kantaro Ohmori (Senior Research Scientist, Division of Fundamental Mathematical Science, RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS))

A matrix is an array of numbers with two indices, composed along a line. A tensor has more indices, and tensors can be composed along a network that fills a region of space — much like how data, signals, or physical states are organized spatially in many areas of science. What conditions on the individual tensors guarantee that the network as a whole has nice properties? I will introduce the notion of a condensation tensor network, where simple algebraic conditions on each tensor — checkable locally — ensure that the entire network behaves coherently at any scale. The resulting structure defines a projection onto a subspace that is independent of the system size. These networks provide a unified language for topological phases of matter and quantum error correction.

2026-03-13

Dipole symmetry from anomaly

Hiromi Ebisu (Research Scientist, Division of Fundamental Mathematical Science, RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS))

Anomalies often signal that a quantum system cannot realize a trivial symmetric phase. In lattice systems, certain combinations of internal and spatial symmetries lead to such anomaly constraints. We discuss that dipole symmetry, a spatially modulated symmetry, can naturally emerge from these anomaly structures. Starting from anomalous lattice models, we demonstrate that gauging part of the internal symmetry leads to the appearance of dipole symmetry in the resulting theory. This perspective provides a simple way to understand the origin of modulated symmetries and highlights how anomaly considerations can give rise to unconventional symmetry structures in quantum lattice systems.

2026-03-06

How many sequences of games are possible in Koshien?

Sungsik Kong (Research Scientist, Division of Fundamental Mathematical Science, RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS))

I address the question “How many sequences of games are possible in Koshien?” using combinatorial techniques from mathematical phylogenetics. I model the tournament as a labeled evolutionary history and apply tree enumeration methods to count the number of distinct outcome sequences. By interpreting each game as an internal node in a rooted labeled history, the problem reduces to counting labeled histories consistent with the tournament structure. I start the talk with basic introduction of evolutionary trees and try to establish a connection between single-elimination tournaments and the combinatorics of evolutionary trees.

2026-02-27

What Are Modular Forms?

Yuya Murakami (Research Scientist, Division of Fundamental Mathematical Science, RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS))

In this talk, I introduce the concept of modular forms and explain some of their surprising applications to number theory, topology, and mathematical physics. Modular forms are holomorphic functions characterized by rich symmetry properties. At first glance, their definition appears purely analytic.Nevertheless, they contain deep arithmetic information and play a central role in modern number theory. In recent developments, modular forms have also emerged in the context of topological quantum field theory. This talk aims to provide an accessible overview of these ideas for a general audience.

2026-02-20

How a player can unilaterally control payoffs in repeated games

Yohsuke Murase (Team Director, Mathematical Social Science Team, Division of Applied Mathematical Science, RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS) / Senior Research Scientist, Discrete Event Simulation Research Team, RIKEN Center for Computational Science (R-CCS))

In repeated interactions, players can choose their actions based on past outcomes, leading to a wide variety of possible strategies. In this talk, I introduce "zero-determinant" strategies, discovered by the famous physicist Freeman Dyson, which show that in repeated games a player can unilaterally enforce linear relations between long-run average payoffs, independent of the opponent's strategy. I will explain the basic idea using a Markov-chain formulation of the repeated Prisoner’s Dilemma.

2026-02-13

Failure of Scale Separation in Physics

Wei-Hsiang Shao (Special Postdoctoral Researcher, Division of Fundamental Mathematical Science, RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS))

The success of modern physics relies heavily on the principle of scale separation, which allows complex systems to be described by simplified effective theories that are largely insensitive to microscopic details. In this talk, I will review this Wilsonian framework and illustrate its usefulness across a wide range of physical contexts. I will then discuss situations in which this separation of scales breaks down, focusing on examples motivated by quantum gravity as well as by certain physical settings in our universe. These examples show how high-energy physics can have unexpectedly strong effects at large scales.

2026-02-06

On how to detect selection in a set of genomes

Aina Colomer i Vilaplana (Postdoctoral Researcher, Mathematical Genomics RIKEN ECL Research Unit, Division of Fundamental Mathematical Science, RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS))

How do organisms adapt and evolve? Population genetics provides us with the theoretical framework to answer this question. A chance mutation can give rise to an advantageous mutation in one individual, but how does this mutation then spread in a population? How quickly does a mutation increase in frequency, what role does chance play in this process, and how does it impact the diversity of our genomes? This talk will introduce how natural selection appears in our genomes and how we can detect it in genetic data. I will introduce the main concepts behind some of the classical selection statistics developed early in the field. I will then show how Ancestral Recombination Graphs have revolutionized our ability to infer selection in recent years. One of the ongoing debates around selection is the extent to which genomes have been (or are currently being) shaped by this force, and what this means for how organisms adapt.

2026-01-30

Chaos bound and thermalization

Osamu Fukushima (Special Postdoctoral Researcher, Division of Fundamental Mathematical Science, RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS))

Chaos refers to complex dynamical behavior, where the long-time behavior becomes effectively unpredictable even though the underlying equations of motion are deterministic. On the other hand, thermalization concerns the relaxation of observables toward equilibrium, which is a pivotal dynamical phenomenon in many-body systems. Chaos and thermalization share some common aspects, and their relation has been extensively discussed. In this talk, I will introduce how the eigenstate thermalization hypothesis, which is a central criterion for thermalization, is related to a universal bound on chaos in quantum systems.

2026-01-23

Evolution of Evolution?: Modifier Theory as a First Step

Kenji Okubo (Special Postdoctoral Researcher, Division of Fundamental Mathematical Science, RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS))

Evolution successfully explains how populations change across generations, but it usually treats key parameters such as mutation and recombination rates as fixed. In this talk, I introduce modifier theory as a first step toward a theory of the evolution of evolution, where these parameters themselves can evolve. Using simple finite-population toy models, I show that mutation-rate modifiers can be favored not by higher fitness, but by producing beneficial mutations earlier. This leads to history-dependent evolutionary outcomes driven by timing rather than averages. I conclude by discussing implications for mutator evolution in bacteria, cancer dynamics, and the possibility of inferring past environments from present-day evolutionary parameters.

2026-01-16

Recent progress in understanding quantum black holes

Masamichi Miyaji (Senior Research Scientist, Division of Fundamental Mathematical Science, RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS))

Black holes are ubiquitous in our universe, yet their microscopic structure is still far from being understood. In particular, they pose serious theoretical puzzles, such as the black hole information paradox and the firewall problem. Recent progress based on holography has shed new light on these issues, as well as on the low-temperature quantum dynamics of black holes, connecting black holes with strongly chaotic quantum systems. In this coffee meeting, I will explain the key ingredients needed to understand these recent and fascinating theoretical developments.

2026-01-09

Many-faceted KP hierarchy

Zhe Wang (Research Scientist, Division of Fundamental Mathematical Science, RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS))

The Kadomtsev-Petviashivili (KP) hierarchy is an integrable hierarchy of partial differential equations generalizing the well-known KdV hierarchy describing the dynamics of shallow water. The KP theory is extremely rich, and it relates different fields of mathematics. In this talk, we will focus on Sato’s theory for KP hierarchy and interpret it using analytic/geometric/algebraic languages.

2025-12-19

Brunn-Minkowski inequality and the Borell-Brascamp-Lieb inequality

Takashi Satomi (Special Postdoctoral Researcher, Division of Fundamental Mathematical Science, RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS))

The Brunn-Minkowski inequality (or Brunn-Minkowski theorem) is one of the fundamental geometric inequalities in Euclidean space. This inequality states that the volume of the sum of two sets (called the Minkowski sum) can be bounded from below in terms of the volumes of the two original sets. There are several proofs of this inequality, and one approach is to establish a functional extension known as the Borell–Brascamp–Lieb inequality. In this talk, we will review these inequalities and briefly indicate how the Borell–Brascamp–Lieb inequality may be proved by mathematical induction.

2025-12-12

Aspects of Quantum Resonance Revisited

Okuto Morikawa (Special Postdoctoral Researcher, Division of Fundamental Mathematical Science, RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS))

Quantum resonances appear in many areas of physics, yet their definitions—through scattering peaks, S-matrix poles, or non-Hermitian eigenvalues—often seem unrelated. In this talk, I revisit these aspects from a unified viewpoint: resonances as pseudo-bound states defined by analytic continuation into the complex plane. This perspective clarifies how methods such as complex scaling, Gamow states, and semiclassical tunneling fit together. I will briefly show how exact WKB naturally captures these structures, without assuming any background in resurgence theory.