Coffee Meeting Log

2025-04-25

 Computers as a Playground for Mathematics

Taketo Sano (Research Scientist, Mathematical Application Research Team, Division of Applied Mathematical Science, RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS))

Computers are invaluable tools not only in the natural sciences but also in pure mathematics, enabling simulations and computational experiments that would be infeasible by hand. In this talk, I take this idea one step further and propose that computers are not just for performing computations—they can also be used to implement mathematical structures as computer programs. There are nice correspondences between concepts in mathematics and programming, rooted in abstraction and inheritance. This approach also allows us to play and interact with mathematical ideas that might otherwise feel vague or untouchable. I will present a demo showing how we can implement the gcd function for Euclidean Rings, which will be automatically inherited to integers and polynomials.

2025-04-18

Bitcoin: A Peer-to-Peer Electronic Cash System

Ching-Kai Chiu (Senior Research Scientist, Division of Fundamental Mathematical Science, RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS))

I am not Satoshi Nakamoto, but I’ll talk about his white paper—the one that laid the foundation for a trillion-dollar economy. I’ll introduce the main idea behind blockchains: a decentralized and trustless system for securely recording transactions without the need for a central authority.

2025-04-11

Where is the limit of the periodic table of elements?

Tomoya Naito (JSPS PD Researcher, Quantum Mathematical Science Team, Division of Applied Mathematical Science, RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS))

Superheavy elements have been synthesised. Then, a question arises: where is the limit of the elements? In this talk, I will explain the current status on the discussion in terms of atomic physics.

2025-03-28

Creativity in convolutional diffusion models

Steffen Backes (Senior Research Scientist, RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS) / Senior Research Scientist, First-Principles Materials Science Research Team, RIKEN Center for Emergent Matter Science (CEMS))

2025-03-21

 The Free Will Theorem in Quantum Mechanics

Christy Koji Kelly (Special Postdoctoral Researcher, RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS))

The free will theorem, discovered by Conway and Kochen, is a technical variation of the Bell-Kochen-Specker theorem with a conclusion directed towards a basic problem in philosophy rather than physics. It has, however, often been seriously misunderstood, including by Conway and Kochen themselves. We discuss the reformulation by Landsman that presents the free will theorem as a no-go theorem for compatibilist forms of deterministic free will.

2025-03-14

 Renormalization revisited

Dongwook Ghim (Postdoctoral Researcher, RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS))

As a supplement to Masazumi’s coffee meeting talk last February, I will talk more about the key concept in modern quantum field theory, renormalization. I will follow the statistical mechanics approach by Kadanoff and Wilson. First, I will briefly sketch Kadanoff’s block decimation idea as an illustrating example of renormalization group flow in real space. Then, I will move on to Wilson’s momentum space renormalization group and show a simple toy model involving ordinary Gaussian integral.

2025-03-07

Steady-State Size Distribution for a Collision Cascade

Misako Tatsuuma (Research Scientist, RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS))

A collision cascade describes a self-similar process where large bodies fragment into smaller ones through successive collisions, maintaining a constant mass flux over time. This phenomenon is observed in various contexts, from space debris evolution to asteroid collisions. In this talk, I will derive the steady-state mass distribution for a collision cascade and introduce its application to the observed grain size distributions in planet-forming disks.

2025-02-28

Space-time as syntax of Particle Physics

Yuto Moriwaki (Special Postdoctoral Researcher, RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS))

In natural language, syntax is the vocabulary and grammar, and semantics is the meaning (model) of a sentence constructed according to syntax. Lawever duality in mathematics states that from all semantics (possible models), the category of syntax (grammar) can be recovered. In particle physics, we interpret syntax as the conditions that a physical theory must satisfy (grammar of the theory), and semantics as specific models (gauge theory, Standard Model, etc.). Then, from all the models of quantum field theories (semantics of QFT), we argue that the category of spacetime is expected to be recovered. In other words, spacetime seems to be the grammar of quantum field theory.

2025-02-21

 Renormalization: Awareness of Ignorance

Masazumi Honda (Senior Research Scientist, RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS))

Renormalization is one of the most complicated concepts in learning quantum field theory despite realistic field theories cannot be predictable without renormalization. In this talk, I am going to introduce the concept of renormalization into broad audience by using a simple example in quantum mechanics which is technically an eigenvalue problem of ordinary differential equation. While I will mainly explain a "physicist" way of doing renormalization, I will also briefly mention more mathematical understanding from perspective of self adjoint extension of Hamiltonian

2025-02-14

Newton polytopes and topology of hypersurfaces

Yuto Yamamoto (Special Postdoctoral Researcher, RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS))

The set of points where a polynomial equals zero, called a hypersurface, is a fundamental object in algebraic geometry. Important information about its shape is encoded in the Newton polytope, which is a convex polytope associated with the polynomial in a specific way. In this talk, I will explain this connection in an intuitive way using ideas from tropical geometry.

2025-02-07

On the Buchdahl’s limit and its relation to black hole mimickers

Che-Yu Chen (Special Postdoctoral Researcher, RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS))

Are black holes really black holes? According to Einstein's General Relativity with a few assumptions, static fluid spheres in hydrostatic equilibrium can only reach a certain value of compactness, dubbed Buchdahl limit. In this talk, I'll discuss how this bound is obtained, and how one can evade it by relaxing some of its underlying assumptions, constructing horizonless compact objects as black hole mimickers.

2025-01-31

A canonical size of sets in mathematics, biology, and statistics -- in physics too?

Ryosuke Iritani (Senior Research Scientist, RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS))

I will talk about "magnitude" (the effective number of a collection of objects) and how we interpret it in terms of mathematical, biological, and statistical viewpoints by drawing a few examples. As the magnitude has strongly to do with entropy maximization, there could be something interesting with physics.

2025-01-24

The Jeans Instability: why it happens, why it doesn't happen, and why it happens (?)

Derek Beattie Inman (Research Scientist, RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS))

2025-01-17

Learning how to count: from infectious virions to tangled brain proteins

Catherine Beauchemin (Deputy Program Director, RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS) / Professor, Department of Physics, Toronto Metropolitan University, Canada)

Being able to count the number of disease-causing agents over the course of an infection is essential for developing mathematical models to correctly describe, predict, and control diseases. In a virus infection, the agents are infectious virions. In neurodegenerative diseases like Alzheimer's, Parkinson's, and prion diseases, the suspected (or confirmed) agents are misfolded proteins that form aggregates, disrupting normal processes, and causing cell death. I will explain why it is difficult to count these agents and show some nice mathematical solutions to some of the problems. I will also describe ongoing challenges that perhaps you would like to help me tackle.

2025-01-10

What is Chaos?

Gabriele Di Ubaldo (Postdoctoral Researcher, RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS))

Chaos is an intuitive concept yet notoriously hard to define and study by nature. I will introduce different notions of chaos that are applicable to classical and quantum systems and discuss their relations, giving examples of very different chaotic systems.

2024-12-20

Re-summing quasi-normal modes - where divergence meets our universe -

Ryo Namba (Senior Research Scientist, RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS))

Series expansions provide a powerful control over problems in physics. Yet such expansions are often divergent, and it is a non-trivial task to interpret their consequences. This is, however, not something that is depressing, but rather something we should be excited about. Even though an expansion is a perturbative one, its infinite series inherits information about fully non-perturbative effects. In this short coffee meeting talk, I present one such example: quasi-normal modes of peturbations around black hole background spacetime. This is essentially to look for eigenvalues of Regge-Wheeler-Zerilli-type equations by re-summing a conventional WKB series solution, which is divergent in general, and applying proper boundary conditions.

2024-12-06

 Recipe for soup of quarks and gluons

Yuuka Kanakubo (Postdoctoral Researcher, RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS))

Can you imagine what the hottest soup on the earth is like? Is it viscous as honey or runny as water? How can we make such a hot soup? The hottest soup of quarks and gluons, known as quark-gluon plasma, has been studied through relativistic heavy-ion collision experiments at the Relativistic Heavy Ion Collider (RHIC) at BNL and the Large Hadron Collider (LHC) at CERN. In this talk, I will explain what is known and unknown about quark-gluon plasma, and how we study the properties with numerical simulations of relativistic heavy-ion collisions.

2024-11-29

What is “equilibrium”?

Kyosuke Adachi (Research Scientist, RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS) / Research Scientist, Nonequilibrium Physics of Living Matter RIKEN Hakubi Research Team, RIKEN Center for Biosystems Dynamics Research (BDR))

In interdisciplinary environments like iTHEMS, effective communication can be challenging due to differences in terminologies. In this 15-minute online talk, I will explore the concept of “equilibrium,” a term whose meaning varies across disciplines, ranging from mathematics to thermodynamics. By examining how “equilibrium” is understood in different research fields, I aim to bridge gaps in communication and foster a deeper interdisciplinary dialogue.

2024-11-22

Quark deconfinement in superdense matter: baryons or quarks? 

Yuki Fujimoto (Postdoctoral Researcher, RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS))

I will explain the qualitative picture regarding the quark deconfinement in superdense matter. Naively, we expect that superdense matter, found at neutron star core densities and beyond, consists of liberated quarks rather than of confined baryons because of the asymptotic freedom. However, QCD at large Nc implies a different interesting possibility: quark confinement persists, so the system is composed of baryons, while the thermodynamics is still governed by quarks.

2024-11-15

Kinetic plasma turbulence and geometry

Motoki Nakata (Visiting Scientist, RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS) / Associate Professor, Faculty of Arts and Sciences, Komazawa University)

Plasmas in the laboratory and in space are often collisionless, but still exhibit collective fluid-like dynamics. Most plasmas are also turbulent, and microscopic fluctuations, vortices, and even large-scale flows develop due to nonlinear interactions. Kinetic description is an effective approach for such collisionless or weakly collisional turbulent plasmas, and the basic ideas will be introduced in this talk. In particular, I will present on the interplay between turbulent dynamics and magnetic geometry such as torus that confine the plasma. This is also a question of how turbulence and flows can be activated or deactivated by geometry.