(The deadline of the registration is on Sep 30.)

100 years have passed since quantum mechanics was born. The mathematical model has been describing the physical world remarkably well. However, the foundations of this model still remain unclear. A comprehensive understanding of quantum theory, including its foundations, is becoming even more important in an era where the demands of realizing quantum information technologies pose significant theoretical and experimental challenges.

The framework of General Probabilistic Theories (GPTs) is a modern approach to the foundations of quantum theory. It deals with mathematical generalizations of both classical and quantum theories and has attracted increasing attention in recent years. Roughly speaking, research on GPTs has three major objectives: characterizing the models of classical and quantum theories, investigating the fundamental limits of physical and information-theoretic properties arising from operational requirements, and deepening our understanding of the mathematical structures underlying classical and quantum theories. The studies of GPTs have provided many new perspectives on these topics. However, at the same time, there remain many important open problems in the field. For this reason, more researchers are encouraged to enter and contribute to research on GPTs.

This intensive three-day lecture series is designed to provide researchers and graduate students with the essential knowledge necessary for research on GPTs, starting from an introduction to the subject. The lectures will cover the mathematical foundations, physical and information-theoretic concepts, and both the established results and future directions of GPT research. The 1st day will present the necessary mathematical structures, including convex geometry, positive cones, and the operational formulation of probabilistic models. The 2nd day will explore composite systems, information-theoretic quantities, symmetries, and Euclidean Jordan algebras. The 3rd day will survey key results on discrimination and communication tasks, the characterization of classical and quantum theories, and open problems that connect GPTs to quantum information science and beyond.

Note: The content of each lecture may extend into the next slot or be covered earlier, depending on the pace of discussion and participant questions.

The 1st day (6th Oct.): Mathematical Introduction to GPTs
Venue: Large Meeting Room, 2F, Wako Welfare & Conference Building
10:30-12:00 Lecture 1 (Introduction and Mathematics on Positive Cones)
12:00-13:30 Lunch time
13:30-15:00 Lecture 2 (Mathematics on Positive Cones)
15:00-15:30 Coffee break
15:30-17:00 Lecture 3 (Introduction to General Models and Relation between Operational Probability Theories)

The 2nd day (7th Oct.): Physical and Information Theoretical Concepts in GPTs
Venue: Large Meeting Room, 2F, Wako Welfare & Conference Building
10:30-12:00 Lecture 4 (Composite Systems in GPTs)
12:00-13:30 Lunch time
13:30-15:00 Lecture 5 (Information Quantities)
15:00-15:30 Coffee break
15:30-17:00 Lecture 6 (Dynamics, Symmetry, and Euclidean Jordan Algebras)

The 3rd day (8th Oct): Previous and Future Studies in GPTs
Venue: Meeting Room 435-437, 4F, Wako Main Research Building
10:30-12:00 Lecture 7 (Discrimination and Communication Tasks)
12:00-13:30 Lunch time
13:30-15:00 Lecture 8 (Characterization of Classical and Quantum Theories)
15:00-15:30 Coffee break
15:30-17:00 Lecture 9 (Other Topics, Open Problems, and Future Directions)
18:00- Dinner

The day of no lecture (9th Oct): Open Discussion and Q&A
Research discussions will take place between the lecturer and participants in areas such as the hallways on the 3rd and 4th floors of the Main Research Bldg, RIKEN Wako Campus.

Incorporating symmetry-inspired inductive biases into machine learning models has led to many significant advances in the field, especially for its application to scientific data. However, recently, a trend has emerged that favors implicitly learning relevant symmetries from data instead of designing constrained equivariant architectures. In this talk, I will first introduce these different modelling alternatives, together with their associated benefits and limitations. Then, I will describe some examples of automatic symmetry discovery methods as a way of mitigating some of those limitations. Finally, I will present our recent work that integrates symmetry discovery and the definition of an equivariant model into a joint learnable end-to-end approach, which further alleviates some of the limitations of current equivariant modelling approaches.

One of the main tools in topological data analysis is the notion of a persistence module. The most prominent example is the persistence module associated with the Vietoris–Rips complex of a finite metric space. On the other hand, the concept of magnitude has become increasingly well known in data analysis. Recently, Nina Otter introduced blurred magnitude homology, which is also a persistence module associated with a metric space. Govc and Hepworth showed that the magnitude of a finite metric space can be uniquely recovered from its blurred magnitude homology. For 1 ≤ p ≤ ∞, we define the ℓ_p-Vietoris–Rips complexes and the associated ℓ_p​-persistent homology of metric spaces, and we study their fundamental properties. We show that for p=∞ this theory recovers the classical theory of Vietoris–Rips complexes and their persistent homology, while for p=1 it recovers the theory of blurred magnitude homology.

This is a lecture series by Prof. Mark Alford (Washington University in St. Louis) on the structure of neutron stars.

Oct. 7 (Tues), 15:30-17:00
Lecture I: Quark matter: the high-density frontier
The densest predicted state of matter is color-superconducting quark matter, which has some affinities to electrical superconductors, but a much richer phase structure because quarks come in many varieties. This form of matter may well exist in the core of compact stars, and the search for signatures of its presence is currently proceeding. I will review the nature of color-superconducting quark matter, and discuss some ideas for finding it in nature.

Oct. 14 (Tues), 15:30-17:00
Lecture II: Solid quark matter
I will review three ways in which quark matter can occur in a solid phase, where translational invariance is broken by some sort of crystalline structure. These include a color superconductor of the Fulde-Ferrell-Larkin-Ovchinnikov type, mixed phases that can arise at a nuclear/quark matter interface, and the strangelet crystal crust of a strange star.

Oct. 21 (Tues), 15:30-17:00
Lecture III: Dissipation in neutron star mergers
In a neutron star merger, nuclear matter experiences dramatic changes in temperature and density that happen in milliseconds. Mergers therefore probe dynamical properties that may help us uncover the phase structure of ultra-dense matter. I will describe some of the relevant material properties, focusing on flavor equilibration and its consequences such as bulk viscosity and damping of oscillations.

Oct. 28 (Tues), 15:30-17:00
Lecture IV: Neutrinos in dense matter: beyond modified Urca
Neutrino absorption and emission (the "Urca process") is an essential aspect of the formation and cooling of neutron stars and of the dynamics of neutron star mergers. In this talk I will describe the traditional way of calculating Urca rates, explain its shortfalls, and propose an alternative approach, the nucleon width approximation.

The gray wolf (Canis lupus) is one of the most emblematic wild species in human history: revered as a symbol of strength and wildness, although unforgivably persecuted as a competitor and pest. Across Europe and much of Eurasia, wolves would still dominate as apex predators... were it not for millennia of human pressure. Today, their evolutionary trajectory is shaped not only by climate fluctuations and habitat loss, but also by a uniquely flexible species boundary. Due to their unique karyotype, canids can admix freely with other related species, a capacity that both threatens the genetic integrity of wild canids like wolves and enriches our understanding of hybridization as a driver of adaptation. In this talk, we will explore recent studies on wolf demography under human pressure and climatic change, with particular attention to admixture with domestic dogs and the consequences for their survival in increasingly anthropized environments. Finally, we will observe how the wolf's distinctive genomic architecture makes it a powerful model for testing population genetics theoretical frameworks and for applying state-of-the-art computational tools, offering new insights into the understanding of evolution as a force for change.

In this meeting, Antoine Diez will give a talk entitled "Mean-field limits a la Tanaka and large deviations for particle systems with network interactions." Feel free to join if you are interested.

Sleep remains one of greatest remaining mysteries. At the Sleep 2012 conference, we conceived a shift from the concept of “sleep substances” to “wake substances” such as calcium, suggesting that sleep homeostasis may arise from the integration of wake-related activity. Inspired by Dr. Setsuro Ebashi’s work on calcium signaling, we investigated calcium’s role in sleep regulation.

Using our Triple-CRISPR method (Sunagawa et al. 2016), we screened 25 genes related to calcium channels and pumps, revealing calcium as a brake on brain activity to promote sleep (Tatsuki et al. 2016). We also developed a tissue-clearing method CUBIC (Susaki et al. 2014; Tainaka et al. 2014) to visualize calcium’s effects on neural circuits. Further work showed that calcium-dependent enzymes, CaMKIIα/β kinases, act as calcium “memory” devices, with phosphorylation sites controlling sleep onset, duration, and termination (Tone et al. 2022). Other direct and indirect calcium-dependent phosphatases, Calcineurin and PP1 (sleep-promoting), and opposing kinases, PKA (wake-promoting), function as synaptic sleep switches (Wang et al. 2024).

We also identified the ryanodine receptor 1, a calcium channel, as a molecular target of inhalational anesthetics, hinting at shared pathways between anesthesia and sleep (Kanaya et al. 2025). Lastly, we proposed the WISE (Wake Inhibition Sleep Enhancement) mechanism, where quiet wakefulness suppresses and deep sleep strengthens synaptic connections, explaining links between sleep, depression, and antidepressant effects (Kinoshita et al. 2025).

Eruptions that occur at volcanoes after periods of quiescence are difficult to forecast. Pathways that connect the source to the surface may have become sealed. The pressurisation of the source leads to the deformation of the crust. Initially the crust deforms elastically, strain is accommodated via ground movement and elastic strain energy is stored to the crust. Then, the deformation transitions to inelastic where strain is accommodated via brittle failure (volcano-tectonic event), and elastic strain energy is transferred from the crust.

We present a novel method to estimate the temporal evolution of elastic strain energy and bulk stress during periods of unrest. We consider the transfer of energy using measurements of surface deformation and seismic activity. We evaluate the temporal evolution of crustal bulk stress and investigate the progression of deformation in the crust. We apply our method to the unrest at the Campi Flegrei caldera, Italy from 2011-2024, and the eruption of Sierra Negra, Galapagos, 2018. Our calculations reveal that the bulk stress follows a characteristic progression, in which the stress initially increases linearly with time prior to the onset of significant seismicity, consistent with elastic deformation. We then observe a transition to inelastic deformation, when rate of elastic strain energy lost via fracturing increases and eventually exceeds the rate of elastic strain energy transferred to the crust. This results in a decrease in the bulk stress stored in the crust with time, indicating a progressive weakening of the crustal material due to seismicity-induced damage. Comparison with laboratory experiments show the behaviour is consistent with bulk failure in extension and the potential formation of new pathways in the crust.

Finally, we demonstrate how our method, along with the understanding of eruption precursors gained from the results, can be used to constrain deformation regimes at reawakening volcanoes after extended repose and to evaluate the hazard posed during periods of unrest.

Multiple nearby Active Galactic Nuclei have been reported as sources of high-energy neutrinos detected by the IceCube observatory. These results strongly suggest efficient proton acceleration to (sub-)PeV energies, likely within Black Hole (BH) coronae, given the lack of γ-ray counterparts. The acceleration mechanisms remain unconfirmed due to limited understanding of coronal environments and challenges in modeling hot, relativistic plasmas. Although diffusive shock acceleration (DSA) has been proposed, a self-consistent treatment incorporating detailed kinetic plasma effects has been lacking. In this study, we present the particle-in-cell (PIC) method as a first-principles approach to investigate particle acceleration by collisionless shocks under conditions inferred from multi-wavelength observations of BH coronae. Using large-scale 1D3V simulations, we surveyed shock parameters, focusing on underexplored effects such as initial ion–electron temperature ratios and trans-relativistic shock velocities, and found that collisionless shocks can form even in hot, low-Mach plasmas. These shocks accelerate protons up to ~100 TeV, consistent with the energies required for IceCube neutrino detections, across a wide range of coronal conditions. The shocks partition ~10% of dissipated energy into nonthermal protons and <1% into electrons, providing critical, observationally testable constraints on the plasma state of BH coronae.

We present the theory of bonded knots and bonded knotoids, as well as their algebraic counterparts, the theory of bonded braids and bonded braidoids. We also discuss some applications to the topological study of proteins.

This workshop will serve as the first meeting of the collaboration between the Leinweber Institute for Theoretical Physics (LITP) at the University of California Berkeley and the RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS). Participation is open and researchers from other institutions are welcome to attend. The workshop will feature talks on recent developments in the field of Quantum Gravity and other relevant topics.

A theorem prover is a tool for the formalization of mathematics, that is, for rigorously expressing and verifying theorems and proofs on a computer. In recent years, the Lean theorem prover has seen progress in the formalization of a wide range of areas of mathematics. In this talk, I will explain formalization of mathematics in Lean from the basics and survey the formalized results achieved to date.

Recently some researchers gave many studies toward algebro-geometric foundation for tropical geometry. I focused on rational function semifields of tropical curves and characterized them. With this characterization, in this talk, I suggest a definition of ``rational function semifield of dimension one". This definition can write out weight in the term of $\boldsymbol{T}$-algebra homomorphism, and can write balancing condition together with harmonic functions, where both weight and balancing condition are fundamental concepts for tropical varieties and $\boldsymbol{T}$ is the tropical semifield $(\boldsymbol{R} \cup \{-\infty\}, \operatorname{max}, +)$.

The ninth installment of the Intensive Lecture Series, organized by the Quantum Gravity Gatherings (QGG) study group at RIKEN iTHEMS, will feature Prof. Norio Kawakami from the Fundamental Quantum Science Program (FQSP) under RIKEN's Transformative Research Innovative Platform (TRIP). Over the course of two days, Prof. Kawakami will deliver a lecture series on quantum many-body systems.

In recent years, insights from quantum many-body physics have become central to research in quantum gravity, where correlation effects induced by gravity play nontrivial roles. By bridging perspectives from gravitational physics and quantum many-body dynamics, one hopes to understand how macroscopic spacetime and its geometric properties emerge from the collective behavior of quantum constituents at microscopic scales.

In this lecture series, Prof. Kawakami will introduce the fundamental properties of correlation effects through representative examples in condensed matter physics. A distinctive aspect of this event is its joint organization with the Fundamental Quantum Science Program (FQSP) at RIKEN. The goal is to further strengthen connections between the quantum gravity, condensed matter, and quantum information communities.

The lectures will be delivered in a blackboard-style format (in English), designed to foster interaction, active participation, and in-depth Q&A discussions. In addition, short talk sessions will be held, giving participants the opportunity to present briefly on topics of their choice. Through this informal and dynamic setting, we hope to spark active interactions among participants and create an environment where ideas can be shared openly and enthusiastically.

Abstract:
Some examples of theoretical methods to treat strongly correlated systems in condensed matter physics are explained. We start with the Kondo effect, which is one of the most fundamental quantum many-body problems and has been intensively studied to date in a wide variety of topics such as dilute magnetic alloys, heavy fermion systems, quantum dot systems, etc. Dynamical mean-field theory (DMFT) is then introduced, which enables us to systematically treat strongly correlated materials such as a Mott insulator. It is shown that the essence of DMFT is closely related to the Kondo effect. Furthermore, we explain how to apply conformal field theory (CFT) to treat correlation effects in one-dimensional electron systems.