Primordial black holes (PBHs) are a major candidate for dark matter, expected to form from the collapse of large density fluctuations generated during inflation. Their abundance is highly sensitive to non-linear effects, some of which can be described through the δN formalism. This approach models the universe as a set of locally homogeneous patches evolving independently throughout inflation. However, accounting for the spatial correlations between these patches is crucial to predicting the spatial distribution of PBHs and the formation of clusters. In this talk, after reviewing the δN formalism, I will show how to include spatial correlations within this framework. As an illustration, I will discuss the ultra-slow-roll model and compute the curvature perturbation ζ — necessary to determine PBH formation — and its spatial correlations at the end of inflation. In the future, this could enable the prediction of PBH binaries and clusters, which may leave observable imprints such as gravitational waves.

Large language models such as ChatGPT are based on deep learning architectures known as Transformers. Owing to their remarkable performance and broad applicability, Transformers have become indispensable in modern AI development. However, it still remains an open question why Transformers perform so well and what the essential meaning of their unique structure is. One possible clue lies in the mathematical correspondence between Hopfield Networks and Transformers.

In this talk, I will first introduce the major developments over the past decade that have significantly increased the storage capacity of Hopfield Networks. I will then review the theoretical correspondence between Hopfield Networks and Transformers. Building on this background, I will present our recent findings: by extending this correspondence to include the hidden-state dynamics of Hopfield Networks, we discovered a new class of Transformers that can recursively propagate attention-score information across layers. Furthermore, we found, both theoretically and experimentally, that this new Transformer architecture resolves the “rank collapse” problem often observed in conventional multi-layer attention. As a result, when applied to language generation and image recognition tasks, it achieves performance surpassing that of existing Transformer-based models.

We propose a conceptual analogy in population genetics to the central dogma of molecular biology. While the central dogma describes the flow of information from DNA to RNA to protein, we posit that under neutrality, a population's demography shapes its underlying genealogy, which in turn determines patterns of genetic variation that give rise to phenotypic variation. At the center of this analogous dogma is the genetic genealogies. Recent advances in inferring the Ancestral Recombination Graph (ARG), a complete record of a population's genealogies, have enabled us to develop a suite of methods that interrogates each stage these fundamental and connected components:

Topological insulators are materials which do not conduct current inside but do conduct at the surface or the edge. The name "topological" comes from the fact that the "shape" of the wavefunction of electrons in topological insulators show non-trivial twist, which can be mathematically characterized by the language of topology. Alongside the development of the study of topological insulators in solids, analogous phenomena were found to exist also in other systems such as photonics, mechanics, geophysics, and active matter. In this seminar, I discuss how the underlying concept of "topology of states" can have a broad impact applicable to various areas in physics, with some emphasis on my own contribution to the field. I aim to structure the first half of my seminar to be accessible to those outside physics, and latter half to be more specialized, covering cutting-edge results.

I will introduce the Uchuu suite of large high-resolution cosmological N-body simulations. The largest simulation, named Uchuu, consists of 2.1 trillion dark matter particles in a box of side-length 2.0 Gpc/h, with particle mass of 3.27e8 Msun/h. The highest resolution simulation, Shin-Uchuu, consists of 262 billion particles in a box of side-length 140 Mpc/h, with particle mass of 8.97e5 Msun/h. Combining these simulations, we can follow the evolution of dark matter haloes and subhaloes spanning those hosting dwarf galaxies to massive galaxy clusters across an unprecedented volume from very high-z. We release N-body data (halo/subhalo catalogs and merger trees) and mock galaxy/AGN catalogs constructed using various models, which cover objects from z=0 to very high-z. These catalogs open a new window on understanding the large-scale structures and galaxy formation. In this presentation, I will also introduce results of cosmological simulations adopting a time-varying dark energy, conducted on the supercomputer Fugaku.

This year's meeting on "Outreach of Mathematical Sciences" will be held from FRI NOV 14 12:30 to SUN NOV 16 15:00 as a face-to-face meeting at Institute of Mathematics for Industry of Kyushu University as "Outreach of Data Descriptive Science and Mathematical Sciences" supported by Grant-in-Aid for Transformative Research Areas (A), 2022-2026 "Establishing data descriptive science and its cross-disciplinary applications" in cooperation with RIKEN iTHEMS SUURI-COOL (Kyushu) using ZOOM for the necessary part as well.

Fermi Gamma-Ray Space Telescope has measured the diffuse extragalactic gamma-ray background (EGB) radiation in the energy range of 100 MeV to 820 GeV. Several candidate γ -ray sources have been proposed as the candidate components of the unresolved EGB, including active galactic nuclei (AGNs), millisecond pulsars, dark matter annihilation, and star-forming galaxies (SFGs), but their quantitative contribution has not yet been precisely determined. In this talk, I will introduce our latest physical model describing the gamma-ray emission mechanism from SFGs, and our estimate of the contribution of SFGs based on careful calibration with gamma-ray luminosities of nearby galaxies and physical quantities (star formation rate, stellar mass, and size) of galaxies observed by high-redshift galaxy surveys.

Mathematical Application Research Team invites Prof. Yoshiko Ogata from RIMS for this meeting. Her talk title will be announced later. You are welcome to join the meeting.

The title and the abstract of her talk are:

Title: Mixed state topological order: operator algebraic approach

Abstract: We consider anyons in mixed states of two-dimensional quantum spin systems within the operator-algebraic framework of quantum statistical mechanics. To each state satisfying a mixed-state version of approximate Haag duality, we associate a braided C*-tensor category, which we interpret as describing the anyonic excitations of the state. We then investigate how these anyonic structures behave under interactions with the environment.

The 4th quantum computing gathering organized by Quantum Computing Study Group

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.

Animal navigation has long been a central topic in behavioral biology. In predator-prey systems, both predators and prey must navigate strategically - predators to capture prey and prey to reach safety - each evolving to outsmart the other through coevolution. To uncover the essence of these navigation strategies, I have investigated behavioral mechanisms across taxa. In bats, my collaborators and I found that they integrate multiple sensory and flight tactics to keep erratically flying moths within detection range. In pigeons, we discovered that individuals anticipating drone attacks adjust their positions toward the rear within the flock. I will also introduce an experimental framework that enables controlled interactions between real animals and virtual agents driven by reactive motion control, allowing quantitative tests of navigation efficiency. Through this seminar, I aim to highlight how studies of predator-prey navigation can bridge biology and engineering, providing insights into adaptive decision-making in dynamic environments.

Accurate prediction of quantum Hamiltonian dynamics and identification of Hamiltonian parameters are crucial for advancements in quantum simulations, error correction, and control protocols. This talk introduces a machine learning model with dual capabilities: it can deduce time-dependent Hamiltonian parameters from observed changes in local observables within quantum many-body systems, and it can predict the evolution of these observables based on Hamiltonian parameters. The model’s validity was confirmed through theoretical simulations across various scenarios and further validated by two experiments. Initially, the model was applied to a Nuclear Magnetic Resonance quantum computer, where it accurately predicted the dynamics of local observables. The model was then tested on a superconducting quantum computer with initially unknown Hamiltonian parameters, successfully inferring them. We believe that machine learning techniques hold great promise for enhancing a wide range of quantum computing tasks, including parameter estimation, noise characterization, feedback control, and quantum control optimization.

14:45-15:00 Teatime discussion
15:00–16:00 Talk by Dr. Isao Ishikawa (Program-Specific Associate Professor, Center for Science Adventure and Collaborative Research Advancement (SACRA), Graduate School of Science, Kyoto University)
16:15–17:15 Talk by Dr. Ken-ichi Kurotani (Associate Professor, Center for Science Adventure and Collaborative Research Advancement (SACRA), Graduate School of Science, Kyoto University)
17:15-18:00 Discussion

I will describe how to measure the forces that drive cultural change, using inference tools from evolutionary theory. We study time series data from large corpora of parsed English texts to identify what drives language change over the course of centuries. We also measure frequency-dependent effects in time series of baby names and purebred dog preferences. The form of frequency dependence we infer helps to explain the diversity distribution of names, and it replicates across the United States, France, Norway and the Netherlands. We find different growth laws for male versus female names, attributable to different rates of innovation, whereas names from the bible enjoy a genuine advantage at all frequencies. Frequency dependence emerges from a host of underlying social and cultural mechanisms, including a preference for novelty that recapitulates fashion trends in dog owners. Studying culture through the lens of evolutionary theory provides a quantitative account of social pressures to conform or to be different; and it provides inference tools that may be used in biology as genetic and phenotypic time series are increasingly available.