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2024-10-11

On mixed-state topological phases

福島 理 (数理創造プログラム 基礎科学特別研究員)

Topological phases are quantum phases of matter characterized by the robustness against local perturbations. While the understanding of topological phases in pure states has reached a mature stage over the past few decades, their mixed-state counterparts remain less explored. In this talk, I will review the concept of symmetries for mixed states, which is essential for characterizing mixed-state topological phases, and introduce an intrinsically mixed-state topological phase that does not belong to the same equivalence class as any pure states.

2024-09-27

Quadratic residues and domino tilings

小泉 淳之介 (数理創造プログラム 基礎科学特別研究員)

Quadratic residues are a classical concept in number theory, with a history tracing back to the times of Fermat and Euler. On the other hand, the number of ways to tile a rectangular grid with dominoes was given an explicit formula by Kasteleyn and Temperley-Fisher in the 1960s, in the context of research on the dimer model. In this talk, I will introduce recent research by myself, Y. Kamio, and T. Nakazawa, which connects these two concepts.

2024-09-20

The correspondence between classical and quantum mechanics via pseudodifferential operators

三上 渓太 (数理創造プログラム 研究員)

In this talk, I will briefly explain how classical mechanical time evolution and quantum mechanical time evolution are related using pseudodifferential operators.

2024-09-13

Gauge field topology on the lattice

森川 億人 (数理創造プログラム 基礎科学特別研究員)

Lattice gauge theory is the most-established framework of non-perturbative quantum field theory (QFT). Nevertheless quite many structures in continuum QFT become sacrifices to gauge invariance. We would like to discuss topology of lattice gauge fields; it is an essential construction of gauge theory and leads us to an important observation of recent generalization of symmetry.

2024-09-06

Operator algebras meet number theory

北村 侃 (数理創造プログラム 基礎科学特別研究員)

Operator algebras are algebras consisting of linear operators, which may be interpreted physically as observables. Their study is interesting on its own, forming a branch of mathematics. We will glimpse an occasion where the theory of operator algebras meets number theory, a different branch of mathematics investigating integers. Such an occasion sometimes emerges when we consider quantum symmetry, a kind of symmetry beyond usual groups. We will try to sketch a rough overview of how these concepts interact.

2024-08-30

Crystal space group

ツォン ツォン・ラ (数理創造プログラム 特別研究員)

In condensed matter physics, the space group is a fundamental theoretical tool for studying the physical properties of crystalline materials, providing a systematic way to understand and predict their behavior. We start with two-dimensional crystal structures, introducing the concepts of rotational and mirror symmetries, which then lead to the definition of point groups and space groups. The discussion is then extended to three-dimensional lattices. Finally, we discuss the application of space groups in electronic structure.

2024-08-23

Towards the unification of the speciation

José Said Gutiérrez Ortega (iTHEMS)

Speciation, the process by which new species originate, occurs due to geographic (physical distance), ecological (different background environments), and historical (divergence time) factors that promote reproductive isolation among lineages. However, we don’t know how these factors interplay; therefore, our empirical and theoretical knowledge about speciation is limited, fragmented, and lacks unification. To fill this knowledge gap, I propose a model and an experiment that treats speciation as a continuum of the interplay between geographic and ecological factors. Empirical evidence has shown that the extremes of this continuum produce high speciation rate (faster speciation), while I expect that intermediate values in the interplay continuum would produce reduced speciation rates. Because my theoretical background is not strong, I would like to receive your feedback about the feasibility of this model and about the accuracy of these expectations. Your comments are greatly appreciated.

2024-08-02

Toward the Quantum Theory of Gravity

野村 泰紀 (数理創造プログラム 上級研究員 / Director, Berkeley Center for Theoretical Physics, University of California, Berkeley, USA)

TBD

2024-07-26

Infrared Triangle

プトゥラク・ジャイアクソナ (数理創造プログラム 特別研究員)

In the low-energy (infrared) regime, there exists a three-way relationship among three key concepts in physics within asymptotically flat spacetime: asymptotic symmetries, soft theorems, and memory effects. In this talk, I will explore these relationships and their significance.

2024-07-12

Less could be more - diagonalize matrices

多田 司 (数理創造プログラム 副プログラムディレクター)

When we handle matrices, which are ubiquitous, especially in quantum physics and information theory, we try to diagonalize them. While diagonalized matrices exhibit familiar features with ordinary numbers, such as commutativity, they sometimes elude our intuition. In this talk, I introduce a new approach that has recently attracted much attention: one that handles matrices by not totally diagonalizing but leaving two upper and lower adjacent elements to the diagonal elements non-zero, which yields tridiagonal matrices.

2024-07-05

Superconductors and superfluids as macroscopic quantum condensates

関野 裕太 (数理創造プログラム 特別研究員 / 理化学研究所 開拓研究本部 (CPR) 濱崎非平衡量子統計力学理研白眉研究チーム 特別研究員)

Superconductors and superfluids are states of matter where dissipationless transport occurs due to macroscopic manifestations of quantum mechanical effects. These states of matter appear in various physical systems, such as Bose-Einstein condensates of ultracold atomic gases, liquid helium, superconductors in solids, and probably nuclear matter inside neutron stars, attracting interest across various fields of science. In this talk, I will explain the basics of quantum condensation, the mechanism behind macroscopic quantum effects in superconductivity and superfluidity.

2024-06-28

Y chromosome – An entity of an evolutionary dead-end?

野澤 昌文 (東京都立大学 准教授)

In many organisms with genetic sex determination, sex chromosomes (X and Y or Z and W, hereafter) have emerged from a pair of autosomes. Then, the X and Y (or Z and W) stop recombination in meiosis to maintain stable sex determination, which is inevitable in many cases. Consequently, many genes on the Y are nonfunctionalized or lost due to inefficacy of natural selection. Indeed, our humans only have ~70 genes on the Y while maintaining >800 genes on the X. However, the Y is still indispensable because the Y harbors the male-determination gene. Therefore, the Y has been regarded as an evolutionary dead-end, i.e., a sandwich between two evolutionary forces: degeneration and maintenance. I will introduce the situation of the Y in several organisms.

2024-06-21

A brief introduction to data-driven dynamical systems

黒澤 元 (数理創造プログラム 専任研究員)

Imagine that you are in a cave. The room is in a cave so that temperature and light-intensity are constant over time. Can you wake up tomorrow or day after tomorrow? In fact, most humans can wake up tomorrow and day after tomorrow almost regularly. How is it possible? To consider such a question, dynamical systems provide a mathematical framework to model interactions between quantities that evolve over time. Usually, the equations governing these systems are unknown or only partially known. Predicting and controlling such systems can be challenging. Recently, data-driven approaches have made significant strides in uncovering the equations of dynamical systems, predicting their behavior, and controlling them. In this presentation, I will review these approaches from the literature, which can be possibly applicable not only to daily rhythms but also to various other fields.

2024-06-14

What is density functional theory?

横田 猛 (数理創造プログラム 基礎科学特別研究員)

Matter in the world consists of numerous quantum particles, such as electrons and nucleons. Its properties are dictated by the Schrödinger equations for many-body systems. However, directly solving these equations poses a formidable computational challenge. Density Functional Theory (DFT), established by Hohenberg, Kohn, and Sham in the 1960s, represents one of the most successful methods for addressing many-body systems. It offers scalable approximations based on the variational principle concerning density. DFT is particularly notable for its perspective on the quantum world, wherein the ground-state density serves as an alternative to the wave function. In this talk, I will provide a brief introduction to DFT.

2024-06-07

An intriguing property of neural networks (up to date)

田中 章詞 (数理創造プログラム 上級研究員 / 理化学研究所 革新知能統合研究センター (AIP) 上級研究員)

Neural networks have played a central role in the recent development of machine learning technology, but their properties remain mysterious, and it would be interesting if these could be mathematically modeled. For example, in word embedding in a language model, it is known that "king vector" representing the word "king" appears in the learning process, and that the vector obtained by subtracting "queen vector" from "king vector" becomes a vector representing the change of words from female to male. In this talk, I would like to briefly explain that this kind of "concept arithmetic," is also possible among the weight parameters of trained neural networks, which is called "task arithmetic".

2024-05-31

An Introduction of Room Acoustics: Theory of Reverberation Time

儀保 伸吾 (数理創造プログラム 特別研究員)

It is important to predict and optimize the acoustics of a room before building the room. One of the most important indexes in the room acoustics is the reverberation time, which is defined as the time it takes for the sound energy to decay by a factor of 10^{-6}. If the reverberation time is too long, understanding speech in the room becomes difficult. Conversely, if the reverberation time is too short, we may not enjoy music in the room. In this talk, I will briefly explain the theory of the reverberation time.

2024-05-24

Unique Characterizations of Thermodynamic Entropy

横倉 祐貴 (数理創造プログラム 上級研究員)

Entropy has special properties related to heat, microscopic degrees of freedoms, and macroscopic irreversibility. I will explain that these are connected each other through dynamics, and add a new characterization: symmetry of entropy.

2024-05-17

Weather forecast and deep learning

大塚 成徳 (数理創造プログラム 研究員 / 理化学研究所 計算科学研究センター (R-CCS) データ同化研究チーム 研究員)

In this talk, I will introduce application of deep learning to weather forecasting. Recent years, tech companies, such as NVIDIA, Huawei, and Google, reported their deep learning-based global weather prediction models. These models were trained on so-called atmospheric reanalyses to emulate computationally demanding numerical weather prediction models. Although we still need physically-based models for various purposes, deep learning may change the future of weather predictions.

2024-05-10

Forming black holes from stars

ルーシー・マクニール (数理創造プログラム 特別研究員)

Black holes which are the remnants of stars are being detected at a rate of a few per month using various optical telescopes and gravitational wave interferometers. They provide fruitful opportunity to test and challenge stellar evolution theory, which depends sensitively on our understanding of general relativity, quantum mechanics, particle physics and nuclear physics. In this coffee talk, I will present the physical concepts and mathematical scalings behind the formation of a black hole, after a star’s iron core collapses. I will quantify the key length, time and energy scales involved, and the (possibly surprising) importance of neutrino transport.

2024-04-26

Exotica in Mathematics

佐野 岳人 (数理創造プログラム 基礎科学特別研究員)

Since the discovery of an exotic 7-dimensional sphere by J. Milnor in 1956, the study of exotic phenomena has become one of the central topics in topology. Here, an exotic sphere is a smooth manifold that is homeomorphic, but not diffeomorphic, to the standard sphere. In this talk, I will briefly explain the history of the discoveries of exotic phenomena and discuss some of the recent achievements related to knot theory.