Various approaches to the sign problem
松本 祥 (数理創造プログラム 特別研究員)
The Monte Carlo simulation is a powerful tool to study the non-perturbative aspect of quantum field theory. However, the Monte Carlo method is applicable to the system with a real action only. If the action is complex, it is difficult to handle the rapidly oscillating phase in the path integral, which is known as the sign problem. This problem prevents us from simulating various interesting systems, such as finite density QCD, topological theta term and real time evolution. In this talk, I introduce several approaches to overcome the sign problem and compare their features.
A primitive derivation of black hole entropy
横倉 祐貴 (数理創造プログラム 上級研究員)
Black holes have entropy. While a black hole occupies a three-dimensional spatial domain, the entropy is given by its two-dimensional surface area. In this sense, the entropy is holographic. However, its true origin is still unknown, and many researchers are studying it using various approaches. In this talk, I will provide an intuitive derivation of the entropy according to Bekenstein's first discussion in 1973. In particular, I will emphasize that it is the result of a combination of quantum theory and gravity. I will also give a brief review of the basics of physics so that people in other fields can enjoy how this mysterious formula appears.
Area law of entanglement entropy in quantum many body systems and its implication in tensor network calculation
ヤンタオ・ウー (数理創造プログラム 特別研究員)
In this coffee talk, I will explain the idea of entanglement entropy and how it has instructed people to construct a class of ground state wavefunction ansatz for quantum many-body systems. I will be pedagogical and explain the general construction in 1D and 2D. If time permits, I will explain how fermionic versions of them are realized.
What’s the value of reproductive value?
トーマス・ヒッチコック (数理創造プログラム 基礎科学特別研究員)
Populations are often heterogenous, composed of individuals of different sexes, ages, and condition. The way that genes flow between these different states across time can structure the ancestry of the population, and subsequently generate changes in allele frequency even in the absence of any other evolutionary forces. In this talk I discuss the concept of reproductive value, which provides a description of the expected long-term contribution each state makes to future populations. This tool allows us to aggregate the effects of different evolutionary forces across these different classes of individual, and thus better understand their relative importance. I briefly illustrate the usefulness of these concepts by discussing the evolution of senescence.
Coarse Notions of Curvature
クリスティ・コウジ・ケリー (数理創造プログラム 基礎科学特別研究員)
Curvature is a fundamental geometric notion with important applications in a variety of physical theories. Typically curvature is defined in smooth (differentiable) contexts but there has been much recent interest in synthetic characterisations of curvature in much rougher spaces than differentiable manifolds---including discrete spaces like networks. In this talk we aim to introduce some of the main coarse curvatures, particular in relation to optimal transport theory.
How to carry out a hadron experiment
冨田 夏希 (数理創造プログラム 客員研究員 / 京都大学 大学院理学研究科 附属サイエンス連携探索センター (SACRA) 特定助教)
I might be the only experimentalist in iTHEMS. I have been working for studying hadrons at SPring-8. Hadron experiments are unique in its large scale of equipment, time, man-power and budget. I would like to introduce how a hadron experimentalist carry out experiments.
Operad and consistency of 2d conformal field theories
森脇 湧登 (数理創造プログラム 基礎科学特別研究員)
An operad is a mathematical notion which describes an algebra with infinitely many multiplication structures. I will explain my recent result that "operads can be used to describe the consistency of two-dimensional conformal field theories.
Outreach of RIKEN iTHEMS 2022
坪井 俊 (数理創造プログラム 副プログラムディレクター / 武蔵野大学)
Overview of artificial selection
ジェフリ・フォーセット (数理創造プログラム 上級研究員)
Humans have been utilizing many plants, animals, and microorganims for several thousand years. As a result of selective breeding, also called artificial selection, domesticated species that we use differ from their wild progenitor species (e.g. dogs vs wolves) and contain a wide range of morphological diversity within them (e.g. different dog breeds). This process of artificial selection has been an excellent model to study evolution and natural selection ever since Charles Darwin. Moreover, studying artificial selection is important in our current efforts to improve the efficiency of selective breeding, and also provides new insights into human history. Here, I will provide an overview of artificial selection and introduce the projects on buckwheat that I'm involved in.
Smale horseshoe: paradigm of chaos
ジジュウ・リ (数理創造プログラム 特別研究員)
Ordinary differential equations (ODEs) are mathematical tools ubiquitous in the field of theoretical biology. Quite often, in their implementations, we simply integrate them carefully (or not) with sophisticated numerical packages and accept whatever the outcome as the “correct” answer. However, according to chaos theory, due to sensitive dependence on initial errors, any numerical integrators are doomed to fail if the time scale for the integration is large enough. One of the central goals of chaos theory is to study the solutions of nonlinear ordinary differential equations from an alternative perspective, namely, qualitative and geometric studies of dynamical systems governed by ODEs. In this week’s coffee meeting time, G-Joe will briefly introduce an oversimplified “geometrization” of ODEs systems using Poincare maps and Smale Horseshoes. Such a route aims to reduce the study of general ODE systems into the investigation of generic toy models, i.e., the “Horseshoe”, to gain insights into the fundamental structures otherwise hidden in the numerical solutions. As for almost everything in pure mathematics, such an approach is simple, elegant, and useless (for now), and I hope you will enjoy it with a cup of coffee.
Geometry in positive characteristic
吉川 翔 (数理創造プログラム 基礎科学特別研究員)
Algebraic geometry is a subject to study spaces defined by algebraic equations. It is separated into algebraic geometry in characteristic zero and algebraic geometry in positive characteristic. The first one is studying spaces which are similar to our living world, but the latter geometry is far from our geometric sense. However, we can regard our living world is a limit of spaces in positive characteristic. By the viewpoint, we can reduce problems in characteristic zero to similar problems in positive characteristic, the thechnic is called the reduction to positive characteristic. In this talk, I will introduce the notion of positive chracteristic and what reduction to positive characteristic is.
Isospin Symmetry Breaking in Nuclear Physics
内藤 智也 (数理創造プログラム 基礎科学特別研究員)
Properties of neutron stars, such as the mass and radius relation, are one of the hot topics in astrophysics. Nuclear interaction determines such properties and available data of neutron stars are rather limited; hence, theoretical and experimental studies on nuclear physics help to understand neutron star properties. Protons and neutrons have almost the same properties apart from their charge, which is called isospin symmetry. Accordingly, the nuclear interaction also has isospin symmetry. However, tiny contribution of isospin symmetry breaking of nuclear interaction gives large systematic uncertainty for discussion of neutron star properties.
Categorification of the Jones polynomial
佐野 岳人 (数理創造プログラム 基礎科学特別研究員)
Jones polynomial is a knot invariant discovered by V. F. R. Jones in 1984. Not only that it is a useful mathematical tool, the discovery led to opening up a new research area, quantum topology, which connects quantum mechanics and low-dimensional topology. In 2000, M. Khovanov introduced a “categorification of the Jones polynomial”, which is now called Khovanov homology, and made categorification one of the fundamental concept in knot theory.
The "species" concept in biology. What is a "species" anyway?
ホセ サイード・グティエレス オルテガ (数理創造プログラム 基礎科学特別研究員)
"Species" is one of the most important concepts in biology. It refers to a group of organisms that share characteristics. Even if we don't study biology, most of the times it is easy to tell when two organisms belong to two different species. However, in biology, there is no a consensus on what a "species" is. There are a lot of definitions, and it seems that there is not a definition that can generalize the whole idea of species. In this short talk, I will discuss why some definitions of species are not applicable to certain fields in biology. Take home message: "species" is a unit that is very useful for research, but in many senses, it seems to be just an arbitrary grid that we put on the continuous biodiversity.
Data analysis, parameter estimation and error bars
カトゥリン・ボシゥメン (数理創造プログラム 副プログラムディレクター / Professor, Department of Physics, Ryerson University, Canada)
Even though my research is focused on virophysics, most of my day-to-day work consists in estimating the values of a model's parameters based on observational data. In this talk, I want to introduce the simple mathematics and computational methods involved in parameter estimation, and some of the common pitfalls. I will use specific example from my past and current work.
How do you measure the distance between the Earth and the Sun?
長瀧 重博 (数理創造プログラム 副プログラムディレクター / 理化学研究所 開拓研究本部 (CPR) 長瀧天体ビッグバン研究室 主任研究員)
Accurate measurement of distance is crucial to understanding the universe. In 1998, about 25 years ago, human beings became convinced that the universe is filled with dark energy, which was revealed by accurately determining the distance to supernovae locations. It is the first step in measuring the distance in the universe to determine the distance between the Earth and the Sun. How do you determine the distance between the Earth and the Sun? Of course, you cannot use a ruler from the Earth to the Sun. Once the distance between the Earth and the Sun is determined, the mass of the Sun can be obtained. Once the distance to the Sun is known, the radius of the Sun can also be determined. Then, by using physics, we can understand what is going on inside the Sun even though we cannot see the inside of the Sun by photons. From this understanding, we know that the Sun has a life span of about 5 billion years and that human beings have only about 1 billion years left to live on the Earth. In this 15-minute talk, I would like to present how to determine the distance between the Sun and the Earth.
Origami Embeddings of flat tori
坪井 俊 (数理創造プログラム 副プログラムディレクター / 武蔵野大学)
Flat tori appear in many places in mathematics; in complex analysis, in geometry, in algebra, ... It cannot be smoothly isometrically embedded in the 3-dimensional Euclidean space but Nash and Kuiper showed that it is possible in C1 smoothability in 1954-55. It is natural to ask whether we can embed flat tori isometrically as a piecewise-linear object, and Burago-Zalgaller showed it possible in 1996. Their construction is theoretically simple but actually complicated to show it as an object. But Henry Segerman gave a nice simple embedding, a Hinged Flat Torus, and this lead us to find a simple isometric piecewise-linear embedding for the flat torus of any modulus, which I am happy to talk about.
A dynamical proposal to resolve the cosmological constant problem
難波 亮 (数理創造プログラム 上級研究員)
Our universe is observed to be expanding at an accelerated rate. The expansion is driven by some unknown object that has a constant energy density, thus called "cosmological constant" (a.k.a. dark energy). Since gravitational effects, which drive the expansion, do not discriminate any forms of matter/energy, this constant is expected to receive various contributions from high-energy physics. However, the observed value of the constant is smaller than the theoretical expectation by many orders of magnitute, the discrepancy called the cosmological constant problem. A mechanism has been proposed to cancel the large contributions by a classical dynamics in the early universe, but it essentially empties the universe altogether, not just the cosmological constant. We propose a concrete scenario that subsequently "reheats" the universe with energetic matter, thus completing the mechanism of the cosmological constant relaxation.
邱 靖凱 (数理創造プログラム 上級研究員)
The transistor invention ushered in the era of conventional computers. However, Moore’s law will fail one day due to the unavoidable quantum limit. Scientists are building quantum computers to continue the computing era. In this talk, I will compare conventional computers and quantum computers. Furthermore, I will briefly introduce that a topological superconductor can be one of the platforms for quantum computing.
Generalized generating function for proportion values and its application
入谷 亮介 (数理創造プログラム 研究員)
I will talk about a potentially interesting and useful methodology I partly devised, based on (probability) generating function methods.