Localization in the directions of Schrödinger equations
三上 渓太 (数理創造プログラム 研究員)
For a particular class of Schrödinger equations, the solutions to the equation localize in the directions as time goes infinity. In this small talk, we review some known results on this subject.
An invitation to algebraic quantum field theory
及川 瑞稀 (数理創造プログラム 大学院生リサーチ・アソシエイト / 数理創造プログラム 研修生 / 東京大学 大学院数理科学研究科 博士課程)
I am a new member of RIKEN iTHEMS and working on mathematics of conformal field theory. In this talk, noninteger dimensions in tensor categories and their relationship to algebraic quantum field theory will be introduced.
A glimpse of enumerative geometry
ヤーロン・ツァオ (数理創造プログラム 研究員)
Toward quantum computation of quantum field theory
伊藤 悦子 (数理創造プログラム 特別研究員 / 理化学研究所 仁科加速器科学研究センター (RNC) ストレンジネス核物理研究室 協力研究員)
Message-passing algorithms for graphical models
許 インイン (数理創造プログラム 基礎科学特別研究員)
Inference problems like marginalization and maximization are NP-hard to solve exactly and approximately in a graphical model. The complexity can be reduced dramatically when the underlying factor graph has some special structure. One extreme case is that of tree factor graphs, in which marginals can be computed in a number of operations which grows linearly with number of notes. This can be done by a ‘dynamic programming’ procedure often called as message passing or belief propagation algorithms. The update rules have been discovered independently in several different contexts: statistical physics (‘Bethe-Peierls approximation’), coding theory (the ‘sum-product’ algorithm), and artificial intelligence (‘belief propagation’, BP). The time evolution of the message’s distributions is known under the name of ‘density evolution’, and the fixed-point analysis of them is done by the replica-symmetric cavity method.
Conformal Bootstrap in AdS/CFT
楠亀 裕哉 (数理創造プログラム 基礎科学特別研究員 / Burke Fellow, Burke Institute, California Institute of Technology, USA)
A consistency condition for a given theory is a very vague concept, but in conformal field theories it can be formulated explicitly, known as the "conformal bootstrap equation". The main applications of the conformal bootstrap in recent years can be roughly classified into two categories: "deriving universality (of energy spectrum, etc.)" and "excluding impossible theories". Here I will introduce an application of the conformal bootstrap in the context of understanding quantum gravity.
Ringing Black Holes
大下 翔誉 (数理創造プログラム 基礎科学特別研究員)
I will provide a brief review of the quasinormal modes of black holes. The study of black hole perturbations is important to model the waveform of ringdown gravitational waves emitted from binary black hole mergers or coalescences of compact objects leading to the formation of black holes. In the latter part of my talk, I will discuss the "ease of excitation" of quasinormal modes. This is indeed important to test the no-hair theorem of balck holes.
Von Neumann algebras and their projections
森 迪也 (数理創造プログラム 基礎科学特別研究員)
The theory of von Neumann algebras began in a work by von Neumann in 1929. A von Neumann algebra is widely regarded as a noncommutative measure space. I am particular interested in the structure of projections of a von Neumann algebra, which play the role of measurable sets in measure theory. In this talk I will invite the audience to the mysterious world of the geometry of noncommutative measurable sets.
Exact WKB and its applications to physics
田屋 英俊 (数理創造プログラム 基礎科学特別研究員)
I explain the exact WKB method, which is a method to solve ordinary differential equations and has been developed (mainly) in mathematics since 1980's. I also discuss its applications to physics, including nonperturbative particle production by strong fields, and mention open problems in this field.
The wave operator and the Oppenheim conjecture
甘中 一輝 (数理創造プログラム 基礎科学特別研究員)
I am a new member of iTHEMS and working on spectral analysis of a Lorentzian manifold in mathematics.In this talk, we will discuss the eigenvalue distribution of a wave operator on flat tori as the simplest case. Through the Oppenheim conjecture about the distribution of values at integer points of indefinite quadratic forms, I would like to explain mathematically interesting aspects of spectral analysis of a wave operator. I don't know the physical meaning of this study, but I hope this talk will be an opportunity to discuss it.
Phase transtion' in Kahler geometry
井上 瑛二 (数理創造プログラム 基礎科学特別研究員)
I am a new member of RIKEN iTHEMS and working on Kahler geometry in mathematics. As I cannot overview my study in this short time, I would like to explain a strange phenomenon now I am facing in Kahler geometry with a specific example. It is reminiscent of `phase transition' or `spontaneous symmetry breaking'. I hope it makes a chance of discussion with researchers in other areas.
The death of a star: the theory of the supernova explosion
原田 了 (数理創造プログラム 基礎科学特別研究員)
At the end of the stellar evolution, the star explodes as bright as a galaxy and leaves a neutron star. This explosion is known as the supernova. Understanding the supernova explosion mechanism is crucial because it plays a vital role in the stellar and cosmic matter evolutions. The explosion mechanism includes a variety of physical processes, and hence it is a challenging problem. In this coffee talk, I would like to introduce the basic features of supernovae and the current understanding of the explosion mechanism.
Canonical form of tensor networks in one and two dimensions
ヤンタオ・ウー (数理創造プログラム 特別研究員)
I will be a new member of RIKEN iTHEMS and work on computational study in condensed matter physics. In this short coffee meeting, I would like to discuss the basics of tensor networks. I will be pedagogical and not assume knowledge of quantum mechanics. I will assume basic linear algebra at the level of singular value decomposition. I will introduce the graphical notation of a tensor network, and the notion of a canonical form in one dimension. If time permits, I will also discuss the canonical form in two dimensions.
The basics of topological band theory
ツォン ツォン・ラ (Post-doctoral research scientist, Max Planck Institute for Chemical Physics of Solids, Germany)
I will be a new member of RIKEN iTHEMS and work on theoretical study in condensed matter. In this short coffee meeting, I would like to disuss the topology properties of photocurrent. Firstly, based on band theory, I will discuss the topological classification of crystalline materials. Secondly, Similar to direct current formular I=U/R, the photocurrents will be discussed. Finally, I will discuss the topology properties of photocurrent in the various topological semimetals.
Cosmology 101 - expanding universe and inflationary cosmology
難波 亮 (数理創造プログラム 上級研究員)
I am a new member of RIKEN iTHEMS and working on several aspects of theoretical cosmology. As a partial self-introduction and introduction to the field, I would like to discuss some basics of cosmology, making it accessible by the iTHEMS members in different areas of expertise. In this short coffee meeting talk, my main focus is the evolution of the universe and the physics during its earliest period.
Reducing complexity and pursuing reality in computational biophysics
杉田 有治 (数理創造プログラム 上級研究員 / 理化学研究所 開拓研究本部 (CPR) 杉田理論分子科学研究室 主任研究員)
The basic unit of all the living matters is a cell, where huge number of biomolecules exist and express their biological functions. When we aim to study biological systems in computational biophysics, we always encounter many problems originated from the complexity of the systems. Reducing complexity has been one of the most essential issues in computational biophysics, while too much simplifications may lose the reality of biological phenomena. I would like to discuss several key mathematical concepts that have been used in computational biophysics for reducing complexity and pursuing reality of biology in the cell.
Computational phases of quantum matter
松浦 俊司 (数理創造プログラム 客員研究員 / Fundamental Researcher, Quantum Simulation Division, 1QBit, Canada)
I will talked about a connection between measurement-based quantum computing and quantum phases in physics.
Building something from nothing: a mathematical framework for aperiodic/amorphous sets
クリストファー・ボーン (数理創造プログラム 客員研究員 / 東北大学 材料科学高等研究所 (AIMR) 助教)
I will introduce a mathematical construction due to Bellissard that allows us to study disordered materials via Delone sets.
Density Functional Theory from Functional Renormalization Group
横田 猛 (数理創造プログラム 基礎科学特別研究員 / 東京大学 物性研究所 特別研究員)
In this talk, I will give a brief introduction of density functional theory. I will also talk about our recent attempt to improve density functional theory for electron systems by use of the functional renormalization group.
Spin transport in ultracold atomic superfluids
関野 裕太 (数理創造プログラム 訪問研究員)
I will briefly introduce transport phenomena of spin in ultracold atomic gases in a superfluid phase