Lecture

Higher Algebra in Geometry

July 31 (Mon) - August 10 (Thu), 2023

Hiro Lee Tanaka (Assistant Professor, Department of Mathematics, Texas State University, USA)

In these lectures, we will shed light on modern tools of higher algebra, where the traditional structures of algebra yield themselves only after controlled deformations. We will introduce infinity-categories, spectra, operads, and other standard tools of the last decade. The main applications will be to encode various higher-algebraic structures that inevitably arise in, and shed light on, geometry and topology. If time permits, we will illustrate how spectra naturally arise in geometric invariants. The audience is imagined to consist of mathematicians interested in applications of infinity-categorical tools -- so a broad range of geometers (including topologists) and algebraists. From Lecture Two onward, I will assume basic knowledge of algebraic topology (e.g., the material of Hatcher) and homological algebra. These lectures will be held between July 31 and August 10, each from 10:30 to 12:00, for a total of 8 lectures. 1st Week: Jul 31(mon), Aug 1(tue) - 3(thu) - Introduction to ideas of higher algebra in geometry, for a general audience. - Introduction to infinity-categories and to spectra. 2nd Week: Aug 7(mon) - 10(thu) - Examples in geometry and topology, including invariants of Legendrian links and generating functions. - Future Directions. Profile: Hiro Lee Tanaka is an assistant professor in the Department of Mathematics. After receiving his Ph.D. from Northwestern University and completing postdoctoral work at Harvard University, he conducted research at the Mathematical Sciences Research Institute in Berkeley, California, and at the Isaac Newton Institute in Cambridge, England. His research aims to fuse the higher structures in modern algebra with geometries emerging from both classical mechanics and supersymmetric field theories. Beyond research, Tanaka engages in efforts to create more equitable and supportive environments throughout the mathematics community.

Venue: #435-437, Main Research Building / via Zoom

Event Official Language: English

3rd QGG Intensive Lectures: Spinfoam path integrals for Quantum Gravity

July 26 (Wed) - 28 (Fri), 2023

Etera Livine (Research Director CNRS, Ecole Normale Supérieure de Lyon, France)

At the crossroads of several approaches to quantum gravity, Spinfoams propose a discrete path integral for quantum general relativity built from topological field theory. With the spectrum of geometric operators directly read from the representation theory of the local symmetry group, they can be interpreted as a quantized version of Regge calculus and can be understood as implementing the dynamics of quantum states geometry in loop quantum gravity. I will explain the basics of the formalism, the motivations, the mathematical framework and the main tools. In three space-time dimensions, the spinfoam quantization of 3d gravity is given by the Turaev-Viro topological invariant, which is intimately related to the quantization of Chern-Simons theory. I will explain in particular how the spinfoam amplitudes solve the Wheeler-de Witt equation, implement the invariance under 3d diffeomorphisms (despite being formulated in a discretized space-time) and lead to a quasi-local version of holography. In four space-time dimensions, general relativity can be formulated as an almost-topological theory and I will explain how the existing spinfoam models introduce a sea of topological defects to re-create the gravitational degrees of freedom from a topological path integral. Finally, I will show how spinfoams are naturally defined in terms of group field theory, which are generalized tensor models, and the prospects that this opens. I will conclude with the main challenges and open lines of research of the field. Program: July 26 10:00 - 10:15 Registration and reception 10:15 - 11:45 Lecture 1 11:45 - 13:30 Lunch & coffee break 13:30 - 15:00 Lecture 2 15:00 - 16:00 Coffee break 16:00 - 17:00 Lecture 3 17:10 - 18:30 Short talk session July 27 10:00 - 11:45 Lecture 4 11:45 - 13:30 Lunch & coffee break 13:30 - 15:00 Lecture 5 15:00 - 16:00 Coffee break 16:00 - 17:00 Lecture 6 17:30 - 20:00 Banquet July 28 10:00 - 11:45 Lecture 7 11:45 - 13:30 Lunch & coffee break 13:30 - 15:00 Lecture 8 15:00 - 16:00 Coffee break 16:00 - 17:30 Lecture 9 & Closing

Venue: #435-437, 4F, Main Research Building

Event Official Language: English

NU-Q-iTHEMS-YITP Lecture: Applications of Quantum Computation in Quantum Field Theory

July 6 (Thu) - 7 (Fri), 2023

Masazumi Honda (Assistant Professor, Yukawa Institute for Theoretical Physics, Kyoto University)

This lecture aims to provide an introductory explanation of the application of quantum computation in numerical simulations of quantum field theory. We will begin by covering the fundamental aspects of quantum computation, followed by a discussion on its application to simulating spin systems. Subsequently, we will delve into introductory explanations of continuous field quantum theory and lattice field quantum theory, and discuss their simulation methods. Additionally, practical exercises utilizing IBM Qiskit for quantum simulations will be conducted. Important Notice for Participants: Please note that loaner laptops for the practical exercises will not be provided, so please bring your own laptops. Prior to the lecture, please ensure that you have set up your environment to use Jupyter Notebook, for example, by installing Anaconda. Organizers: Quantum Research Center (NU-Q), Niigata University / Yukawa Institute for Theoretical Physics (YITP), Kyoto University Co-organizer: RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS)

Venue: #A317, Building A, Faculty of Science, Niigata University / via Zoom

Event Official Language: Japanese

2nd QGG Intensive Lectures: Large gauge transformation and infrared regularity in the inflationary universe

June 19 (Mon) - 20 (Tue), 2023

Takahiro Tanaka (Professor, Division of Physics and Astronomy, Graduate School of Science, Kyoto University)

In this lecture we will start with the general framework to analyse the density perturbation in the inflationary universe. Then, we will introduce various infrared (IR) phenomena, including IR divergences, delta N formalism and consistency relation. The underlying symmetry originally coming from 3D diffeomorphism invariance leads us to a harmonic and unified understanding of these phenomena. Program: June 19 10:00 - 10:15 Registration and reception (with coffee) 10:15 - 11:45 Lecture 1 11:45 - 13:30 Lunch & coffee break 13:30 - 15:00 Lecture 2 15:00 - 16:00 Coffee break 16:00 - 17:30 Lecture 3 17:45 - 18:30 Short talk session June 20 10:00 - 10:15 Reception (with coffee) 10:15 - 11:45 Lecture 4 11:45 - 13:30 Lunch & coffee break 13:30 - 15:00 Lecture 5 15:00 - 16:00 Coffee break 16:00 - 17:30 Lecture 6 17:30 - 18:30 Discussions & Closing

Venue: #535-537, 5F, Main Research Building

Event Official Language: English

Introduction to the Quantum Theory of Gravity via Asymptotic Safety

January 24 (Tue) - 26 (Thu), 2023

Ohta Nobuyoshi (Visiting Professor, Department of Physics, National Central University, Taiwan)

We give an introduction to the formulation towards the quantum theory of gravity using the functional (or exact) renormalization group, the so-called asymptotic safety. First we briefly explain the necessity of quantization of gravity and why the Einstein gravity is not sufficient for this purpose. Second, we introduce the functional renormalization group equation and explain what is the asymptotic safety program to achieve the quantum theory of gravity. This includes the notion of relevant, irrelevant and marginal operators, and it is important that there are finite number of relevant operators to make any prediction of quantum effects. This gives a nonperturbatively renormalizable theory of gravity. We then discuss various examples how the program may be applied to various theories, and summarize the current status of this approach. (Tentative schedule) [Day 1: Jan. 24, 2023] Free discussion: 9:30 - 10:30 Lecture 1: 10:30 - 12:00 Lunch: 12:00 - 13:30 Lecture 2: 13:30 - 15:00 Break: 15:00 - 15:30 Lecture 3: 15:30 - 17:00 [Day 2: Jan. 25, 2023] Free discussion: 9:30 - 10:30 Lecture 4: 10:30 - 12:00 Lunch: 12:00 - 13:30 Lecture 5: 13:30 - 15:00 Break: 15:00 - 15:30 Lecture 6: 15:30 - 17:00 [Day 3: Jan. 26, 2023] Q&A + discussion: 9:30 - 15:00

Venue: #535-537, 5F, Main Research Building

Event Official Language: English

An Introduction to Quantum Measurement Theory for Physicists

November 10 (Thu) - 12 (Sat), 2022

Masahiro Hotta (Assistant Professor, Department of Physics, Graduate School of Science, Tohoku University)

In this lecture, basic concepts in quantum measurement theory are introduced, including measurement operators and POVM's. The related topics are also picked up. Lecture 1: Nov. 10, 10:30 - 12:00 Lecture 2: Nov. 10, 13:30 - 15:00 Lecture 3: Nov. 10, 15:30 - 17:00 Lecture 4: Nov. 11, 10:30 - 12:00 Lecture 5: Nov. 11, 13:30 - 15:00 Lecture 6: Nov. 12, 10:30 - 12:00

Venue: #345-347, 3F, Main Research Building (Main Venue) / via Zoom

Event Official Language: English

Introduction to Topological Insulators: From Quantum to Classical Physics 4

April 27 (Wed) at 15:00 - 17:00, 2022

Tomoki Ozawa (Associate Professor, Advanced Institute for Materials Research (AIMR), Tohoku University)

In this set of lectures, I give an introduction to topological insulators. A goal is to provide an overall understanding of basic concepts of the physics of topological insulators to mathematicians and physicists with no prior knowledge on the subject. Very roughly speaking, topological insulators are materials whose wavefunctions show nontrivial topological structure in momentum space. Materials with topologically nontrivial wavefunction in momentum space have been found to host modes which are localized at the surface (edge) of the material: a property known as the bulk-edge correspondence. The bulk-edge correspondence results in experimentally observable signature of somewhat abstract notion of topology of the wavefunction in momentum space. Originally, topological insulators were found and studied for electrons in solid-state materials, which are quantum mechanical. However, certain properties of topological insulators, including the bulk-edge correspondence, have been found to hold also for purely classical materials, such as electromagnetic waves obeying Maxwell’s equations, or waves described by Newtonian mechanics. I will try to introduce topological insulators in a way general enough to be applied to quantum as well as classical materials. In the final part of the lectures, I take this opportunity to discuss some of my own works, where I studied some relations between the two-dimensional topological insulators and Kähler geometry.

Venue: via Zoom

Event Official Language: English

Introduction to Topological Insulators: From Quantum to Classical Physics 3

April 21 (Thu) at 15:00 - 17:00, 2022

Tomoki Ozawa (Associate Professor, Advanced Institute for Materials Research (AIMR), Tohoku University)

In this set of lectures, I give an introduction to topological insulators. A goal is to provide an overall understanding of basic concepts of the physics of topological insulators to mathematicians and physicists with no prior knowledge on the subject. Very roughly speaking, topological insulators are materials whose wavefunctions show nontrivial topological structure in momentum space. Materials with topologically nontrivial wavefunction in momentum space have been found to host modes which are localized at the surface (edge) of the material: a property known as the bulk-edge correspondence. The bulk-edge correspondence results in experimentally observable signature of somewhat abstract notion of topology of the wavefunction in momentum space. Originally, topological insulators were found and studied for electrons in solid-state materials, which are quantum mechanical. However, certain properties of topological insulators, including the bulk-edge correspondence, have been found to hold also for purely classical materials, such as electromagnetic waves obeying Maxwell’s equations, or waves described by Newtonian mechanics. I will try to introduce topological insulators in a way general enough to be applied to quantum as well as classical materials. In the final part of the lectures, I take this opportunity to discuss some of my own works, where I studied some relations between the two-dimensional topological insulators and Kähler geometry.

Venue: via Zoom

Event Official Language: English

Introduction to Topological Insulators: From Quantum to Classical Physics 2

April 14 (Thu) at 15:00 - 17:00, 2022

Tomoki Ozawa (Associate Professor, Advanced Institute for Materials Research (AIMR), Tohoku University)

In this set of lectures, I give an introduction to topological insulators. A goal is to provide an overall understanding of basic concepts of the physics of topological insulators to mathematicians and physicists with no prior knowledge on the subject. Very roughly speaking, topological insulators are materials whose wavefunctions show nontrivial topological structure in momentum space. Materials with topologically nontrivial wavefunction in momentum space have been found to host modes which are localized at the surface (edge) of the material: a property known as the bulk-edge correspondence. The bulk-edge correspondence results in experimentally observable signature of somewhat abstract notion of topology of the wavefunction in momentum space. Originally, topological insulators were found and studied for electrons in solid-state materials, which are quantum mechanical. However, certain properties of topological insulators, including the bulk-edge correspondence, have been found to hold also for purely classical materials, such as electromagnetic waves obeying Maxwell’s equations, or waves described by Newtonian mechanics. I will try to introduce topological insulators in a way general enough to be applied to quantum as well as classical materials. In the final part of the lectures, I take this opportunity to discuss some of my own works, where I studied some relations between the two-dimensional topological insulators and Kähler geometry.

Venue: via Zoom

Event Official Language: English

Introduction to Topological Insulators: From Quantum to Classical Physics 1

April 7 (Thu) at 15:00 - 17:00, 2022

Tomoki Ozawa (Associate Professor, Advanced Institute for Materials Research (AIMR), Tohoku University)

In this set of lectures, I give an introduction to topological insulators. A goal is to provide an overall understanding of basic concepts of the physics of topological insulators to mathematicians and physicists with no prior knowledge on the subject. Very roughly speaking, topological insulators are materials whose wavefunctions show nontrivial topological structure in momentum space. Materials with topologically nontrivial wavefunction in momentum space have been found to host modes which are localized at the surface (edge) of the material: a property known as the bulk-edge correspondence. The bulk-edge correspondence results in experimentally observable signature of somewhat abstract notion of topology of the wavefunction in momentum space. Originally, topological insulators were found and studied for electrons in solid-state materials, which are quantum mechanical. However, certain properties of topological insulators, including the bulk-edge correspondence, have been found to hold also for purely classical materials, such as electromagnetic waves obeying Maxwell’s equations, or waves described by Newtonian mechanics. I will try to introduce topological insulators in a way general enough to be applied to quantum as well as classical materials. In the final part of the lectures, I take this opportunity to discuss some of my own works, where I studied some relations between the two-dimensional topological insulators and Kähler geometry.

Venue: via Zoom

Event Official Language: English

Public Lecture for Darwin Day

February 17 (Wed) at 9:00 - 10:00, 2021

Catherine Beauchemin (Deputy Program Director, iTHEMS / Professor, Department of Physics, Ryerson University, Canada)

Japan, February 17, 2021, 09:00 AM JST Canada/USA, Feb 16, 2021, 07:00 PM Eastern Time Through mutations and genetic reassortment, a virus can mutate and the resulting virus variants can evade our drugs, our vaccines, and our body's own immune response. Using specific viruses like influenza, HIV or SARS-CoV-2 (the virus responsible for COVID-19) as examples, I will introduce the basics of how viruses replicate, and the processes via which mutations arise. *Detailed information about the seminar refer to the Prof. Beauchemin’s email.

Venue: via Zoom

Event Official Language: English

Toward the Practical Use of Quantum Computers

December 4 (Fri) at 10:30 - 12:00, 2020

Shunji Matsuura (Visiting Scientist, iTHEMS / Fundamental Researcher, Quantum Simulation Division, 1QBit, Canada)

量子コンピュータは古典コンピュータとは異なる原理に基づいて動いており、自然科学を含む様々な分野において大きな変化をもたらすと考えられている。特にこの数年の進展は著しく、量子計算の古典計算に対する優位性が実験的に初めて示されるなど、期待されているマイルストーンが着実に達成されていっている。一方で量子コンピュータの発展において常に障害となっているのがノイズである。量子状態はノイズの影響を受けやすく、現在の量子コンピュータにおいては量子ゲート操作を行うごとに状態の精度が減衰していってしまう。そのため、量子コンピュータにかける負担をできるだけ減らすようなアルゴリズムの開発や、計算結果からエラーを取り除く方法、観測回数をできるだけ減らす方法等、様々な研究が行われている。本講義ではこれら量子コンピュータの実用化に向けた最近の研究と今後の課題について話す。

Venue: via Zoom

Event Official Language: Japanese

Nara Women's University, Faculty of Science, Continuous Lecture Series: Forefront of Modern Science - Frontiers in Mathematics, Astronomy, Physics, Biology and Computation

October 2 (Fri) at 16:20 - 17:50, 2020

Tetsuo Hatsuda (Program Director, iTHEMS)
Yuka Kotorii (Visiting Scientist, iTHEMS / Associate Professor, Mathematics Program, Graduate School of Advanced Science and Engineering, Hiroshima University / Visiting Scientist, Mathematical Analysis Team, RIKEN Center for Advanced Intelligence Project (AIP))
Shigehiro Nagataki (Deputy Program Director, iTHEMS / Chief Scientist, Astrophysical Big Bang Laboratory, RIKEN Cluster for Pioneering Research (CPR))
Makiko Nio (Senior Scientist, Quantum Hadron Physics Laboratory, RIKEN Nishina Center for Accelerator-Based Science (RNC))
Ryosuke Iritani (Research Scientist, iTHEMS)
Ai Niitsu
Shigenori Otsuka (Research Scientist, iTHEMS / Research Scientist, Data Assimilation Research Team, RIKEN Center for Computational Science (R-CCS))
Emi Yukawa (Assistant Professor, Department of Physics, Faculty of Science Division I, Tokyo University of Science)

Venue: Changed to Zoom

Event Official Language: Japanese

Public Lecture : Math meets Quantum Materials

September 29 (Tue) at 19:00 - 20:30, 2020

Hidetoshi Nishimori (Senior Visiting Scientist, iTHEMS / Specially Appointed Professor, Tokyo Institute of Technology)
Tomoki Ozawa (Visiting Scientist, iTHEMS / Associate Professor, Advanced Institute for Materials Research (AIMR), Tohoku University)

Public Lecture "Math meets Quantum Materials" for high school students and above will be held. The lecture will introduce the latest topics in mathematics and physics, such as topology and quantum computers, in an easy-to-understand manner. For more information and to register for the event, please click on the related links.

Venue: via Online

Event Official Language: Japanese

iTHEMS Intensive Course [5] : "Adaptive strategies of organisms, their mathematical bases" - Evolution of cooperation

June 26 (Fri) at 13:30 - 15:00, 2020

Yoh Iwasa (Senior Advisor, iTHEMS / Professor, Kwansei Gakuin University / Professor Emeritus, Kyushu University)

Living systems exhibit features distinct from nonliving physical systems: their structure and behaviors appear to be chosen adaptive. They are the outcomes of evolution. Mathematical formalisms developed in engineering and social sciences (e.g. control theory, game theory, evolutionary game theory) are sometimes very useful in biology.

Venue: via Zoom

Event Official Language: English

iTHEMS Intensive Course [3] : "Adaptive strategies of organisms, their mathematical bases" - Masting, synchronized reproduction of trees: Coupled chaotic system

June 25 (Thu) at 13:30 - 14:30, 2020

Yoh Iwasa (Senior Advisor, iTHEMS / Professor, Kwansei Gakuin University / Professor Emeritus, Kyushu University)

Living systems exhibit features distinct from nonliving physical systems: their structure and behaviors appear to be chosen adaptive. They are the outcomes of evolution. Mathematical formalisms developed in engineering and social sciences (e.g. control theory, game theory, evolutionary game theory) are sometimes very useful in biology.

Venue: via Zoom

Event Official Language: English

iTHEMS Intensive Course [2] : "Adaptive strategies of organisms, their mathematical bases" - Dynamic optimization models for growth and reproduction

June 19 (Fri) at 13:30 - 15:00, 2020

Yoh Iwasa (Senior Advisor, iTHEMS / Professor, Kwansei Gakuin University / Professor Emeritus, Kyushu University)

Living systems exhibit features distinct from nonliving physical systems: their structure and behaviors appear to be chosen adaptive. They are the outcomes of evolution. Mathematical formalisms developed in engineering and social sciences (e.g. control theory, game theory, evolutionary game theory) are sometimes very useful in biology.

Venue: via Zoom

Event Official Language: English

iTHEMS Intensive Course [1] : "Adaptive strategies of organisms, their mathematical bases" - Sex expression and sex allocation of marine organisms

June 18 (Thu) at 13:30 - 15:00, 2020

Yoh Iwasa (Senior Advisor, iTHEMS / Professor, Kwansei Gakuin University / Professor Emeritus, Kyushu University)

Living systems exhibit features distinct from nonliving physical systems: their structure and behaviors appear to be chosen adaptive. They are the outcomes of evolution. Mathematical formalisms developed in engineering and social sciences (e.g. control theory, game theory, evolutionary game theory) are sometimes very useful in biology.

Venue: via Zoom

Event Official Language: English