Lecture
40 events

Lecture
Differential Topology Seminar: Rigidity and Flexibility of Isometric Embeddings
July 16 (Tue) at 15:00  16:30, 2024
Dominik Inauen (Academic Staff, University of Leipzig, Germany)
The problem of embedding abstract Riemannian manifolds isometrically (i.e. preserving the lengths) into Euclidean space stems from the conceptually fundamental question of whether abstract Riemannian manifolds and submanifolds of Euclidean space are the same. As it turns out, such embeddings have a drastically different behaviour at low regularity (i.e. C^{1}) than at high regularity (i.e. C^{2}). For example, by the famous NashKuiper theorem it is possible to find C1 isometric embeddings of the standard 2sphere into arbitrarily small balls in R^{3}, and yet, in the C^{2} category there is (up to translation and rotation) just one isometric embedding, namely the standard inclusion. Analoguous to the Onsager conjecture in fluid dynamics, one might ask if there is a sharp regularity threshold in the Holder scale which distinguishes these flexible and rigid behaviours. In my talk I will review some known results and argue why the Holder exponent 1/2 can be seen as a critical exponent in the problem.
Venue: ＃609, Department of Mathematics, Faculty of Science Bldg. No. 6, , Kyoto University
Event Official Language: English

Lecture
Obstructions to Lagrangian surgery
June 27 (Thu) at 15:00  17:00, 2024
Emmy Murphy (Professor, Princeton University, USA)
Given a Lagrangian immersion with a transverse double point, we can surger this point to obtain an embedded Lagrangian with more complicated topology. As a classical example, both the Clifford and Chekanov tori in C^{2} are obtained via Lagrangian surgery on a immersed sphere called the Whitney sphere. In the talk we'll discuss a Floertheoretic obstruction to this: that is, showing that a Lagrangian cannot be realized as a surgery. An interesting dilemma is that PH invariants of an immersed Lagrangian itself cannot detect the fact that it is immersed. Instead, we have to consider families of Floer invariants coming from all possible surgeries, and use properties specific to SFT Lagrangian cobordism maps.
Venue: Room 201 in Building No.15, RIMS, Kyoto University
Event Official Language: English

Lecture
Liouville symmetry groups and pseudoisotopies
June 25 (Tue) at 17:00  18:30, 2024
Emmy Murphy (Professor, Princeton University, USA)
Even though C^{n} is the most basic symplectic manifold, when n>2 its compactly supported symplectomorphism group remains mysterious. For instance, we do not know if it is connected. To understand it better, one can define various subgroups of the symplectomorphism group, and a number of Serre fibrations between them. This leads us to the Liouville pseudoisotopy group of a contact manifold, important for relating (for instance) compactly supported symplectomorphisms of C^{n}, and contacomorphisms of the sphere at infinity. After explaining this background, the talk will focus on a new result: that the pseudoisotopy group is connected, under a LiouvillevsWeinstein hypothesis.
Venue: Room 056, Graduate School of Mathematical Sciences, The University of Tokyo (Main Venue) / via Zoom
Event Official Language: English

Lecture
Rigidity and Flexibility of Isometric Embeddings
June 20 (Thu) at 17:00  18:30, 2024
Dominik Inauen (Academic Staff, University of Leipzig, Germany)
The problem of embedding abstract Riemannian manifolds isometrically (i.e. preserving the lengths) into Euclidean space stems from the conceptually fundamental question of whether abstract Riemannian manifolds and submanifolds of Euclidean space are the same. As it turns out, such embeddings have a drastically different behaviour at low regularity (i.e. C^1) than at high regularity (i.e. C^2). For example, by the famous NashKuiper theorem it is possible to find C1 isometric embeddings of the standard 2sphere into arbitrarily small balls in R^3, and yet, in the C^2 category there is (up to translation and rotation) just one isometric embedding, namely the standard inclusion. Analoguous to the Onsager conjecture in fluid dynamics, one might ask if there is a sharp regularity threshold in the Holder scale which distinguishes these flexible and rigid behaviours. In my talk I will review some known results and argue why the Holder exponent 1/2 can be seen as a critical exponent in the problem.
Venue: Graduate School of Mathematical Sciences, The University of Tokyo
Event Official Language: English

Lecture
An introduction to the exact WKB analysis via the hypergeometric differential equation
February 19 (Mon)  22 (Thu), 2024
Takashi Aoki (Professor Emeritus, Faculty of Science and Engineering, Kinki University)
This is an introductory course to the exact WKB analysis. Firstly we review some basic facts concerning formal power series and WKB solutions. Secondly we give an overview of the connection formulas for WKB solutions to ordinary differential equations of second order with a large parameter. Next, after recalling some classical theory for the Airy equation and the Gauss hypergeometric differential equation, we show how the exact WKB analysis is used for these equations and what are obtained. One of the main results to be presented in this course is the relation the between the classical hypergeometric function and the Borel resummed WKB solutions to the hypergeometric differential equation with a large parameter. Some applications and recent topics are also given. [Schedule (Tentative)] Day 1 10:00  11:30 Lecture 1 14:00  16:00 Lecture 2 Day 2 10:00  11:30 Lecture 3 14:00  16:00 Lecture 4 Day 3 10:00  11:30 Lecture 5 14:00  16:00 Lecture 6 Day 4 10:00  11:30 Lecture 7 14:00  16:00 Lecture 8
Venue: Seminar Room #359 (Main Venue) / via Zoom
Event Official Language: English

Introduction to Effective Field Theory and ManyBody Problems
December 27 (Wed)  28 (Thu), 2023
Masaru Hongo (Assistant Professor, Department of Physics, Faculty of Science, Niigata University)
Quantum field theory (QFT) has been formulated as a theoretical tool to describe elementary particles and nuclei. However, after introducing the concept of "effective field theory," QFT has been providing a general and powerful theoretical framework for describing various universal phenomena in broader range of physical systems, including condensed matter physics and statistical physics. In this lecture, we will explore the basic aspects of field theory by employing it to address quantum manybody problems in simple nonrelativistic systems. The topics covered will include: Lecture 1: Lowenergy scattering and renormalization in quantum mechanics Lecture 2: Effective field theory of lowenergy scattering Lecture 3: Spontaneous symmetry breaking in weaklyinteracting bose gas Lecture 4: Effective field theory of superfluid Lecture 5: Introduction to inmedium potential Lecture 6: Complexvalued inmedium potential between heavy impurities in ultracold atoms The aim is to provide an introductory overview and explanation of basics concepts in field theory. Schedule: Wed., Dec. 27 10:00  11:30: Lecture 1 13:00  14:30: Lecture 2 15:00  16:30: Lecture 3 Thur., Dec. 28 10:00  11:30: Lecture 4 13:00  14:30: Lecture 5 15:00  16:30: Lecture 6
Venue: Hybrid Format (3F #359 and Zoom), Main Research Building
Event Official Language: English

Lecture
Rapid development of coldatom quantum computers and their prospect
December 26 (Tue) at 13:30  17:00, 2023
Takafumi Tomita (Assistant Professor, PhotoMolecular Science, Institute for Molecular Science)
Note for participants: For onsite participants, please register via the registration form. For online participants finding the Zoom link, you can get it after filling the registration form. Program: 13:3015:00 Lecture 1 15:0015:30 Coffee break 15:3017:00 Lecture 2 Abstract: In this talk, I will give an overview of the recent rapid progress of coldatom quantum computers. In a coldatom quantum computer, a lasercooled atomic gas in a vacuum chamber is captured with a twodimensional trap array called an optical tweezers array, which is an array of tightly focused laser beams. An array of cold single atoms thus created is initialized, gate operated, and readout with other laser beams. Because of its controllability and scalability, the coldatom quantum computer has been attracting much attention, as one of the most promising candidates in the race to develop quantumcomputer hardware. I will describe the characteristics and development trends of the coldatom hardware, as well as the development of a coldatom quantum computer at Institute for Molecular Science including the realization of an ultrafast quantum gate using ultrashort laser pulses.
Venue: #435437, 4F, Main Research Building (Main Venue) / via Zoom
Event Official Language: English

Transforming Industries and Society: The Power of Advanced Math and AI Technologies
December 12 (Tue) at 16:30  18:00, 2023
Hirokazu Anai (Principal Research Director, FUJITSU RESEARCH, FUJITSU Ltd.)
In this talk, we will review the history and the latest trends in artificial intelligence (AI) and mathematical technologies in recent years. We will also introduce various realworld problemsolving efforts that utilize stateoftheart mathematics and artificial intelligence technology. Additionally, we will explore the role of mathematical and AI technologies and the social value they bring, while providing examples of their applications in a wide range of fields, such as manufacturing, disaster prevention, medical care, and institutional design in society. Furthermore, we will consider the thinking and skills required to address industrial and social issues using mathematical and AI technologies. The technologies that will be discussed in this talk include the following keywords: mathematical modeling, simulation, optimization, deep learning, topological data analysis, causal discovery, game theory, matching theory, and social mathematics.
Venue: Okochi Hall (Main Venue) / via Zoom
Event Official Language: English

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 infinitycategories, spectra, operads, and other standard tools of the last decade. The main applications will be to encode various higheralgebraic 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 infinitycategorical 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 infinitycategories 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: #435437, Main Research Building / via Zoom
Event Official Language: English

Lecture
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 spacetime dimensions, the spinfoam quantization of 3d gravity is given by the TuraevViro topological invariant, which is intimately related to the quantization of ChernSimons theory. I will explain in particular how the spinfoam amplitudes solve the Wheelerde Witt equation, implement the invariance under 3d diffeomorphisms (despite being formulated in a discretized spacetime) and lead to a quasilocal version of holography. In four spacetime dimensions, general relativity can be formulated as an almosttopological theory and I will explain how the existing spinfoam models introduce a sea of topological defects to recreate 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: #435437, 4F, Main Research Building
Event Official Language: English

NUQiTHEMSYITP 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 (NUQ), Niigata University / Yukawa Institute for Theoretical Physics (YITP), Kyoto University Coorganizer: RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS)
Venue: #A317, Building A, Faculty of Science, Niigata University / via Zoom
Event Official Language: Japanese

Lecture
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: #535537, 5F, Main Research Building
Event Official Language: English

Lecture
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 socalled 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: #535537, 5F, Main Research Building
Event Official Language: English

Lecture
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: #345347, 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 bulkedge correspondence. The bulkedge 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 solidstate materials, which are quantum mechanical. However, certain properties of topological insulators, including the bulkedge 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 twodimensional 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 bulkedge correspondence. The bulkedge 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 solidstate materials, which are quantum mechanical. However, certain properties of topological insulators, including the bulkedge 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 twodimensional 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 bulkedge correspondence. The bulkedge 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 solidstate materials, which are quantum mechanical. However, certain properties of topological insulators, including the bulkedge 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 twodimensional 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 bulkedge correspondence. The bulkedge 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 solidstate materials, which are quantum mechanical. However, certain properties of topological insulators, including the bulkedge 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 twodimensional topological insulators and Kähler geometry.
Venue: via Zoom
Event Official Language: English
40 events
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 iTHEMS Colloquium
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