[NHK Culture] A series of online mathematics courses where professors from famous universities such as the University of Tokyo introduce the world of modern mathematics Image

URL: NHK Cultural Center Co., Ltd. Press release: October 1, 2024 [NHK Culture] A series of online mathematics courses where professors from famous universities such as the University of Tokyo introduce the world of modern mathematics. 2 weeks of missed delivery starting 3 days after the course ends

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Mathematics, Kyushu University) Graduated from the Department of Mathematics, Faculty of Science, University of Tokyo in 1983, and completed the doctoral course at the same Graduate School of Science in 1988. After serving as an assistant at the Faculty of Science at Osaka University and an assistant professor at the Faculty of Industrial Arts at Kyoto Institute of Technology, he became an assistant professor at the Graduate School of Mathematics, Kyushu University in April 1996, and assumed his current position in January 2002. 4. Tomoki Kabira (Professor, Hitotsubashi University Graduate School of Economics) Completed the Graduate School of Mathematical Sciences, University of Tokyo. Ph.D. (Mathematical Sciences). Specializes in complex dynamical systems theory. His publications include “Lectures on Mathematica” (Pleiades Publishing), “Calculus – One Variable and Two Variables” (Nippon Hyoronsha), and

“Introduction to Complex Functions” (Shokabo). 5. Ogitake Shimizu (Professor, Graduate School of Science, Kyoto University) Recipient of the Bessel Prize of the Alexander von Humboldt Foundation (Germany) in 2014, former president of the Mathematical Society of Japan, currently acting president of the Mathematical Society of Japan, and professor at the Graduate School of Science, Kyoto University. His specialty is partial differential equation theory, especially Navier-Stokes equations. 6. Shunsuke Takagi (Professor, Graduate School of Mathematical Sciences, University of Tokyo) Born in Tokushima Prefecture. Graduated from the Department of Mathematics, Faculty of Science, University of Tokyo in 2000, and completed the doctoral course at the same university’s Graduate School of Mathematical Sciences in 2004. He assumed his current position in 2018 after serving as an assistant at the Graduate School of Mathematical Sciences at Kyushu University, a specially appointed assistant professor at the same graduate school, and an associate professor at the Graduate School of Mathematical Sciences at the University of Tokyo. 1.10/26 (Sat) [Matrix of infinite size and mathematics of quantum computers] Operator algebra theory, my specialty, was introduced by von Neumann in connection with the mathematical foundations of quantum mechanics, and considers a set of matrices (called operators) of infinite size. Currently, it is being developed in connection with various topics in mathematics and theoretical physics. On the other hand, quantum computers are attracting attention as a hot topic and are related to various problems in mathematics, physics, and computer science. Many methods have been proposed for realizing quantum computers, but nothing definitive has yet been found. Among these, the so-called topological quantum computer is based on the most mathematical approach and is closely related to operator algebra theory, so I will provide an overview of it. It does not assume that you know anything about operator algebras. 2.11/9 (Sat) [Knot theory and its applications] Knot theory is a field that studies how to tie strings from a topological perspective, and research has been conducted for over 100 years. First, I will introduce how to mathematically discuss the different ways of tying. As an application of knot theory, it has been proven that it is natural for earphone cords to become tangled, for example. Recently, knots have appeared in DNA and vortices, and it has become clear that their topology has important meaning. We will also explain how knot theory is applied to research in other fields. 3.12/14 (Sat) [Elliptic modular j-function or youthful dream] Modular functions are a type of “high-level periodic functions” and are derived from elliptic functions, which are generalized trigonometric functions, which are historically well-known periodic functions, as double periodic functions with complex variables. , born in the mid-19th century. Since then, the theory of modular functions has continued to develop and plays a central role in modern number theory. In particular, we will focus on the elliptic modular function, which is the most basic modular function, and especially the function known as the “(elliptic modular) j-function,” and the theory of imaginary multiplication known as “Kronecker’s youthful dream.” We will overview some interesting properties, such as the relationship with the “monster”, a scattered finite simple group of maximum order. 4.1/25 (Sat) [Complex dynamical systems and fractals] The jagged edges of a coastline or the warts on a cauliflower have a property called “self-similarity”, meaning that no matter how small you zoom in, the entire shape remains very similar. This is what is called a “fractal shape.” Mathematical structures with self-similarity have been the subject of research since the 19th century. Especially when considering sequences of complex numbers. You can see that surprisingly complex and diverse fractal figures can be generated from a very simple recurrence formula. The “complex dynamical systems theory” that explains this principle emerged in France about 100 years ago, when complex analysis was making remarkable progress. In this lecture, I would like to talk about how the theory of complex dynamical systems was born, including the state of mathematics at the time. 5.2/22 (Sat) [Free boundary problem of fluid equation] When solving nonlinear (parabolic) partial differential equations, the method of expressing the solution using operators called semigroups and constructing the solution in an appropriate function space using reduction mapping and successive approximation is a highly versatile and innovative method. This is a method. This semigroup method is effective for semilinear nonlinear equations, but it causes a loss of regularity for quasilinear nonlinear equations, and one way to avoid this is maximum regularity. The Navier-Stokes equation that describes the motion of a fluid is a semilinear nonlinear equation, but in a free boundary problem, it becomes a semilinear nonlinear equation by converting the free boundary to a fixed boundary. In this talk, I will give an overview of maximum regularity, and show that its application allows us to obtain the unique existence of a solution to a free boundary problem described by the Navier-Stokes equation. 6.3/22 (Sat) [Algebraic geometry and singularity] A figure expressed as a set of common zeros of several polynomials is called an algebraic variety, and a point on the algebraic variety that is not smooth, twisted, or sharp is called a singularity. Algebraic geometry is a field of study that

investigates the properties of algebraic varieties by making full use of various techniques from algebra, geometry, and analysis. In modern algebraic geometry, it is essential to analyze singularities of algebraic varieties, and for this purpose various invariants have been introduced to measure the badness of singularities. In this lecture, I will explain some invariants while touching on Heisuke Hironaka’s singularity resolution theorem, Mikio Sato’s b function (Bernstein Sato polynomial), etc. Modern Mathematics Exploration 2024 Lecturer: Yasuyuki Kawato (Professor, University of Tokyo), Koya Shimokawa (Professor, Ochanomizu University), Masanobu Kaneko (Professor at Kyushu University), Tomoki Kabira (Professor at Hitotsubashi University), Takeshi Shimizu (Professor at Kyoto University), Shunsuke Takagi (Professor, University of Tokyo) Date and time: First lecture day (or 1st lecture) October 26th (Sat) 13:30-15:00 Course fee: Members/general (no membership required) 23,100 yen including tax (6 lessons in total) *Some missed broadcasts Sponsored by: NHK Cultural Center Aoyama Classroom Apply here (online course)