Teaching/Classes
授業
Course list
For NTHU grad students
○ Introduction to String Theory
For advanced undergraduate and graduate students interested in modern theoretical physics.
Basic knowledge of special relativity and quantum mechanics is assumed.
2026/fall
Brief course description: This course offers an accessible introduction to string theory, with emphasis on its physical motivation and its role in modern theoretical physics.
It introduces the basic ideas of strings, extra dimensions, compactification, D-branes, and string phenomenology at an introductory level. The emphasis is on building a broad physical picture of why string theory became important, rather than giving a fully technical treatment.
Course keywords: String theory, quantum gravity, special relativity, quantum theory, extra dimensions, compactification, D-branes, string phenomenology.
Syllabus: 1) Review of basic ideas from special relativity and quantum theory
2) Introduction: why string theory?
3) Relativistic point particles and the worldline description
4) Limitations of point-particle theory and motivation for strings
5) Open strings, closed strings, and the worldsheet picture
6) Classical strings and their basic motion
7) Quantization of strings and the basic spectrum
8) Extra dimensions and compactification
9) T-duality and basic stringy features
10) D-branes: basic ideas and gauge fields on D-branes
11) String theory and particle phenomenology: a broad view
12) Moduli stabilization, brane inflation, KKLT, and string cosmology
13) Why string theory became important in modern theoretical physics
14) Student presentations / discussion
○ Introduction to Quantum Theory of Black Holes and Holography (II)
For students who have taken Part I and wish to study more advanced topics.
2027/spring, 2026/spring, 2025/spring
Brief course description: This is the second part of a year-long course designed to introduce advanced students to the (still developing) quantum theory of gravity through an understanding of the quantum theory of black holes.
The topic we cover in this course includes entanglement (again!), but we do it at a more advanced level.
Syllabus: 1) Haar random states
2) The detailed derivation of the Page curve using the Haar random states
3) "Feynman diagrams" for Haar random states
4) Tri-partite states (GHZ-state, W-state) and (genuine) multi-partite states
5) What does entanglement entropy represent?
6) Various other entanglement measures, such as (logarithmic) negativity, multi-entropy, ...
7) How to evaluate these new measures explicitly using Feynman diagrams and related methods
8) Attractor mechanism
9) Large N limit ('t Hooft limit) of gauge theories
10) AdS/CFT correspondence (holography)
11) Black holes in AdS
12) Hawking-Page transition and confinement/deconfinement transition
13) Holographic entanglement entropy
14) Black holes and chaos
15) Student presentations / discussion
Note: Depending on the pace of the course, the spring term may occasionally revisit or reorder topics from the fall term.
○ Introduction to Quantum Theory of Black Holes and Holography (I)
For advanced students who know the Einstein equation and quantum mechanics.
2026/fall, 2025/fall, 2024/fall
Brief course description: This is the first part of a year-long course designed to introduce advanced students to the (still developing) quantum theory of gravity through an understanding of the quantum theory of black holes.
Course keywords: Black holes, quantum Mechanics, causal structure of spacetime, Hawking radiation, entanglement.
Syllabus:
1) Introduction
2) Basics of black holes I) D-dimensional spacetime and Schwarzschild black hole solutions 3) Basics of black holes II) Space-time hates singularities and black hole thermodynamics 4) Penrose diagrams and white holes
5) Raychaudhuri equation and Hawking's black hole area theorem
6) Penrose's singularity theorem
7) Hawking radiation
8) Constraints on the stress-tensor and averaged null energy condition 9) Entanglement and Einstein-Rosen-Podolsky/Bell pair
10) Pure states vs mixed states
11) Low energy effective theory and nice slice argument 12) Unruh effects
13) Page curve and black hole remnants
14) Firewall paradox and to what extent do pure and mixed states differ?
15) Why do we need quantum gravity and how should quantum gravity resolve all these paradoxes?
16) Student presentations / discussion
For freshman/sophomore/junior/学部１年・２・３年生向け
○ Thermodynamics and statistical mechanics essentials (for sophomores in the department of physics)
熱学・統計力学要論
2024/Spring&Summer
Content: Equilibrium, Works, Adiabatic change, Absolute temperature, Isothermal change, Quasi-static change, Helmholtz's free energy, Inner energy, Heat, 1st law of thermodynamics, Carnot cycle, Entropy, 2nd law of thermodynamics, More on free energy, Maxwell's relations, Canonical ensemble, Partition function, Boltzmann's entropy, Comparison between thermodynamics and statistical mechanics, etc
○ Quantum Mechanics II (exercises): advanced course (for juniors in the department of physics)
量子力学 II 演義（アドバンスコース）
2024/Spring&Summer, 2023/Spring&Summer
Content: Brief review of Quantum Mechanics I. Harmonic Oscillators, Solving Schrödinger equations in one, two and three dimensions for various potentials. Special functions. Laplacian in polar coordinates. Quantization of angular momentum and spin. Perturbations and non-perturbative phenomena. etc
○ Mechanics II (for freshmen in the department of math/biology)
力学詳論 II
2022/fall&winter, 2021/fall&winter, 2020/fall&winter, 2019/fall&winter,
Content: Brief review of Mechanics I. Coordinate changes. Inertial/fictitious forces, Coriolis force. Center of masses. Two-body and Three-body problem. Torque. Motion of rigid bodies, Moment of inertia (angular mass). Precession of a gyroscope, precession of the equinoxes, etc
○ Mechanics I (for freshmen in the school of engineering)
力学詳論 I
2022/spring&summer, 2021/spring&summer, 2020/spring&summer
Content: Brief history. Basics of math and physics such as vector analysis, calculus. Newton’s laws of motion. Equations of motion. How to solve various differential equations. Taylor expansion. Conservation laws. Thought experiment. Motion in polar coordinates. Central force. Conservation laws. Planetary motion. Properties of waves, etc
○ Mathematics (exercises) for physics: advanced course (for sophomores in the department of physics)
数理物理学演義（アドバンスコース）
2019/spring&summer, 2018/spring&summer, 2017/spring&summer, 2016/spring&summer, 2015/spring&summer,
Content: Vector and vector operations. Derivatives. Differentiation of vectors (gradient, divergence, rotation). Integration of vectors (line integral, Gauss’ theorem, Stokes’ theorem). Preparation for mathematics (trigonometric functions, complex numbers, Euler’s formula). Oscillation of multiple degrees of freedom. Fourier series (periodic functions, trigonometric series, sine, cosine series, complex Fourier series). Properties of Fourier series (Perceval’s equality, orthogonal function system, differentiation
and integration by terms, Gibbs’ phenomenon).
Fourier transform (from Fourier series to Fourier transform, Fourier integral formula, inverse
transform). Properties of Fourier transform (folding, differential and integral rules).
Delta function. Green's function.
Laplace transform, etc
○ Thermodynamics (exercises): advanced course (for sophomores in the department of physics)
熱物理学演義（アドバンスコース）
2017/fall&winter, 2016/fall&winter, 2015/fall&winter, 2014/fall&winter,
Content: Basic concepts of thermodynamics. Heat and work. Ideal gas. Adiabatic change. Carnot cycle. 1st law of thermodynamics and internal energy. Absolute thermodynamic temperature. Entropy. 2nd law of thermodynamics, Free energy. Total derivatives, partial derivatives, and Maxwell’s relations. Chemical potential. Phase and phase equilibrium. Landau's theory of phase transitions, etc
○ Mechanics I (exercises): advanced course (for freshmen in the department of physics)
力学I演義（アドバンスコース）
2014/fall&winter,
Content: Basics of mathematics. Calculus. Vectors and its differential. Equations of motion. How to solve differential equations. More on mathematics (Complex number, Euler’s formula, Taylor expansion etc). Thought experiments. Polar coordinates. Centrifugal force. Conservation laws. Energy, momentum. Planetary motion, etc
○ Special Seminar in Physics (for freshmen, sophomores, juniors)
物理学ゼミナール
2020/fall&winter, 2015/spring&summer, 2014/spring&summer,
Content: Students discuss with faculty and find their own interesting topics and conduct their own research under the guidance of faculty.
* In 2015, 2014, Linear algebra and basics of quantum mechanics
* In 2020, Advanced content of quantum mechanics, such as quantum entanglement, quantum information etc
○ Experiments in physics (for freshmen in the school of engineering)
物理学実験
2018/fall&winter,
Content: Basics of experiments, oscilloscope, Borda's pendulum to measure the gravitational acceleration, etc
For senior/beginning master course student/学部４年・M1向け
○ Introduction to string theory for undergrad (for senior in particle theory group, seminar style)
四年生ゼミ:弦理論入門
2022/spring&summer,
Content: Brief history of string theory, relativity, relativistic point particle and its quantization, Nambu-Goto action, symmetry, relativistic strings, Polyakov action, spectrum, etc
○ Introduction to general relativity for undergrad (for senior in particle theory group, seminar style)
四年生ゼミ:一般相対性理論入門
2021/spring&summer, 2018/spring&summer,
Content: Special relativity, Lorentz transformation, general principle of relativity, Principle of covariance, Equivalence principle, Manifolds, Tensor, Curvature, Einstein's equation, Black holes, etc
○ Quantum field theory for beginning grad student (for 1st year master course student in particle theory group, seminar style)
M1ゼミ:場の量子論
2017/spring&summer, 2016/spring&summer, 2015/spring&summer, 2014/spring&summer ,
Content: Basics of quantum mechanics, Basics of quantum fields, Quantization of fields, Path-integral, Perturbation, Loop corrections, Renormalization, etc
○ Advanced topics in quantum mechanics for undergrad (for senior in particle theory group, seminar style)
四年生ゼミ:アドバンス量子力学
2020/spring&summer,
Content: Basics of quantum mechanics, Path-integral, Soliton, Instanton, Non-perturbative effects, etc