Video

# <학부생을 위한 ɛ 강연> Mathematics and music: Pythagoras, Bach, Fibonacci and AI

Lecturer 임현정 피아니스트 Oct 12, 2021

In this talk, I will introduce the audience to the original beauty that leads to exploring the mathematical elements in music. I will cover the following topics on the connection between music and mathematics.
- Harmonics & equations
- Pythagoras tuning & Equal temperament tuning
- Logic, structure, symmetry, geometry, pattern in Bach’s music and in the musical form of the fugue, the most mathematical of musical structures.
- Fractals and their musical translations
- AI and music generation
- AI transcription of piano music
- (String quartet performance of HJ Lim’s fugue that uses geometric and other mathematical elements; Vn1. 피예나 Vn2. 류경주 Va. 임혜진 Vc. 김상민)
- Fibonacci sequence
- (Performance by HJ Lim of her piano piece 'Infinity' inspired by the Fibonacci sequence)

 Subject+ContentSubjectContentCommentUser NameNick NameUser IDTag
1. ### <정년퇴임 기념강연> 리만 가설에 관련된 옌센 다항식의 영점

Sufficient conditions for the Jensen polynomials of the derivatives of a real entire function to be hyperbolic are obtained. The conditions are given in terms of the growth rate and zero distribution of the function. As a consequence some r...
CategoryMath Colloquia Dept.서울대학교 Lecturer김영원
2. ### 2021-2 Rookies Pitch: Representation Theory(김영훈)

CategoryBK21 FOUR Rookies Pitch Dept.QSMS Lecturer김영훈
3. ### 2021-2 Rookies Pitch: Representation Theory(장일승)

CategoryBK21 FOUR Rookies Pitch Dept.서울대학교 Lecturer장일승
4. ### Infinite order rationally slice knots

A knot is a smooth embedding of an oriented circle into the three-sphere, and two knots are concordant if they cobound a smoothly embedded annulus in the three-sphere times the interval. Concordance gives an equivalence relation, and the se...
CategoryMath Colloquia Dept.카이스트 수리과학과 Lecturer박정환
5. ### 2021-2 Rookies Pitch: Regularity for PDEs (수미야)

CategoryBK21 FOUR Rookies Pitch Dept.서울대학교 Lecturer수미야
6. ### 2021-2 Rookies Pitch: Harmonic Analysis (이진봉)

CategoryBK21 FOUR Rookies Pitch Dept.서울대학교 Lecturer이진봉
7. ### Random matrices and operator algebras

Free probability is a young mathematical theory that started in the theory of operator algebras. One of the main features of free probability theory is its connection with random matrices. Indeed, free probability provides operator algebrai...
CategoryMath Colloquia Dept.서울대학교 수학교육과 Lecturer윤상균
8. ### Symplectic topology and mirror symmetry of partial flag manifolds

Soon after Gromov’s applications of pseudo-holomorphic curves to symplectic topology, Floer invented an infinite-dimensional Morse theory by analyzing moduli spaces of pseudo-holomorphic curves to make substantial progress on Arnold&r...
CategoryMath Colloquia Dept.부산대학교 수학과 Lecturer김유식
9. ### 2021-2 Rookies Pitch: Number Theory (김지구)

CategoryBK21 FOUR Rookies Pitch Dept.이화여자대학교 Lecturer김지구
10. ### 2021-2 Rookies Pitch: Arithmetic Statistics (이정인)

CategoryBK21 FOUR Rookies Pitch Dept.KIAS Lecturer이정인
11. ### 돈은 어떻게 우리 삶에 돈며들었는가? (불확실성 시대에 부는 선형적으로 증가하는가?)

1. 금본위제, 달러, 비트코인 등 돈의 흐름으로 보는 세계사 2. 사람은 어떻게 생각하고 행동하는가 ? (행동경제학, 비선형성) 3. 돈에 대한 생각, 행동, 습관을 바꾸어보자. (부자들은 무엇이 다른가 ? 지금부터 준비해보자.) 4. 주식, 부동산 등 자산관리 [...
CategoryMath Colloquia Dept.농협은행 Lecturer홍순옥
12. ### <학부생을 위한 ɛ 강연> Mathematics and music: Pythagoras, Bach, Fibonacci and AI

In this talk, I will introduce the audience to the original beauty that leads to exploring the mathematical elements in music. I will cover the following topics on the connection between music and mathematics. - Harmonics & equations - ...
CategoryMath Colloquia Dept.피아니스트 Lecturer임현정
13. ### Topological surgery through singularity in mean curvature flow

The mean curvature flow is an evolution of hypersurfaces satisfying a geometric heat equation. The flow naturally develops singularities and changes the topology of the hypersurfaces at singularities, Therefore, one can study topological pr...
CategoryMath Colloquia Dept.고등과학원 Lecturer최경수
14. ### Heavy-tailed large deviations and deep learning's generalization mystery

Abstract: While the typical behaviors of stochastic systems are often deceptively oblivious to the tail distributions of the underlying uncertainties, the ways rare events arise are vastly different depending on whether the underlying tail ...
CategoryMath Colloquia Dept.Northwestern University Lecturer이창한
15. ### Diophantine equations and moduli spaces with nonlinear symmetry

A fundamental result in number theory is that, under certain linear actions of arithmetic groups on homogeneous varieties, the integral points of the varieties decompose into finitely many orbits. For a classical example, the set of integra...
CategoryMath Colloquia Dept.서울대학교 Lecturer황준호
16. ### <정년퇴임 기념강연> Hardy, Beurling, and invariant subspaces

The invariant subspace problem is one of the longstanding open problem in the field of functional analysis and operator theory. It is due to J. von Neumann (in 1932) and is stated as: Does every operator have a nontrivial invariant subspace...
CategoryMath Colloquia Dept.서울대학교 Lecturer이우영
17. ### <정년퇴임 기념강연> The Elements of Euclid

The thirteen books "Elements" were written or collected by Euclid of Alexandria about 300 BCE. Many think that "Elements" is the most important example of deductive mathematics. In fact, the Common Notions and the Postulates of Elements are...
CategoryMath Colloquia Dept.서울대/광주과학기술원 Lecturer김홍종
18. ### On circle diffeomorphism groups

For each natural number k, the C^k diffeomorphisms of the circle form a group with function compositions. This definition even extends to real numbers k no less than one by Hölder continuity. We survey algebraic properties of this grou...
CategoryMath Colloquia Dept.고등과학원 Lecturer김상현