2020.11.18 21:54

# [Seminar 2020.11.25] On the ordering of the Markov numbers (AM 10:00~12:00)

조회 수 4885 추천 수 0 댓글 0
?

#### 단축키

Prev이전 문서

Next다음 문서

크게 작게 위로 아래로 댓글로 가기 인쇄
?

#### 단축키

Prev이전 문서

Next다음 문서

크게 작게 위로 아래로 댓글로 가기 인쇄
일정시작 2020-11-25 #FF5733

Date: November 25, 2020

Time: AM10~12
Speaker: Kyungyong Lee (University of Nebraska-Linocln)

Title : On the ordering of the Markov numbers

Abstract:

The Markov numbers are the positive integers that appear in the solutions of the equation x2+y2+z2=3xyz. These numbers are a classical subject in number theory and have important ramifications in hyperbolic geometry, algebraic geometry and combinatorics. It is known that the Markov numbers can be labeled by the lattice points (q,p) in the first quadrant and below the diagonal whose coordinates are coprime. In this paper, we consider the following question. Given two lattice points, can we say which of the associated Markov numbers is larger? A complete answer to this question would solve the uniqueness conjecture formulated by Frobenius in 1913. Using tools from cluster algebras, we give a partial answer in terms of the slope of the line segment that connects the two lattice points. We prove that the Markov number with the greater x-coordinate is larger than the other if the slope is at least −87 and that it is smaller than the other if the slope is at most −54. As a special case, namely when the slope is equal to 0 or 1, we obtain a proof of two conjectures from Aigner's book "Markov's theorem and 100 years of the uniqueness conjecture". This is joint work with Li Li, Michelle Rabideau, and Ralf Schiffler.

 제목+내용제목내용댓글이름닉네임아이디태그
1. No Image notice by qsms 2021/09/09 by qsms
Views 13395

QSMS Mailing List Registration

2. No Image 18Nov
by qsms
2020/11/18 by qsms
Views 0

weekplan_672_2020

3. No Image 18Nov
by qsms
2020/11/18 by qsms
Views 9610

[QSMS Monthly Seminar] Canonical basis

4. No Image 18Nov
by qsms
2020/11/18 by qsms
Views 9161

[QSMS Monthly Seminar] Introduction to cluster algebras (and monoidal categorification)

5. No Image 18Nov
by qsms
2020/11/18 by qsms
Views 23309

[QSMS Monthly Seminar] Peterson conjecture via Lagrangian correspondences and wonderful compactifications

6. No Image 18Nov
by qsms
2020/11/18 by qsms
Views 4885

[Seminar 2020.11.25] On the ordering of the Markov numbers (AM 10:00~12:00)

7. No Image 18Nov
by qsms
2020/11/18 by qsms
Views 6687

[초청강연 2020.11.20] Zeta함수와 L함수에 대한 역사적 고찰

8. No Image 23Nov
by qsms
2020/11/23 by qsms
Views 34973

[초청강연 2020.11.27] Zeta함수와 L함수에 대한 역사적 고찰II

9. No Image 02Dec
by qsms
2020/12/02 by qsms
Views 4126

[QSMS Monthly Seminar]Introduction to modular curves and modular forms

10. No Image 02Dec
by qsms
2020/12/02 by qsms
Views 5062

[Seminar 2020.12.03~05]Visual Studio Code를 사용하여 편리한 LaTeX 환경 구축하기

11. No Image 07Dec
by qsms
2020/12/07 by qsms
Views 4230

[Seminar 2020.12.23]Machine-learning for mathematics: case study of number fields and elliptic curves

12. No Image 08Dec
by qsms
2020/12/08 by qsms
Views 3849

[Seminar 2020.12.10] Zeta함수와 L함수에 대한 역사적 고찰III

13. No Image 08Dec
by qsms
2020/12/08 by qsms
Views 3667

[Seminar 2020.12.17] Zeta함수와 L함수에 대한 역사적 고찰IV

14. No Image 21Dec
by qsms
2020/12/21 by qsms
Views 3942

[Seminar 2020.12.23] Zeta함수와 L함수에 대한 역사적 고찰V

15. No Image 28Dec
by qsms
2020/12/28 by qsms
Views 3917

[Seminar 2020.12.29] Zeta함수와 L함수에 대한 역사적 고찰VI

16. No Image 04Jan
by qsms
2021/01/04 by qsms
Views 3873

[Seminar 2021.01.07] Zeta함수와 L함수에 대한 역사적 고찰VII

17. No Image 11Jan
by qsms
2021/01/11 by qsms
Views 4212

[QSMS Monthly Seminiar] Symplectic homology and the McKay correspondence

18. No Image 18Jan
by qsms
2021/01/18 by qsms
Views 4122

[Seminar 2021.01.21] Zeta함수와 L함수에 대한 역사적 고찰VIII

19. No Image 22Feb
by qsms
2021/02/22 by qsms
Views 4225

[Seminar 2021.02.25] Zeta함수와 L함수에 대한 역사적 고찰IX

20. No Image 02Mar
by qsms
2021/03/02 by qsms
Views 12029

[Seminar 2021.03.03] Zeta함수와 L함수에 대한 역사적 고찰X

21. No Image 04Mar
by qsms
2021/03/04 by qsms
Views 4415

[Seminar 2021.03.19] Introduction to zeta functions of groups and rings

Board Pagination Prev 1 2 3 4 5 6 7 8 Next
/ 8