2024-10-09 ラトガース大学
◆彼の成果の1つは「有限単純群」の研究に関わり、これにより対称性の理論がさらに進展しました。
◆もう1つの成果は、ランダムな行動が集団全体に及ぼす影響を分析する確率論の問題の解決です。
◆これらの問題は、集団の構造やランダムな変動の中でどのように秩序が現れるかを理解するのに役立つとされ、各種の応用が考えられています。これにより、自然現象や複雑なシステムのシミュレーションが可能となるほか、工学や社会科学のモデルにおいても貢献が見込まれます。
＜関連情報＞
- https://www.rutgers.edu/news/double-breakthrough-mathematician-solves-two-long-standing-problems
- https://annals.math.princeton.edu/2024/200-2/p04
- https://annals.math.princeton.edu/2024/200-1/p01
- https://link.springer.com/article/10.1007/s00222-023-01221-5
ブラウアーの高さゼロ予想 Brauer’s Height Zero Conjecture
Gunter Malle, Gabriel Navarro, A. A. Schaeffer Fry, Pham Huu Tiep
Annals of Mathematics Published:30 August 2024
DOI:https://doi.org/10.4007/annals.2024.200.2.4
Abstract
We complete the proof of Brauer’s Height Zero Conjecture from 1955 by establishing the open implication for all odd primes.
有限古典群の均一指標境界 Uniform character bounds for finite classical groups
Michael Larsen, Pham Huu Tiep
Annals of Mathematics Published:3 July 2024
DOI:https://doi.org/10.4007/annals.2024.200.1.1
Abstract
For every finite quasisimple group of Lie type G, every irreducible character χ of G, and every element gg of G, we give an exponential upper bound for the character ratio |χ(g)|/χ(1 with exponent linear in log|G||gG|, or, equivalently, in the ratio of the support of g to the rank of G. We give several applications, including a proof of Thompson’s conjecture for all sufficiently large simple symplectic groups, orthogonal groups in characteristic 2, and some other infinite families of orthogonal and unitary groups.
有限古典群の指標レベルと指標境界 Character levels and character bounds for finite classical groups
Robert M. Guralnick,Michael Larsen & Pham Huu Tiep
Inventiones mathematicae Published:29 September 2023
DOI:https://doi.org/10.1007/s00222-023-01221-5
Abstract
The main results of the paper develop a level theory and establish strong character bounds for finite classical groups, in the case that the centralizer of the element has small order compared to|G| in a logarithmic sense.
