报告题目: The Nature of Equations and the Equations of Nature
报告人: James Yorke, University of Maryland，教授，博导
报告时间: 21:20-22:10, 27th August 2020.
报告地点: 889 9240 5158 (Zoom ID)
Abstract:
Our understanding of the structure of complex networks is inadequate in many areas. We need tools to explain why some networks are robust to perturbations, but others are vulnerable. Differential equations and graph theory has been used as ubiquitous tools by scientists in the studying a vast group of networks. Even though there is an extensive literature available on studying linear system of equations using graphs and matrices, the interactions between netwprl members in most cases are nonlinear.
We began this investigation to understand ecological networks. There was much more written about stability of ecosystems than about the question of whether the ecosystem had a robust equilibrium.
Some ecological networks can have a steady state that depends on the system improbably being perfectly balanced, where arbitrarily small changes result in the absence of a steady state.
We find that some networks can have robust steady states and others cannot and we can tell what the difference independent of the actual details of the equations. We do not address the question of stability of robust solutions, but our theory opens the door to such investigations.
To understand this problem we had to attack a much broader question: How do we know if a system of N equations in N unknowns, F(X)=C has a robust solution. That is, if some X and C satisfy the equation and arbitrarily small changes in C still have solutions. It is surprising to us how general our solution is that we came up with.
简介:
Yorke Biographical Information
A.B., Columbia University 1963;
Yorke has been at the University of Maryland since 1963.
Ph.D. in Mathematics, University of Maryland College Park 1966
Distinguished Univ. Research Professor of Mathematics and Physics
James Yorke is perhaps best known for coining the mathematical term chaos in his 1975 paper with Tien-Yien Li “Period Three Implies Chaos”. He came to the University of Maryland as a math graduate student in 1963 hoping to explore interdisciplinary mathematics. Those hopes were fully realized after he received his Ph.D. and joined the faculty of the University of Maryland. His current research projects range from chaos theory and DNA sequencing research. He feels that a degree in mathematics is a license to investigate the universe.
In 2003 he was awarded the Japan Prize jointly with Benoit Mandelbrot for their work in chaos and fractals in a ceremony presided over by the Emperor of Japan.
Recent honors:
Doctores Honoris Causa from Le Havre University 2014
Doctores Honoris Causa from Rey Juan Carlos Universidad 2014
Recipient of the University of Maryland President’s Medal October 2013
Fellow of the AAAS since 1998; of the American Physical Society, 2003; American Mathematics Association since 2013; of Society for Industrial and Applied Mathematics (SIAM), 2013.
SIAM’s Jurgen Moser lecture/award 2011 presented in Snowbird Utah
