清華大學高等研究院

科學與創新系列報告

主持人：張首晟教授

時間： 2013年5月23日（周四）下午3:00-5:00 地點：清華大學高等研究院科學館104報告廳 1. Kuramoto model of syncing 報告人：高蘋摘要：每當夏日來臨，我們便會經常看到成群的螢火蟲在天空中一起閃爍着美麗的熒光，但是我們是否想過這麼多螢火蟲為什麼會這麼整齊地閃爍？幾個同伴一起走在大街上，如果你足夠細心，你可能會注意到相互之間的步伐可能會漸漸整齊，你是否想過有什麼簡單模型來解釋這一現象？心髒的跳動時，成千上萬的瓣膜細胞總是按照同樣的周期的和相位作周期運動來完成一次次的瓣膜開關動作，你是否想過為什麼它們會有如此同步的細胞震蕩？一個精彩的節目落幕，掌聲雷動，我們是否發現掌聲常常很快從淩亂趨向于一緻？生活中我們常常會遇到這樣那樣的巧合，這些巧合很多呈現出“同步”這樣的特征。為了研究這些現象，一門名為共時學的學科正在興起。在本次報告中，我将介紹共時理論中最經典的模型Kuramoto model。通過這一簡單的非線性模型，我們可以初步解釋為什麼會有這樣常見而又神奇的共時現象。 2. Galois Theory 報告人：李星河摘要： The solution of linear and quadratic equations are well-known by all ancient civilizations. However the methods for solving cubic and quartic equations were not discovered until the Renaissance. French mathematician Vieta and Lagrange made pioneering contributions to theories of algebraic equations. Nearly all prestigious mathematicians at that time had ever tried to solve quintic equations but all of them just failed. In the early 1800s', Norwegian mathematician N.Abel and Italian mathematician Ruffini proved that a general quintic equations can not be solved by radicals. However, they did not give a real quintic equations that cannot be solved by radicals. During the 1820s', a young French mathematician Evariste Galois successfully and completely solved similar problems and built up the foundations of modern algebra.
In this talk, I'll give a brief introduction on how to solve cubic and quartic equations and the relation of algebraic equations and permutation groups. Next, I'll give an introduction to Galois theory and prove the insolvability of quintic equations using Galois theory.