英國劍橋大學(xué)考切爾.比爾卡爾教授講代數(shù)幾何

形狀和方程

Shapes and Equations

演講人/Speaker

考切爾.比爾卡爾教授Professor Caucher Birkar

英國劍橋大學(xué)

University of Cambridge

Time/時間

2019年8月15日, 10:00-11:00, 星期四August 15th, 2019, 10:00-11:00, Thursday

Venue/地點

清華大學(xué)廖凱原樓107報告廳Tsinghua Law Library-Leo KoGuan Building Lecture Hall 107

關(guān)于演講人

About Speaker

考切爾.比爾卡爾現(xiàn)為英國劍橋大學(xué)教授。2018年8月獲得了數(shù)學(xué)界最高獎菲爾茲獎。他的主要研究領(lǐng)域是代數(shù)幾何(高維雙有理幾何，極小模型理論)，因在對不同類型的多項式方程進(jìn)行的分類所作出的杰出貢獻(xiàn)而獲得2018年的菲爾茨獎。他證明了這類方程的無限多樣性可以被分割成有限數(shù)量的類別，這在代數(shù)幾何領(lǐng)域中是重大的突破。他對Fano簇的有限性的證明是他最有影響力的數(shù)學(xué)成果之一。

Caucher Birkar is a professor at the University of Cambridge in the United Kingdom. His research area is algebraic geometry. In the International Congress of Mathematicians in 2018, Prof. Caucher Birkar was awarded the Fields medal, the highest honor for mathematicians, for his works on boundedness of Fano varieties and the minimal model program.

演講摘要

Abstract

代數(shù)幾何是核心數(shù)學(xué)的一個重要分枝，它和數(shù)學(xué)的其它分枝以及物理都有重要的聯(lián)系。該報告將深入淺出地介紹代數(shù)幾何中的一些基本概念。代數(shù)幾何將代數(shù)和幾何融合在一起，它起始于求解多項式方程組，這類問題引導(dǎo)人們?nèi)タ紤]這些方程定義的空間的形狀，空間的幾何反過來為研究抽象方程的提供了形象的直覺。

This talk is a gentle introduction to some basic notions of algebraic geometry, a central field of mathematics with connections to many other parts of mathematics and also physics, etc. As the name suggests, algebraic geometry is a mixture of algebra and geometry. It all starts with solving polynomial equations but soon leads to considering the shapes of these equations which provides a way for our intuition to guide us through the world of abstract equations.