以表彰他在代數、幾何和數學物理,特別是形變量子化,Motivic積分和鏡像對稱的開創性工作。
近年來物理學的一些觀念激發了代數和幾何的深刻進展。馬克西姆・康采維奇 (Maxim Kontsevich) 是這些進展的領路人。
自從海森堡 (Heisenberg) 引入量子力學以來,量子化的數學過程,即從古典力學到量子力學的過程已經成為一個中心研究課題。其中一個版本是關於 泊松 (Poisson) 流形的形變量子化。除了某些特殊情形,這是一個非常困難的問題。康采維奇使用了量子場論的思想完美地解決了這個問題。
Traditionally the interaction between mathematics and theoretical physics has been concerned with topics ranging from dynamical systems and partial differential equations to differential geometry to probability theory. For the last two decades, modern algebra and algebraic geometry (which is the study of the solutions of systems of polynomial equations in several variables via algebraic methods) have taken a central position in this interaction. Physical insights and intuition, especially from string theory, have led to a number of unexpected and striking predictions in both classical and modern algebraic geometry. Thanks to the efforts of many mathematicians new techniques and theories have been developed and some of these conjectures have been proven.
Maxim Kontsevich has led the way in a number of these developments. Among his many achievements is his early work on Witten’s conjecture concerning the topology and geometry of the moduli (that is parameter) spaces of all algebraic curves of a given genus, his solution of the problem of deformation quantization, his work in mirror symmetry and in a different direction the theory of motivic integration.
馬克西姆・康采維奇 (Maxim Kontsevich) 1964年於俄羅斯希姆基出生,自1999年起成為法國公民。現為法國高等科學研究所教授暨安盛研究基金數學主席。1992年他獲德國波恩大學博士學位。自1990至1993年,他曾於不同機構擔任客席,包括德國馬克斯普朗克研究所、美國哈佛大學及普林斯頓高等研究院。1993至1995年為美國加州大學柏克萊分校教授。他曾獲許多獎項,其中包括1997年龐加萊獎 (Henri Poincaré Prize)、1998年菲爾茲獎 (Fields Medal) 及2008年克拉福德獎 (Crafoord Prize)。現為歐洲科學院及法國研究院成員。