ncku-talk2011-11-24

NCTS(South)/ NCKU Math Colloquium

DATE 2011-11-24　16:10-17:00

PLACE 國家理論科學中心R204室(成功校區)

SPEAKER 林正洪研究員（中央研究院數學研究所）

TITLE 怪物與月光--淺談1998年Fields Medal得主Richard Borcherds的數學工作

ABSTRACT The classification of finite simple groups is one of the important achievements of the 20th century mathematics. In addition to 16 infinite series (alternating groups and simple groups of Lie type), there are exactly 26 sporadic groups. The biggest member is called the Monster, whose order is of magnitude $8\times10^{53}$. When the Monster was discovered in 1973, mathematicians already noticed that there are some mysterious relations between the characters table of the Monster and certain important functions, called modular functions, in number theory. John Conway called such a phenomenon {\it Moonshine}. He and Simon Norton also did many explicit calculations and conjectured an exact relation between these two set of objects. The conjecture was proved by Richard Borcherds in 1990 and he also awarded a Fields Medal in 1998. In this talk, we will give some stories about the Monster and Moonshine. In particular, we will give a brief account on Borcherds work and his contributions.

NCTS(South)/ NCKU Math Colloquium

DATE	2011-11-24　16:10-17:00

PLACE	國家理論科學中心R204室(成功校區)

SPEAKER	林正洪研究員（中央研究院數學研究所）

TITLE	怪物與月光--淺談1998年Fields Medal得主Richard Borcherds的數學工作

ABSTRACT	The classification of finite simple groups is one of the important achievements of the 20th century mathematics. In addition to 16 infinite series (alternating groups and simple groups of Lie type), there are exactly 26 sporadic groups. The biggest member is called the Monster, whose order is of magnitude $8\times10^{53}$. When the Monster was discovered in 1973, mathematicians already noticed that there are some mysterious relations between the characters table of the Monster and certain important functions, called modular functions, in number theory. John Conway called such a phenomenon {\it Moonshine}. He and Simon Norton also did many explicit calculations and conjectured an exact relation between these two set of objects. The conjecture was proved by Richard Borcherds in 1990 and he also awarded a Fields Medal in 1998. In this talk, we will give some stories about the Monster and Moonshine. In particular, we will give a brief account on Borcherds work and his contributions.