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The Semigroup of n×n Matrices: Some Open Problems
文章来源:[]  作者:[撰写:张朝辉]  时间:[2016-10-12]  阅读: 次

报告题目:The Semigroup ofnnMatrices: Some Open Problems报告人:John C. Meakin, Professor,University of Nebraska-Lincoln, USA

邀请人:刘三阳教授、杨丹丹老师

报告时间:2016年10月14日下午3:00

报告地点:信远楼II206

报告人简介:Professor John C. Meakin received his PhD on Mathematics from Monash University (Australia). He has been worked in Department of Mathematics,University of Nebraska-Lincoln, since 1969.Professor John C. Meakin’s main research interests are in semigroup theory and geometric group theory. Some of his particular interests are in the theory of inverse semigroups (essentially semigroups of partial symmetries of mathematical objects) and in the study of algorithmic problems in semigroups and infinite groups. His work uses geometric and topological techniques as well as ideas from automata theory, formal language theory, and mathematical logic. He has more than 70 research papers published in prestigious mathematical journals and has undertaken many research grants from NSF.

报告摘要:

It is well known that the setM_n(Z) ofnnmatrices with integer entries forms asemigroupwith respect to matrix multiplication, i.e.A(BC) = (AB)Cfor alln nmatrices with integer entries. This remains true more generally if the entries come from any ring (e.g if the entries are real or complex numbers, or integers (modm), or come from a finite field etc). Despite the fact that matrix multiplication is one of the basic operations that permeates much of mathematics, there remain open problems that are active areas of current research in mathematics.

This talk will discuss a few such problems, some connected with unsolvedalgorithmic problemsconcerning multiplication of matrices with integer entries, and some concerningthe structure of certaingroupsbuilt from idempotent matrices (i.e. matrices satisfyingA^2=A.)

Virtually all of the talk should be accessible to anyone who knows how to multiply

matrices together. For the last part of the talk, it might be helpful to know what agroupis, although the minimal knowledge of group theory that is necessary will be explained inthe talk.

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