2nd Mile High Conference on Nonassociative Mathematics

美国国家科学基金会提案#09013282nd Mile High Conference on Nonassociative Mathematics的摘要--抽象数学理论的发展通常与研究人员在其中进行计算的能力有关。如果通常的算术定律在理论中不成立，计算往往很困难，通常需要电子计算机的帮助。在非结合数学中，交换律和结合律都不成立。非结合数学是一个广泛的领域，与许多传统的数学学科相互作用。它包括拟群（非结合群）和李代数的代数理论，拉丁方的组合理论（数独是一个非常特殊的情况），网和网的几何理论（最初是从诺模学产生的），以及非结合代数在粒子物理学中的应用。最近，人们对非结合数学的兴趣又重新抬头。这部分是由于改进的计算工具，部分是由于工作了许多问题，在联想数学，部分是由于自组织的努力，研究人员在该领域的工作。拟议的第二英里高会议非联想数学将是一个国际会议上的所有方面的非联想数学，预计观众100名研究人员。会议将于2009年6月21日至27日在科罗拉多丹佛市丹佛大学举行。第二届英里高会议的主要目标如下：（一）建立一个世界范围内的非联想数学的领先会议;（二）汇集来自非联想数学所有领域的科学家，从而促进跨学科研究;（三）使研究生和博士后学生能够参加会议，同时也为这些年轻的研究人员提供一个论坛;（iv）鼓励和支持来自代表性不足和弱势群体的研究人员的参与;（v）收集该领域最重要的未决问题清单，并促进其传播和维护。

Abstract for NSF proposal #09013282nd Mile High Conference on Nonassociative Mathematics---------The development of an abstract mathematical theory is often tied to researchers' ability to perform calculations within it. If the usual laws of arithmetics do not hold in a theory, calculations tend to be difficult and often require the aid of electronic computers. In nonassociative mathematics, neither the commutative law nor the associative law are assumed to hold. Nonassociative mathematics is a broad field that interacts with many traditional mathematical disciplines. It includes the algebraic theories of quasigroups (nonassociative groups) and Lie algebras, the combinatorial theory of Latin squares (with Sudoku being a very special case), the geometric theories of nets and webs (that originally arose from nomography), and applications of nonassociative algebra to particle physics. Lately, there has been a resurgence of interest in nonassociative mathematics. This is due partly to improved computational tools, partly to the working out of many problems in associative mathematics, and partly due to the self-organizing efforts by researchers working in the field.The proposed 2nd Mile High Conference on Nonassociative Mathematics will be an international conference on all aspects of nonassociative mathematics, with an expected audience of 100 researchers. The meeting will take place at the University of Denver, Denver, Colorado, June 21-27, 2009. The main goals of the 2nd Mile High Conference are as follows: (i) to establish a leading conference on nonassociative mathematics world-wide; (ii) to bring together scientists from all areas of nonassociative mathematics, thereby promoting cross-disciplinary research; (iii) to make the conference accessible to graduate and post-doctoral students while also providing a forum for these young researchers; (iv) to encourage and support the participation of researchers from underrepresented and underprivileged groups; (v) to assemble a list of the most important open problems in the field and to facilitate its dissemination and maintenance.