The 3rd Mile High Conference will take place at the University of Denver from August 11-17, 2013. The Mile High Conferences on Nonassociative Mathematics provide a unique forum for all aspects of nonassociative mathematics. This conference will bring together researchers working in various areas of nonassociative mathematics, including quasigroups and loops, Lie algebras and Jordan algebras, latin squares, 3-nets and latin square designs, and applications of octonions and nonassociative structures in physics. The interdisciplinary spirit of the conference is reflected not only in the selection of main speakers from various fields, but also in the composition of the Program and Organizing Committee. About 70 researchers are expected to participate. The main goals of the 3rd Mile High Conference are as follows: (i) To reinforce the Mile High Conferences as a leading series of conferences in nonassociative mathematics worldwide; (ii) To bring together scientists from all areas of nonassociative mathematics, hence 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 participation of researchers from underrepresented and underprivileged groups; (v) To publish conference proceedings in order to promote original research; (vi) To disseminate open problems in the various fields of nonassociative mathematics. All these goals address both the intellectual merit and the broader impact of the conference.

Nonassociative mathematics is a broad field that interacts with many traditional areas of mathematics as well as mathematical sciences. For example, quasigroup theory and the octonions have found applications in relativistic physics and particle physics. Jordan algebras have proven to be useful in both physics and statistics, and latin squares also show up routinely in the latter field. Finally, the ubiquity of Lie algebras in mathematical sciences is well known. The Mile High Conferences in Nonassociative Mathematics strive to be one of the primary opportunities for people working in diverse parts of nonassociative mathematics to come together, exchange ideas and learn about the cutting edge of the field. For further information about this year's conference, see .

Project Report

The familiar operations of addition and multiplication of numbers are associative operations, that is, one can always rearrange parentheses. In other words, (2 + 3) + 5 = 2 + (3 + 5) regardless of the order in which we do the calculation. However, there are many important operations in abstract algebra, in geometry and in physics which are not associative. These different areas of mathematics all fall under the general heading of nonassociative mathematics. The 3rd Mile High Conference on Nonassociative Mathematics took place at the University of Denver, August 11-17, 2013.This was an interdisciplinary conference featuring participants in many areas of nonassociative mathematics.The Conference was truly international in scope, with 56 participants from 18 countries. Further information canbe found at the official Conference website: The breadth of nonassociative mathematics covered by the Conference is reflected in the choice of Main Speakers,each of whom is an expert in their respective fields: Georgia Benkart, University of Wisconsin-Madison Charles Colbourn, Arizona State University Alberto Elduque, University of Zaragoza, Spain Pavel Kolesnikov, Sobolev Institute of Mathematics, Russia Peter Plaumann, University of Erlangen-Nuremberg, Germany and UABJO, Mexico Jonathan Smith Iowa State University Tony Sudbery, University of York In addition, most of the other participants gave 20 minute contributed talks. Highlighted accomplishments include thefollowing. The Conference reinforced the Mile High Conferences as a leading series of conferences in nonassociative mathematics worldwide.It brought together scientists from all areas of nonassociative mathematics, hence promoting cross-disciplinary research.The conference was accessible to graduate and postdoctoral students and also provided a forum for these youngresearchers. The organizers encouraged and supported participation of researchers from underrepresented and underprivileged groups.The Conference Proceedings were published in two issues of the mathematics journal Commentationes Mathematicae Universitatis Carolinae. Finally, the conference made researchers aware of the most important open problems in nonassociative mathematics,and facilitated their dissemination.

National Science Foundation (NSF)
Division of Mathematical Sciences (DMS)
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Tie Luo
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University of Denver
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