NSF East Asia and Pacific Summer Institute (EAPSI) for FY 2013 in China

Mangum Chad R, Raleigh NC

Investigators

Abstract

This action funds Chad Mangum of North Carolina State University to conduct a research project in the Mathematical and Physical Sciences area during the summer of 2013 at Xiamen University in Xiamen, Fujian, China. The project title is "An Alternative Description of Infinite Dimensional Algebras: Representations of Twisted Toroidal Lie Algebras." The host scientist is Dr. Shaobin Tan. The representation theory of Lie algebras has been a significant area of mathematical research for several decades, particularly that of affine Lie algebras (an infinite dimensional generalization of finite dimensional semisimple Lie algebras). A generalization of affine algebras known as toroidal Lie algebras will be the topic of this research endeavor, in particular the twisted 2-toroidal (a natural generalization of the so-called twisted affine algebras, as opposed to nontwisted). The realization of affine algebras as a one-dimensional universal central extension of a loop algebra is expanded to include Laurent polynomials in 2 variables (hence the term 2-toroidal), with the universal central extension now itself being infinite dimensional. A Drinfeld realization of such algebras (which defines the algebra via generators and relations) will be sought, as well as progress toward both fermionic and bosonic representations of such algebras. Broader impacts of an EAPSI fellowship include providing the Fellow a first-hand research experience outside the U.S.; an introduction to the science, science policy, and scientific infrastructure of the respective location; and an orientation to the society, culture and language. These activities meet the NSF goal to educate for international collaborations early in the career of its scientists, engineers, and educators, thus ensuring a globally aware U.S. scientific workforce. Furthermore, since the host researcher is an expert in toroidal Lie algebras, the Fellow has the opportunity to begin cultivating an international network of pioneers in the field. The Fellow plans to present the results of this work at a seminar upon returning to the U.S., aiding the dissemination of results into the relevant mathematical and scientific communities. The results themselves are likely to have applications to other areas of mathematics and physics (such as particle physics), which is itself a broader impact. Sharing not only results but also other aspects of the Fellow's EAPSI experience with others will advance the program's goals further by making more scientists aware of them, helping to establish even more broadly the goals of long run international collaborations and globally aware scientists.