Noah Maxwell Arbesfeld
MASSACHUSETTS
Noah Maxwell Arbesfeld, 17, of Lexington, entered a mathematics project in
the Intel Science Talent Search that concerned the structure of the free
associative algebra on finitely many generators. The free algebra has no special
properties; as such it is important because all other algebras can be built from
it. Using both theoretical and computational tools (representation theory and
MAGMA, respectively) Noah studied the dimension of certain subspaces inside
quotients of the lower central series. In the case of two generators he improved
a known bound from quadratic to linear, and he also gave a precise description
of the first few quotients. Noah attends Lexington High School where he
participates in the multicultural club and the Chinese Exchange. The recipient
of numerous awards in math, debate and science, he enjoys playing the saxophone
in the school band. In his spare time Noah also enjoys amateur astronomy,
geography, and improvisational theater. He plans to continue researching
mathematics at MIT or Harvard, and hopes that his work will help communicate
complex ideas to a non-scientific audience. He is the son of Stuart and Lisa
Arbesfeld.
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