$50,000 Scholarship Recipient
Project Title: “Infinitesimal Cherednik Algebras of gl_n.”______ _______ ________ ____ _______
David did his project on infinitesimal Cherednik algebras, which are deformations of a certain symmetry algebra. Abstract algebra is a field connected to many other fields of math and provides powerful tools to solve diverse problems. His main goal was to study representations of infinitesimal Cherednik algebras, which are all the different ways these algebras can act on vector spaces. Representation theory thus connects the study of infinitesimal Cherednik algebras to linear algebra. He found that the deformation expanded the symmetry algebra’s palette of possible representations. Because the undeformed symmetry algebra appears frequently in math and in nature, its representation theory is already well understood and has deep ramifications on many subjects, such as on the structure of the periodic table. The study of infinitesimal Cherednik algebras could not only shed light on how a deformation could change a well-understood theory, but also prove useful in describing the symmetries of mysterious phenomena such as super-symmetry.
The results of David’s research clarified a new facet of representation theory. Representation theory is incredibly rich, and there are representation theories for various algebras, such as Lie algebras and rational Cherednik algebras. Infinitesimal Cherednik algebras help bridge together these different algebras as a continuous analogue of rational Cherednik algebras that happen to be deformations of a Lie algebra. Because representation theory is one of the mathematical pillars of particle physics, a better understanding of representation theory could lead to a better understanding of how the universe works. And although it is difficult to imagine now how elementary particles could lead to an improved quality of life, it was just as impossible to imagine back in the 1920s how quantum mechanics would lead to the transistors found in modern electronics.
David won fourth place in the Intel Science Talent Search as is a National Merit Finalist and participated in MIT PRIMES (MIT Program for Research in Mathematics, Engineering and Science for high school students). He will attend Harvard in the fall and plans to major in math and physics.
Click the links below to view hi-res photos of David:
Click here to view the full listing of the 2012 Davidson Fellows.
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