Mathematical Sciences: Quadratic Regular Algebras

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This award supports the research of Professor M. Vancliff to work in non-commutative ring theory with special emphasis on problems arising from the theory of graded regular algebras. In particular, Professor Vancliff will try to classify the quadratic regular algebras of global dimension n with Hilbert series the same as that of the polynomial ring on n variables that map onto a certain twisted homogeneous coordinate ring of a quadric lying in n-1 dimensional projective space. She hopes that this will lead to methods of constructing examples of Artin-Schelter algebras with new behavior. This is research in the subfield of algebra called non-commutative ring theory. Algebra can be thought of as the study of symmetry in the abstract. As such, algebra has direct applications to areas of physics and chemistry. In fact, much of non-commutative ring theory generalizes structures found in quantum mechanics and this proposal continues to explore areas that connect directly with modern quantum field theory.