Mathematical Sciences: Ring Homorphisms and Resolutions

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9623405 Avramov This award supports the research of Professor L. Avramov to work in commutative ring theory with special emphasis on problems arising from the interplay between structure homomorphisms and free resolutions of modules. He intends to study complete intersections as well as regularity properties of these homomorphisms. He will also study properties of Hochschild and Andre-Quillen homology. This is research in the subfield of algebra called 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. Moreover much of commutative ring theory is designed to generalize structures found in the solutions of equations. As such it has direct connections to such diverse 0areas as robotics and coding theory.