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My research is on abstract math, specifically commutative algebra. I am particularly interested in local cohomology modules; these objects are defined in a very abstract way, and yet can be understood with friendly, concrete calculations.

In some number systems, there are ways to factor numbers uniquely; for example, over the integers, every number can be written as a product of primes, and this factorization is unique (up to reordering). We can ask if there's an analog of prime numbers over the real numbers, or for polynomials with variable x, or for matrices, etc.  Local cohomology modules were initially invented to answer questions about unique factorization domains, but they have many other uses and are fascinating in their own right.

Courses Taught at Â鶹´«Ã½

Linear Algebra, Abstract Algebra