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	My research area is in commutative algebra. The work that I did for my thesis is related to Serre's vanishing conjecture. It deals with the intersection properties of subspaces. For example, if your "space" is a table-top, or 2-dimensional space, and if you have two lines A and B (each of dimension 1), you can always wiggle the lines a bit so they intersect. Thus if the dimension of A + the dimension of B = dimension of your space, there should be an intersection. Similarly, if your space is 3-dimensional space and you have two lines A and B, then you can easily wiggle the lines so they don't intersect. In other words, if the dimension of A + the dimension of B < the dimension of your space, then there should be no intersection, or the intersection should be zero. This latter idea is called vanishing. The idea generalizes to other spaces and subspaces, and what we find is that we have situations where the dimension of A + the dimension of B < the dimension of the space, but the intersection is not zero. I came up with certain conditions needed on a space and its subspaces so there are counterexamples to vanishing or where vanishing will hold. I am also interested in questions relating to topologically and algebraically Cohen-Macaulay posets, problems dealing with Falting's connectedness theorem, and other problems in homological algebra. CV Access notes on cryptography, modular arithmetic, scaling laws, etc. Clock Arithmetic and Euclid's Algorithm Handout for Euclid's Algorithm Modular Powers Scaling Classical Fractals Fractals in Computers Least Squares handout and Least Squares Maple worksheet.
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