This is an old page; it only loosely represents my current activities

I am a graduate student in Mathematics at the University of Illinois in Urbana-Champaign. Currently, I am studying group extensions using (co)homological methods. My advisor is Derek Robinson. My research with him started as a REGS project in the summer of 2006.

More generally, I am interested in algebra, especially in the structure of extensions. Examples of these occur in groups, rings, fields, topological spaces (fibrations), algebras, representations,... It's especially interesting to me when one can understand an extension as an interaction of the smaller parts. This is, in a sense, precisely what an extension is, so the key word in my previous sentence is "understand."

Often the "interaction" of the smaller parts involves a group action (galois group, structure group of a fibration). This is especially interesting to me, as it reveals certain symmetries of the object. It's also interesting to see how extensions in two categories play together. Beautiful examples of this are galois theory and the theory of covering spaces.

Another interseting phenomenon is when an extension in a given cagegory can be understood by applying an exact functor and considering the resulting extension in the new category. A simple example of this is in modules over a k-algebra A, k a field. We can forget the action of the algebra and focus only on the k-action. We make this precise by applying the "forgetful functor" from the category of A-modules to k-modules. k-modules are just vector spaces, and all extensions here are split, i.e., direct sums. We thus know that at least as vector spaces, extensions of A-modules are direct sums.

Another curiousity is how subobjects behave in extensions, for example, rings of integers in fields (viewed as rings).

Academic past

Click here if you want to know about my past.

Last updated 4 June 2007