Welcome to my webpage. My name is Khoa Lu Nguyen. I am currently a junior at Massachusetts Institute of Technology. I am majoring in theoretical math with interests in analysis, geometry and topology. My email address is: nglukhoa at mit dot edu
This summer I am working with Professor Chris Woodward on toric varieties associated with bicolored metric trees. This is a great way to begin studying algebraic geometry. In short, a toric variety is a variety that contains the torus as a Zariski dense open set and the torus action which acts on itself can be extended to an action acting on that variety. Well, if you understand that previous statement, you are probably an expert in toric variety. Otherwise, you can look at the introduction in the first-half of my Power Point presentation
What I do is to investigate some special kind of toric varieties that are associated with bicolored metric trees. Toric variety is a special variety that arises from the geometry of fan of cones. To understand some certain toric variety, it is best to give a nice description of the fan that generates it. Toric varieties associated with bicolored metric trees are affine and thus they arise from cones. In the paper and in my Power Point presentation, I give a description of those cones by an inductive argument. The bicolored metric tree can be splitted into smaller subtrees and hence, the inductive argument can be established.
I will soon upload some more explanations. The final paper will also be uploaded as soon as I get it done.
Department of Mathematics at Rutgers University
Department of Mathematics at Massachusetts Institute of Technology