Last summer, Christopher passed his qualifying exams. Since then he has been taking courses and doing independent reading with his advisor Weiqiang Wang in preparation for research. He is currently working on a small research project and preparing for his oral exams. In the next year he will take fewer classes and begin to focus more on his research.
Christopher is currently studying quantum groups and categorification. Quantum groups give a precise language with which to describe certain symmetries and have found many applications in both mathematics and theoretical physics. The idea of categorification is to add another level of complexity to quantum groups. This makes them more complicated and so in some ways harder to study, but the extra information can reveal information that would otherwise be hidden. Categorification is a very new and promising area of research. It has already provided answers to some long unanswered questions and looks like it will be an important tool in the study of quantum groups in the future.