Currently, I study the representation theory of Lie algebras which is a branch of the larger field of Algebra.
I am working towards understanding the structure of representations of infinite dimensional Lie algebras. One such example is studying the representation theory of the Insertion-elimination Lie algebra which is an infinite dimensional Lie algebra indexed by the space of rooted trees. Another such example is studying the representation theory of the current algebra associated with Lie algebra of type A and D.
Of late, as an active participant in the MRC (mathematical research community): Finding needles in Haystacks, I am learning about the Inverse Eigenvalue problem of a graph and how it connects with Zero forcing and throttling of a graph.
I am also active in undergraduate research. I have joined Dr. Andrea Arauza Rivera in RUMBA (Research for Undergraduates on the Mathematics of the Bay Area). RUMBA consists of collaborative projects which unite the skills of students (undergraduate and graduate), faculty, and Bay Area groups, so that they may use mathematics to study the cultural, political and social systems in the Bay Area.
Prior, I have done three projects thus far which can be found here. One project was exploring mutations of Quivers, and finding a beginning quiver along with a sequence of mutations that will produce a number sequence. Our project did find one with a sequence of mutations that gave a modified Fibonacci sequence. Another project was exploring the game of Cops and Robbers on graphs. We began with simple graphs, then looked at graphs determined by moves of chess pieces. Our project ended with proving a result of the Knights graph on 16 vertices.
While I was an undergrad, I always wondered what research was going to entail, and I have come to find out that research consists of a lot of reading, coffee, and struggling. What I have learned is that struggling is good! That is something I think is lost early on in our education. Some things you will get and understand, while other things you just need to spend more time to gain a deeper understanding.