Im majoring in physics, and I would highly appreciate some ideas and some orientation about what I'm getting into. Im beginning the third year of the major and I need ideas for a thesis. I consider that the thesis could take around 2 years. I have been teaching myself the main subjects about the math major. Analysis, Abstract Algebra, Topology and some Functional Analysis. Im still in the process of studying these subjects. Eventually I would like to study some Differential Geometry, some Algebraic Topology, and Quantum Mechanics as well. The fields that I'm interested in per suing, "not now but in the future", are Topological quantum field theory and Gauge Theory I'm also interested in Category theory. I would kindly appreciate any suggestion or idea about any possible undergraduate problems in those areas or in related areas. Your comments and suggestions are very valuable to me. Thanks.