I am getting my Bachelors in mathematics and need to write a

I am getting my Bachelor\'s in mathematics and need to write a research paper on an \"open problem\" in abstract algebra. Does anyone have any suggestions on a topic to research that is fairly easy to contribute my own ideas to? Remember this is an undergraduate paper, not a doctoral research paper.

Solution

1) Failure of von Neumann\'s inequality.

2) Hodge theory and Electromagnetism. (Algebraic topology/Physics) the time of Maxwell has been an important source of new mathematics. This is particularly true for topology, specially for what is called \"algebraic topology\". One fundamental topic in algebraic topology with strong ties to electromagnetism is the so called \"Hodge-de Rham theory\". Although in its general form this is a difficult and technical topic