Learn more about the real and complex bistochastic groups [math]B_N,C_N[/math], and write down a brief account of what you learned.

Check the symplectic geometry literature, and write down a concise proof for the Idel-Wolf theorem, based on that, by explaining the main ideas involved.

Find the best bound for the support of the glow of the complex Hadamard matrices, by using the moment method, and combinatorics.

Study the deformations of the Fourier matrix [math]F_6[/math], with the aim of putting them in bistochastic form, and write down what you found.

Study the Paley matrix [math]P_{12}[/math], with the aim of putting it in bistochastic form, over the complex numbers, and write down what you found.