1. Percolation and other models (free: several projects available): We will try to simulate various models of statistical physics like percolation and determine various quantities like noise sensitivity.
2. Laplacian and matrix tree formulas for high incidence operators for graphs (related to graph rigidity) . (free)
3. Radon and Tverberg points of configurations of points (Taken):
4. Face numbers of quasi simplicial poytopes and flag numbers of general polytopes (Taken)
5. Algebraic shifting and face-rings. (free) Given a family of k-subsets of {1,2,...,n} we will construct the shifted family (exterior and symmetric).
6. Others.