Coincidences in Poincare Polynomials of Projective Homogeneous Varieties
This is a very old paper 2011 which I completed as an undergraduate student at the University of Ottawa under supervision of Kirill Zaynullin. He was looking for coincidences in the poincare polynomials of PHVs. The key question was whether there were any blowup relations (or monoidal transformations in Manin's terminology) between the E8 and F4 type root systems. Our results were inconclusive, and we have not revisited the problem in a long time. These days I would program something in Wolfram MATHEMATICA and try brute-force search for such coincidences.