Schubert calculus and torsion explosion
The author observes that certain numbers occurring in Schubert calculus for SL also occur as entries in intersection forms controlling decompositions of Soergel bimodules in higher rank. These numbers grow exponentially. This observation gives many counter-examples to the expected bounds in Lusztig’s conjecture on the characters of simple rational modules for SL over fields of positive characteristic. The examples also give counter-examples to the James conjecture on decomposition numbers for symmetric groups.