The University of Michigan Combinatorics Seminar
Pattern avoidance has been used to classify several notions
for permutations and signed permutations. In this talk, we propose a
new generalization of pattern avoidance which can be applied to
all root systems and their Weyl groups. The main theorem shows that
for any semisimple Lie group G and maximal Borel subgroup B,
smooth Schubert varieties in G/B can be characterized by this new
method with a very short list of patterns.