Francesco Brenti

Recent progress in Kashdan-Lusztig theory

In this talk we will survey some recent results on Kazhdan-Lusztig polynomials, with an emphasis on combinatorial aspects. In particular, we will present a new combinatorial description of these polynomials in terms of lattice paths, and we will survey the state of the art on two long-standing conjectures on Kazhdan-Lusztig polynomials, namely the nonnegativity conjecture, and the combinatorial invariance conjecture.