Maciej Dołęga: Positivity of various cumulants - results and conjectures

Time: Wed 2019-05-08 10.15 - 11.15

Lecturer: Maciej Dołęga (Polish Academy of Sciences, Institute of Mathematics)

Location: Room 3418, Lindstedtsvägen 25. Department of Mathematics, KTH

Abstract: We are going to introduce new families of symmetric functions through notion of cumulants. We will be particularly interested in generalization of Macdonald symmetric functions and LLT symmetric functions. We are going to refine certain positivity results concerning coefficients of aforementioned functions expressed in some classical bases. Finally, we will state some positivity conjectures refining Schur-positivity of Macdonald and LLT polynomials, and we will provide some evidences for our conjectures.