In this talk we will present the basic ideas that led to a symmetric function proof of the Delta conjectrue for q=0. In a recent unpublished work Jim Haglund and Meesue Yoo proved that the Delta conejcture at q=0 is equivalent to the validity of an equality of the form A_{k;\lambda} = B_{k;\lambda}, for all \lambda a partition of n and 1\le k \le n. Our argument starts by showing that these identities are equivalent to symmetric function identities of the form A_{k;\lambda} = B_{k;\lambda} for all 1\le k \le n. What is perhaps more important than the result itself is the introduction of a new method of proving symmetric function identities by means of multiple uses of Cauchy kernels.

### CAGE: Philadelphia Area Combinatorics and Alg. Geometry Seminar

Thursday, November 2, 2017 - 3:00pm

#### Adriano Garsia

UCSD