Symmetric functions are very interesting combinatorial objects. After decomposing certain symmetric functions in terms of different bases, we can often combinatorially interpret the resulting coefficients. This is made particularly easy if those coefficients are positive (or controllably negative). The chromatic symmetric function is one such symmetric function, and its decomposition has been of interest for decades. There are easy (but not nice) decompositions of this function in terms of some bases, such as the power sum basis, but the Stanley-Stembridge conjecture of 1993 suggests that the chromatic symmetric function has a nice decomposition in terms of the elementary basis. In this talk, we will cover the basics of symmetric functions, in particular the chromatic symmetric function, and we might even take a shallow dip into some of the ways in which this conjecture is being attacked.

Zoom Meeting link:  https://ncsu.zoom.us/j/92762214990?pwd=MnA1TnNVQUpzUlo3cTM5RmlNWVF4Zz09

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