Speaker: Foster Tom (Dartmouth College)
Title: On the e-positivity of chromatic symmetric functions
Abstract: We describe how the chromatic symmetric function of two graphs glued at a single vertex can be expressed as a matrix multiplication using certain information of the two individual graphs. We then prove new e-positivity results by using a connection between forest triples and Hikita's probabilities associated to standard Young tableaux. We also prove new non-e-positivity results by considering connected partitions of our graph.