Partitions and Juggling: A story of unifying parts and seeking balance in mathematics.

Kostant’s partition function is a vector partition function that counts the number of ways one can express a vector as a nonnegative integer linear combination of a fixed set of vectors. Multiplex juggling sequences are generalizations of juggling sequences (describing throws of balls at discrete heights) that specify an initial and terminal configuration of balls and allow for multiple balls at any particular discrete height. In this talk, I will give an introduction to a combinatorial equivalence between Kostant’s partition function and multiplex juggling sequences. Throughout I will talk about how partitioning my authentic self from my mathematical work makes it impossible to juggle and find balance in my professional work.