The two sides of the extended Shuffle Conjecture

Eugene Gorsky and Andrei Negut have recently put the finishing touches to what may be viewed as the symmetric function side of the general m,n-Shuffle conjecture. Earlier, Tatsuyuki Hikita gave a beautiful construction of the combinatorial side as a weighted enumeration of m,n-Parking Functions. All these developments are gravid with challenging Combinatorial problems. In this talk I will report on my findings in an effort to translate some of the contents of these remarkable publications in a language that is more accessible to the general combinatorial audience. In particular I have made an effort to state the resulting m,n-Shuffle Conjecture using notation that is as close as possible to the statement of the original Shuffle Conjecture.