Zurückliegende Veranstaltungen

The 3x+1 Problem is a long-standing conjecture. Let T be 
a map from the positive integers into itself, where T(x)=x/2 if x is even 
and T(x) = (3x+1)/2 if x is odd. The conjecture asks whether, under 
iteration of the map T, any positive integer eventually reaches the value 
one. This talk gives a survey of the various approaches and results, 
intersecting areas such as number theory, dynamical systems, and 
functional equations. The speaker's approach involving generating
functions is also presented.

In recent work with S. Naito, D. Sagaki, A. Schilling, and M. Shimozono, we show that in all untwisted affine types the specialization of a Macdonald polynomial at t=0 is the graded character of a tensor product of one-column Kirillov-Reshetikhin (KR) modules.