Earlier this month, in Lecture Theatre 2 in the Andrew Wiles Building, a collection of talented Oxford Mathematics students, together with colleagues in STEM subjects and beyond, performed Fermat's Last Tango to sell-out crowds over five performances.
Written in 2000 by Joanne Sydney Lessner and Joshua Rosenblum, Fermat's Last Tango tells the story, in words and music, of a 300 hundred-year-old mathematical mystery and the man who spent seven years trying to solve it. Sound familiar?
A complex irreducible admissible representation of a reductive p-adic group is typically infinite-dimensional. To quantify the "size" of such representations, we introduce the concept of canonical dimension. To do so we have to discuss the Moy-Prasad filtrations. These are natural filtrations of the parahoric subgroups. Next, we relate the canonical dimension to the Harish-Chandra local character expansion, which expresses the distribution character of an irreducible representation in terms of nilpotent orbital integrals. Using this, we consider the wavefront set of a representation. This is an invariant the naturally arises from the local character expansion. We conclude by explaining why the canonical dimension might be considered a weaker but more computable alternative to the wavefront set.