From the function-sheaf dictionary to quasicharacters of pp-adic tori

We consider the rigid monoidal category of character sheaves on a smooth commutative group scheme $G$ over a finite field $k$ and expand the scope of the function-sheaf dictionary from connected commutative algebraic groups to this setting. We find the group of isomorphism classes of character sheaves on $G$ and show that it is an extension of the group of characters of $G(k)$ by a cohomology group determined by the component group scheme of $G$. We also classify all morphisms in the category character sheaves on $G$. As an application, we study character sheaves on Greenberg transforms of locally finite type N\'eron models of algebraic tori over local fields. This provides a geometrization of quasicharacters of $p$-adic tori.Comment: Added examples and incorporated referee's suggestions. To be published in Journal of the Institute of Mathematics of Jussie

Pauldron

The International Fashion Art Biennale in Seoul, hosted by the Korea Fashion and Culture Association, is one of the most significant international exhibitions of fashion framed as art. The 2010 Biennale was notable as it coincided with the 60th anniversary of the Korean War and the hosting of the 2010 G-20 summit, shaping the themes of the exhibition. It showcased 104 artists selected globally. The exhibition was held at the Hangaram Design Museum, Seoul Arts Centre, and received substantial press and media including coverage on national Korean TV. My participation was noteworthy as I was the only Australian invitee. ‘Pauldron’ explores the tensions between the residual sense of tribal primitivism associated with the practices of scarification versus the highly refined craft skills that are required in the fabrication of armour, whether it be Japanese or European. These tensions are further explored by the introduction of a new material, wool, and a new technique, not associated with the usual inert materials of armour whether they be lacquer or steel. A result is a re-gendering of the notion of protective coverings. It also re-positions the sense of decorum of inner and outer garments. As the fashion scholar Valerie Steele argued in the exhibition ‘Love & War: The Weaponised Woman’ (The Museum at Fashion Institute of Technology, NYC, 2006), there is a paradox in the way women’s fashion consistently uses elements from warfare and military garments over a long period of time to reinvent feminine identity in clothing. The work continues my broader research investigation into the application of knitting techniques to create new body constructions and forms

On the computability of some positive-depth supercuspidal characters near the identity

This paper is concerned with the values of Harish-Chandra characters of a class of positive-depth, toral, very supercuspidal representations of $p$-adic symplectic and special orthogonal groups, near the identity element. We declare two representations equivalent if their characters coincide on a specific neighbourhood of the identity (which is larger than the neighbourhood on which Harish-Chandra local character expansion holds). We construct a parameter space $B$ (that depends on the group and a real number $r>0$) for the set of equivalence classes of the representations of minimal depth $r$ satisfying some additional assumptions. This parameter space is essentially a geometric object defined over \Q. Given a non-Archimedean local field \K with sufficiently large residual characteristic, the part of the character table near the identity element for G(\K) that comes from our class of representations is parameterized by the residue-field points of $B$. The character values themselves can be recovered by specialization from a constructible motivic exponential function. The values of such functions are algorithmically computable. It is in this sense that we show that a large part of the character table of the group G(\K) is computable