The supercuspidal representations of p-adic classical groups

Let G be a unitary, symplectic or special orthogonal group over a locally compact non-archimedean local field of odd residual characteristic. We construct many new supercuspidal representations of G, and Bushnell-Kutzko types for these representations. Moreover, we prove that every irreducible supercuspidal representation of G arises from our constructions.Comment: 55 pages -- minor changes from 1st version (mostly in sections 2.2, 4.2 and 6.2). To appear in Inventiones mathematicae, 2008 (DOI is not yet active as at 12 Nov 2007

Asymptotics and local constancy of characters of p-adic groups

In this paper we study quantitative aspects of trace characters $\Theta_\pi$ of reductive $p$-adic groups when the representation $\pi$ varies. Our approach is based on the local constancy of characters and we survey some other related results. We formulate a conjecture on the behavior of $\Theta_\pi$ relative to the formal degree of $\pi$, which we are able to prove in the case where $\pi$ is a tame supercuspidal. The proof builds on J.-K.~Yu's construction and the structure of Moy-Prasad subgroups.Comment: Proceedings of Simons symposium on the trace formul

Biased competition through variations in amplitude of γ-oscillations

Experiments in visual cortex have shown that the firing rate of a neuron in response to the simultaneous presentation of a preferred and non-preferred stimulus within the receptive field is intermediate between that for the two stimuli alone (stimulus competition). Attention directed to one of the stimuli drives the response towards the response induced by the attended stimulus alone (selective attention). This study shows that a simple feedforward model with fixed synaptic conductance values can reproduce these two phenomena using synchronization in the gamma-frequency range to increase the effective synaptic gain for the responses to the attended stimulus. The performance of the model is robust to changes in the parameter values. The model predicts that the phase locking between presynaptic input and output spikes increases with attention