How natural speech is represented in the auditory cortex constitutes a major challenge for cognitive neuroscience. Although many single-unit and neuroimaging studies have yielded valuable insights about the processing of speech and matched complex sounds, the mechanisms underlying the analysis of speech dynamics in human auditory cortex remain largely unknown. Here, we show that the phase patte...

We consider the problem of the semidefinite representation of a class of non-compact basic semialgebraic sets. We introduce the conditions of pointedness and closedness at infinity of a semialgebraic set and show that under these conditions our modified hierarchies of nested theta bodies and Lasserre’s relaxations converge to the closure of the convex hull of S. Moreover, if the PP-BDR property...

We continue a recently developed systematic approach to the Bousinesq (Bsq) hierarchy and its algebro-geometric solutions. Our formalism includes a recursive construction of Lax pairs and establishes associated Burchnall-Chaundy curves, Baker-Akhiezer functions and Dubrovin-type equations for analogs of Dirichlet and Neumann divisors. The principal aim of this paper is a detailed theta function...

Abstract. We study and generalize the connection between the phylogenetic Hilbert functions of Buczynska and Wisniewski [BW] and the Verlinde formula, as discovered by Sturmfels and Xu in [StX]. In order to accomplish this we introduce deformations of algebras of non-abelian theta functions for a general simple complex Lie algebra g structured on the moduli stack of stable punctured curves. We ...

In [6] the second author proved that the image of the Galois representation mod λ attached to a Hilbert modular newform is “large” for all but finitely many primes λ, if the form is not a theta series. In this brief note, we give an explicit bound for this exceptional finite set of primes and determine the images in three different examples. Our examples are of Hilbert newforms on real quadrati...

These notes were written for the workshop on the Theta correspondence held at the University of Maryland, May 1994. They have circulated informally for many years. Except for minor changes and some improvements to the references they have not been changed. There have been too many developments in the field since 1994 to try to bring them up to date. This is dedicated to Roger Howe, who introduc...