ar X iv : m at h / 03 11 27 5 v 1 [ m at h . A P ] 1 7 N ov 2 00 3 REPRESENTATION OF MULTIVARIATE FUNCTIONS VIA THE POTENTIAL THEORY

ar X iv : m at h - ph / 0 11 10 07 v 1 5 N ov 2 00 1 FREDHOLM DETERMINANTS , JIMBO - MIWA - UENO TAU - FUNCTIONS , AND REPRESENTATION THEORY

The authors show that a wide class of Fredholm determinants arising in the representation theory of " big " groups such as the infinite–dimensional unitary group, solve Painlevé equations. Their methods are based on the theory of integrable operators and the theory of Riemann–Hilbert problems.

ar X iv : h ep - t h / 03 11 04 8 v 1 6 N ov 2 00 3 Wavelet based regularization for Euclidean field theory and stochastic quantization

It is shown that Euclidean field theory with polynomial interaction, can be regularized using the wavelet representation of the fields. The connections between wavelet based regularization and stochastic quantization are considered with φ 3 field theory taken as an example.

ar X iv : m at h / 04 05 17 6 v 3 [ m at h . R T ] 1 7 N ov 2 00 4 QUANTIZED SYMPLECTIC OSCILLATOR ALGEBRAS OF RANK ONE

A quantized symplectic oscillator algebra of rank 1 is a PBW deformation of the smash product of the quantum plane with Uq(sl2). We study its representation theory, and in particular, its category O.

ar X iv : h ep - p h / 00 11 11 7 v 1 8 N ov 2 00 0 1 ( Mis ) Understanding the Atmospheric Neutrino Anomaly

ar X iv : m at h / 06 11 45 2 v 1 [ m at h . A G ] 1 5 N ov 2 00 6 UNIRATIONALITY OF CERTAIN SUPERSINGULAR K 3 SURFACES IN CHARACTERISTIC

We show that every supersingular K3 surface in characteristic 5 with Artin invariant ≤ 3 is unirational.