ar X iv : m at h / 06 03 35 8 v 1 [ m at h . N T ] 1 4 M ar 2 00 6 Representation of integers by quadratic forms

ar X iv : m at h / 04 06 24 5 v 2 [ m at h . N T ] 1 4 M ar 2 00 5 1 Graphical patterns in quadratic residues

Plots of quadratic residues display some visual features that are analyzed mathematically in this paper. The graphical patterns of quadratic residues modulo m depend only on the residues of m modulo the lowest positive integers.

ar X iv : m at h / 06 05 35 5 v 1 [ m at h . G R ] 1 3 M ay 2 00 6 Axes in Outer Space

ar X iv : m at h / 03 06 23 5 v 2 [ m at h . D G ] 8 N ov 2 00 6 GEOMETRIC CONSTRUCTION OF MODULAR FUNCTORS FROM CONFORMAL FIELD

We give a geometric construct of a modular functor for any simple Lie-algebra and any level by twisting the constructions in [16] and [19] by a certain fractional power of the abelian theory first considered in [13] and further studied in [2].

ar X iv : m at h / 06 10 50 1 v 2 [ m at h . G T ] 1 8 O ct 2 00 6 INTRINSIC LINKING IS ARBITRARILY COMPLEX

We prove that given any n, λ ∈ N, there is a graph G which has the property that every embedding of G in R contains an ncomponent link all of whose components are pairwise linked with linking number greater than λ.

ar X iv : h ep - t h / 06 03 12 5 v 1 1 5 M ar 2 00 6 hep - th / 0603125 ITP – UH – 05 / 06 Noncommutative Instantons on C

We construct explicit solutions of the Hermitian Yang-Mills equations on the noncommutative space C θ . In the commutative limit they coincide with the standard instantons on CP written in local coordinates.