It is argued that fractional quantum Hall effect wavefunctions can be interpreted as conformal blocks of two-dimensional conformal field theory. Fractional statistics can be extended to nonabelian statistics and examples can be constructed from conformal field theory. The Pfaffian state is related to the 2D Ising model and possesses fractionally charged excitations which are predicted to obey n...

We provide a survey of results concerning both the direct and inverse problems to the Cauchy-Davenport theorem and Erdős-Heilbronn problem in Additive Combinatorics. We formulate a conjecture concerning the inverse Erdős-Heilbronn problem in nonabelian groups. We prove an inverse to the Dias da Silva-Hamidoune Theorem to Z/nZ where n is composite, and we generalize this result for nonabelian gr...

We study magnetically charged black holes in the Einstein-Yang-Mills-Higgs theory in the limit of infinitely strong coupling of the Higgs field. Using mixed analytical and numerical methods we give a complete description of static spherically symmetric black hole solutins, both abelian and nonabelian. In particular we find a new class of extremal nonabelian solutions. We show that all nonabelia...

Let G be a semisimple compact connected Lie group. An N-fold reduced product of is the symplectic quotient Hamiltonian system Cartesian N coadjoint orbits under diagonal action G. Under appropriate assumptions, it orbifold. Using technique nonabelian localization and residue formula Jeffrey Kirwan, we investigate volume an Suzuki Takakura gave for $$ \mathbf {SU}(3) in [25] by using geometric q...

If M = Z, and G is a finite (nonabelian) group, then G is a compact group; a multiplicative cellular automaton (MCA) is a continuous transformation F : G − ←⊃ which commutes with all shift maps, and where nearby coordinates are combined together using the multiplication operator of G. We provide equivalent conditions for MCA to be group endomorphisms of G, and show how MCA on G inherit a natura...

Weak mixing is an important property for group extensions because its absence is the principal obstruction to lifting a large number of stronger mixing properties. Whether or not an extension is weakly mixing can be determined by studying the sub-extension corresponding to the quotient by the commutator subgroup. Several conditions equivalent to weak mixing are given. In particular, an extensio...

Using the left regular action of a group on itself, we develop a general representation theory for constructing groups of permutation polynomials. As an application of the method, we compute polynomial representations of several abelian and nonabelian groups, and we determine the equivalence classes of the groups of polynomials we construct. In particular, when the size of the group is equal to...