We study the partition function for the low-energy edge excitations of the incompressible electron fluid. On an annular geometry, these excitations have opposite chiralities on the two edges; thus, the partition function takes the standard form of rational conformal field theories. In particular, it is invariant under modular transformations of the toroidal geometry made by the angular variable...

An important problem in combinatorial noncommutative algebra is to give an asymptotic characterization the growth functions of finitely generated algebras (equivalently, semigroups, or hereditary languages). The function every generated, infinite-dimensional increasing and submultiplicative. question what extent these natural necessary conditions are also sufficient—and particular, whether they...

Several neurological disorders are linked to tandem nucleotide repeat expansion in the mutated gene. Jain and Vale (2017. Nature. https://doi.org/10.1038/nature22386) show that, above a pathological threshold repeat number, base pairing interactions drive phase separation of RNA into membrane-less gels, suggesting that RNA can scaffold the assembly of phase-separated compartments that sequester...

In this paper, the exact value for the norm of directional derivatives, of all orders, for symmetric tensor powers of operators on finite dimensional vector spaces is presented. Using this result, an upper bound for the norm of all directional derivatives of immanants is obtained. This work is inspired in results by R. Bhatia, J. Dias da Silva, P. Grover, and T. Jain.