Braid group and

Filling factors and Braid group

We extract the Braid group structure of a recently derived hierarchy scheme for the filling factors proposed by us which related the Hausdorff dimension, h, to the statistics, ν, of the collective excitations in the context of the Fractional Quantum Hall Effect (FQHE).

Braid Group Cryptography

In the last decade, a number of public key cryptosystems based on combinatorial group theoretic problems in braid groups have been proposed. We survey these cryptosystems and some known attacks on them. This survey includes: Basic facts on braid groups and on the Garside normal form of its elements, some known algorithms for solving the word problem in the braid group, the major public-key cryp...

On a Braid Group Action

We discuss some consequences of the braid group action on a categorified quantum group. Results include a description of reflection functors for quiver Hecke algebras and a theory of restricting categorical representations along a face.

Braid Group Cryptography Preliminary Draft

In the last decade, a number of public key cryptosystems based on combinatorial group theoretic problems in braid groups have been proposed. Our tutorial is aimed at presenting these cryptosystems and some known attacks on them. We start with some basic facts on braid groups and on the Garside normal form of its elements. We then present some known algorithms for solving the word problem in the...

Derivative Varieties and the Pure Braid Group