Representation theory and cohomology of Khovanov-Lauda-Rouquier algebras

This expository paper is based on the lectures given at the program `Modular Representation Theory of Finite and $p$-adic Groups' at the National University of Singapore. We are concerned with recent results on representation theory and cohomology of KLR algebras, with emphasis on standard module theory.Comment: arXiv admin note: text overlap with arXiv:1210.655

On the Classification Problem for Rank 2 Torsion-Free Abelian Groups

We study here some foundational aspects of the classification problem for torsion-free abelian groups of finite rank. These are, up to isomorphism, the subgroups of the additive groups (Q^n, +), for some n = 1, 2, 3,.... The torsion-free abelian groups of rank ≤ n are the subgroups of (Q^n, +)