Topological phases of non-Hermitian systems

Non-Hermitian fermionic systems are known to exhibit features strikingly different from their Hermitian counterparts, a quintessential example being the lack of a bulk-boundary correspondence in the conventional sense. In this talk, I will describe a transfer matrix approach to these systems. The algebraic structure of the transfer matrix and a Riemann surface associated with the complex energies provide a clear and intuitive picture of various topological aspects of these systems.