Seminar at SMU Delhi

In this talk we enumerate domino tilings of an Aztec rectangle with arbitrary defects of size one on all boundary sides. This result extends previous work by different authors: Mills-Robbins-Rumsey and Elkies-Kuperberg-Larsen-Propp. We use the method of graphical condensation developed by Kuo and generalized by Ciucu, to prove our results; if time permits, a common generalization of both Kuo's and Ciucu's result will also be presented. The talk is mostly self-contained and only basic ideas from graph theory would be assumed.