TITLE: Two-Sided Matching Markets with One-Sided Preferences SPEAKER: David Abraham ABSTRACT: This talk is in partial fulfilment of the speaking requirement. In many countries, new medical graduates are required to take a one-year intern position before achieving full accreditation. Some graduates prefer hospitals that are close to their home, whilst others base their preferences on prestige, money etc. Unfortunately, there are only a limited number of positions, and so some graduates may not be allocated one of their top choices. How do we decide which graduates go where? If hospitals have preferences over graduates, this is just the well-known Stable Marriage problem. However, if the market only has one-sided preferences, the answer is not so clear. In this talk, we will discuss several alternative objective functions. We will focus on the problem of finding a popular matching - one for which there is no other matching that more graduates prefer.