Our proposal is in Microeconomic theory. The subfields for this proposal are Matching Markets and Auctions.Our objectives are to: a) provide a generalized framework which would subsume matching and auction settings; b) in our generalized framework, to show how the assumptions on agents preferences in matching and auction settings relate to each other, via fundamental mathematical properties; c) to find new ways, analytically tractable, that would enable market participants to express their increasingly complex preferences.Our envisioned results are hoped to help towards improving the functioning of: a) entry-level job markets that include an increasing fraction of couples which need to express complex preferences, such as in the National Resident Matching Program or in other similar clearinghouses throughout the UK; b) auction processes in which bidders need to express complex preferences over mixes of indivisible goods, such as the auction ran by the Bank of England to provide liquidity to financial institutions or the auctions ran by the European Central Bank to provide liquidity to European Union member states in need to finance their sovereign debt.This proposal will contribute to the European excellence by advancing the frontier of the theoretical knowledge on topics that have practical applications of paramount importance for the EU.The fellow is an experienced researcher who's publication track record includes contributions at the interface between matching markets and auctions. These contributions have appeared in top economic journals. The outgoing and return hosts of the fellow are Stanford University and the University of St Andrews, respectively.