Research projects

Project CEMAPRE internal

TitleApplications of algebro-geometric techniques to the study of market design problems
ParticipantsAlberto Lopez Martín (Principal Investigator), Joana Pais, Yosuke Yasuda
SummaryTropical geometry is at the interface between algebraic geometry, combinatorial optimization, and
matroid theory. Market design lies at the intersection of economics, computer science, and
operations research, and it is concerned with the design of real-world markets. Matching markets are
one of the focus points of market design and important for the functioning of society (e.g. in the
assignment of students to courses or in kidney transplants). Tropical geometry has managed to
capture the combinatorics behind allocation problems in economics, allowing for more elegant proofs,
novel approaches and new results. In this project, we intend to develop and apply tools and
techniques developed in the realm of tropical geometry (and more broadly discrete convex analysis)
to tackle allocation problems that have thus far resisted other approaches.