Generated Jacobian Equations: from Geometric Optics to Economics (17w5078)
Robert McCann (University of Toronto)
Nestor Guillen (University of Massachusetts Amherst)
Jun Kitagawa (Michigan State University)
These themes would (tentatively) be distributed throughout the week as follows:
- General theory of GJE and practical models (geometric optic problems) (1.5 days).
- Numerical analysis of OT and GJE (1 day).
- Convex and differential geometry (1 day).
- Economics: matching and pricing problems (1 day).
We believe the nascent field of GJEs has much to gain at this early stage in its development from an international meeting, such as one at BIRS. Each of the specific cases of GJEs mentioned in the overview section are rich, but mainly independent, ongoing areas of research. A quick look at the widely international list of researchers in these fields indicates that a workshop at BIRS would be an excellent chance to facilitate the exchange of ideas and techniques among researchers from all over the world, and form new connections between these previously established fields. A set of more concrete objectives for the workshop are as follows:
- To speed up the development of a more mature overall theory of GJEs (for example, construction of weak solutions, uniqueness, regularity, and analogues of the Kantorovich problem).
- To capitalize on recent increased activity in numerics for OT to develop specialized numerical schemes for GJEs in geometric optics and beyond.
- To deepen the connections between GJEs/OT and models in economics, particularly those dealing with stable matchings and principal-agent problems.
- To develop a framework using the theory of GJEs to analyze generalizations of the Minkowski problem.