Generated Jacobian Equations: from Geometric Optics to Economics (17w5078)

Arriving in Banff, Alberta Sunday, April 9 and departing Friday April 14, 2017

Organizers

(Michigan State University)

(University of Toronto)

(University of Massachusetts Amherst)

Objectives

A major objective of the workshop is to bring together and foster interaction between researchers working in the general theory of GJEs, the theory for specific problems in engineering and economics that can be modeled by certain GJEs, the numerical analysis of OT and/or geometric optics problems, and related geometric and variational problems.

These themes would (tentatively) be distributed throughout the week as follows:
  1. General theory of GJE and practical models (geometric optic problems) (1.5 days).
  2. Numerical analysis of OT and GJE (1 day).
  3. Convex and differential geometry (1 day).
  4. 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:
  1. 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).
  2. To capitalize on recent increased activity in numerics for OT to develop specialized numerical schemes for GJEs in geometric optics and beyond.
  3. To deepen the connections between GJEs/OT and models in economics, particularly those dealing with stable matchings and principal-agent problems.
  4. To develop a framework using the theory of GJEs to analyze generalizations of the Minkowski problem.
Finally, this workshop will benefit from continuing the momentum of other recent programs, such as the thematic semesters in optimal transport and variational problems held in recent years at the MSRI and the Fields Institute, respectively.