This is a list of questions and topics I would like to research. If you find any of them interesting and would like to collaborate, drop me an email.
Working papers
These papers need coauthors in order to realize their full potential:

Fair cakecutting among groups: Mostly related to economics but contains some algorithmic content. It is about fair division of resources that are enjoyed by a whole group, such as a family or a country, rather than by a single individual. A collaborator could help to improve and add new results.

How to redivide a cake fairly?: Combines computational geometry, combinatoris, economics and social choice. I am looking for experts in any of these fields in order to help verify and improve the results.

A Tradeoff Between Fairness and Efficiency in CakeCutting: Motivated by economics, but the techniques are mostly combinatorial. A collaborator who is proficient in combinatorics will surely find new results easily.
Reasearch projects

Experiments in fair division. I have some simulation results on fair division of land, and an online game for experiments with humans on fair cakecutting. I need partners to advance.

Implementing fair division algorithms in realestate projects. Currently, apartments are divided by lottery and/or protection… There are better ways and I would like to check how they can be implemented.
Open Questions
I would very much like to know the answer to the following questions.

When valuedensities can be both positive and negative, does there always exist a connected envyfree division for 4 or more agents? Mainly a question in algebraic topology. May be related to combinatorics. My working paper has a solution for 3 agents.

How many cuts are required for cakecutting when the agents have different entitlements? Mainly a combinatorics question. May be related to measure theory and topology. My MathOverflow question has some preliminary results.

Does there always exist a Paretoefficient envyfree allocation of “family goods”? Mainly an economics question. My economics.SE question has some more details. Our group cakecutting paper solves a related but easier problem.

Is it possible to find in bounded time an envyfree and proportional cakedivision with connected pieces? Mainly an algorithmic question. The Wikipedia page I wrote on envyfree cakecutting gives some background. Our wastemakeshaste paper presents the current status.

Given a collection of points in the plane, what is the largest possible collection of pairwisedisjoint wetsquares? Mainly a geometric question. This draft presents the question formally and gives some directions. Our fairandsquare papers (extended abstract and full preprint) present the economic motivation.