I'm interested in research topics that both involve interesting math and have some direct applications to the world. I'm most interested in applications that may make a positive social impact.
(Please contact me if you have any insights on any of these topics.)
Improving Allocation Mechanisms in School Choice
In many US cities--such as Boston, San Francisco, New York, Denver and Los Angeles--parents can choose where to send their kids within the public school system. Typically, parents would submit a ranked list of preferred schools to a centralized mechanism, which uses some randomized algorithm to assign kids to schools, while taking into account the different schools' quotas, priorities for students, and other constraints. Such a mechanism needs to optimize the assignment for all kids, taking into account fairness, strategic behavior by parents, and global objectives of the school board (such as diversity). While prior literature in economics and in market design has studied such mechanisms, some issues remain unresolved and some are newly emerging from the field. For example, in Boston, while a reform in 2005 fixed a previous issue of requiring parents to behave strategically in their choice process, the new mechanism is again under review (see Boston Globe article) because it scatters kids across the city (see Boston Globe report), resulting in harm to community formation and in high busing costs (representing 10% of school board budget). I am working on developing new mathematical and algorithmic machinery to tackle these issues in a practical way, while maintaining the previously desirable properties such as fairness, efficiency, and strategyproofness. See my current working papers for details.
Incentive Issues in National Kidney Exchange:
There are many issues involved with successfully running a national paired kidney exchange program. (A kidney exchange is where incompatible donor-patient pairs can donate to one another in cycles and chains to improve the quality and quantity of live kidney transplants.) Perhaps the most pressing issue is the low rates of participation, both for patients and their donors to join a kidney exchange, and for hospitals and regional networks to join the national exchange. However, due to the highly sensitization of the patients who would benefit from kidney exchange, the "compatibility graph" is very sparse, so for the exchange to be effective there needs to be a large pool of participants. It is an open-ended question how one would try to increase the participation rates. Directions I'm examining include how to design the exchange mechanism to better incentivize hospital participation, and how to allow the expressions of more preferences of individual participants in the exchange mechanism. (Given that it is living donor's kidneys that are on exchange, one may not be able to simply "allocate" as with cadaver kidneys, but one must consider also the incentives of the kidney owners.) This is joint work with my advisor Prof. Itai Ashlagi.
Fair Allocation of Intensive Care Units (ICUs) between competing hospital programs:
Intensive Care Units (ICUs) represent an important but scarce resource in modern hospitals. Often there are competing patient care programs that require the ICU, such as the Emergency Department (ED), various surgical departments, and specialized quaternary care programs. In the last few years, there has especially been a rise in the quaternary care programs, which offer very complex procedures that require many weeks if not months of stay in the ICU. (The usual length of stay for medical and surgical patients is a few days.) It is on-going research how to allocate ICU among competing programs in a fair and effective way, to best serve the multiple goals of hospitals and satisfy all the stakeholders. This is joint work with Dr. Michael McManus from Boston's Children's Hospital.