I am looking for a PhD student to work with me at LSE.

See my research and publications pages for an idea of my research interests, which lie primarily in fundamental mathematical aspects of algorithms and discrete optimization. Below are some indicative potential directions (but this is by no means an exhaustive list).

• Network connectivity. Given a network, and a specified subset of nodes in the network called terminals, a very basic network design problem is the Steiner tree problem— find the cheapest way of connecting the terminals. There is a lot we still do not understand about this seemingly basic problem!
• Network design under uncertain demands. What is the best way of building a communication or transport network to handle varied and uncertain demand patterns? The robust network design model provides one framework for considering these problems, and there are many challenging but beautiful open problems in this area.
• Network flow algorithms. Flow problems, such as maximum flow, minimum cost flow, and generalized flow, are amongst the most fundamental and classical ones in combinatorial optimization. Finding better algorithms – faster, simpler, “strongly polynomial” – is an important and popular pursuit.
• Dynamic traffic models. A seemingly “simple” model of traffic is the following. We have a road network; each road has a fixed travel time, but also a fixed capacity. Traffic is modeled as a time-varying flow, and if the amount of flow trying to enter a particular road at a particular moment in time exceeds its capacity, a queue grows on that road, increasing the time required to traverse the road. A main goal is then to understand equilibrium behaviour in this model. Equilibria turn out to have a fascinating combinatorial structure, and some very basic questions are completely open.

### Conditions and application procedure

The position is in the Department of Mathematics. We have a substantial Operations Research group (other faculty are Laci Vegh, Greg Sorkin, Giacomo Zambelli, Ahmad Abdi and Katerina Papadaki), with close ties to both the Game Theory and Discrete Mathematics group (e.g., we have a joint seminar).

The position comes with an LSE studentship; this can be augmented by doing some teaching for the department. Much more information can be found here.

The deadline is April 29th. Before making a formal application (see here), we recommend potential applicants send an informal enquiry to Enfale Farooq (e.farooq@lse.ac.uk) as soon as possible. Informal enquiries should include a CV, unofficial transcripts, and (optionally) published papers, manuscripts, or dissertations.

The formal application requests a research proposal. For this application, a full research proposal is not required. Applicants may instead include a short (approximately 1 page) discussion of a research problem, or more broadly a research area, that they find particularly interesting. This may relate to a topic mentioned above, or to previous work the candidate has done, or to anything else. It does not need to indicate a project of the scale needed to complete a PhD, and is primarily an opportunity to illustrate an appetite for research.