What my research is about...
(more on the Research Blog)
History has taught us that the attempt to independently preserve the safety of individual parts of a financial system can potentially lead to the system as a whole becoming more unstable. As an example, regulation aimed at making individual banks more prudent can generate systemic risks by prompting deleveraging of riskier assets whose price impact may start spiralling dynamics, further depressing prices with the overall effect of increasing risk and spreading marked-to-market losses via overlapping portfolios.
This shift of paradigm in understanding systemic risks, whereby risks are conceived as endogenous to the system, has brought about a new understanding of the interaction between agents and market participants, the mechanisms responsible for risks amplification, and the channels through which financial contagion spreads, ultimately providing a new conceptual and analytical framework within which to design better (now macro-) prudential regulation.
One crucial characteristic of a network of interconnected agents is its topological structure: the degree to which financial exposures are concentrated plays a pivotal role in determining the extent to which financial contagion can spread through the system, turning even moderate exogenous distress event into a systemic one. My core work and research focus on the role of the network's topology in giving rise to systemic risk, in particular focusing on the design and evaluation of efficient macroprudential regulation and the associated implications for financial stability.
What my research was about...
Superfluidity is an exotic state of matter occurring in physical systems ranging from liquid helium to neutron stars to ultracold atomic gases. One curious feature of superfluidity is found in the way angular momentum is acquired: instead of spinning as rigid bodies do, superfluids acquire angular momentum by nucleating vortices which themselves carry angular momentum. All this is the product of the collective quantum mechanical behaviour of the atoms, how they move around and interact with each other, and it is very difficult to describe these large interacting systems exactly. For this reason a few approximations are in order to make progress. Probably one of the most important ones needed is the so-called mean-field approximation where the whole many-body system is approximated by an averaged one-body system. What one finds is an equation, known as the Gross-Pitaevskii equation, which describes the evolution of the superfluid.
Things are still not quite simple enough to solve this problem just using pen and paper. Instead, we use a computer to solve the problem numerically. One approach is to directly tackle the full confined system with many vortices numerically. But this approach, though often used, has its drawbacks. In particular, it can be very computationally intensive. We instead consider another limit which simplifies our calculations and from where we can understand what is going on.
Let's look at the problem a bit closer. First of all, what are we looking for? Often one is interested in the ground state of a system, namely the state with lowest energy. This is where things are often calm and tidy and one can observe some pattern or order. In our problem, we look for the ground state in a "non-inertial" reference frame which rotates with the superfluid. In this frame our problem translates to the question: what is the most stable arrangement of the quantum vortices?
Secondly, is there a regime in which we can extract more fundamental information and which at the same time simplifies things more? The limit we consider is the ideal case where one has an infinite number of vortices. It might sound like we are complicating things but actually if this infinite number of vortices is arranged in a periodic way, we can study only a single period of the system — also known as the unit cell — with only a few vortices. We are glossing over a few subtle aspects of this problem. For instance the wavefunction, which is what we are trying to compute, does not quite have the periodicity of the votex lattice. But this is the main idea.
To make things richer, one can then consider a system consisting of two interacting superfluids which are commonly made in the laboratory. Vortices in different superfluids interact in a very different way than vortices in the same superfluid interact. How do these vortices like to arrange? Will such configurations be periodic? In hope of shedding light on these questions and several others, we have developed a scheme to investigate nature a bit further.
In ultracold atomic gases, superfluidity often occurs thanks to a phenomenon called Bose-Einstein condensation. Here is a nice video explaining what we are talking about (credits to QuantumMadeSimple).