I have a firm belief that unstructured play is important for intellectual development. This is true both for small children and for grown up scientists! A lot of the projects listed here are ideas that I have "played" with, to varying degrees of success. They can all be described, if you want, as belonging to classical condensed matter and statistical physics.

**Theory of supercapacitors and electrochemical interfaces**

This line of research deals with describing the structure of electrochemical interfaces using ideas from the physics of correlated electron systems. When electrons have a sufficiently strong interaction with each other, they are crystallized by their mutual repulsion and form a "Wigner crystal". This arrangement is highly compressible, since electrons that avoid each other pay a lower energy cost when their density is increased.

Similarly, when charged ions are arranged at the interface with an electrode, they can form a crystal-like arrangement, and this arrangement is also highly compressible. The implication is that a large amount of charge can be stored at the interface for a relatively low driving voltage. In other words, the interface has a large capacitance, and therefore a great capacity for energy storage.

This general idea has found a number of applications to so-called "supercapacitors", which are energy storage devices that are designed to store energy like batteries without relying on any slow chemical reactions.

Relevant past publications:

*Model of large volumetric capacitance in graphene supercapacitors based on ion clustering*, BS, M. M. Fogler, and B. I. Shklovskii, Phys. Rev. B**84**, 235133 (2011).*Theory of volumetric capacitance of an electric double-layer supercapacitor*, BS, Tianran Chen, M. S. Loth, and B. I. Shklovskii, Phys. Rev. E**83**, 056102 (2011).*Non-mean-field theory of anomalously large double layer capacitance*, M. S. Loth, BS, and B. I. Shklovskii, Phys. Rev. E**82**, 016107 (2010).*Anomalously large capacitance of an ionic liquid described by the restricted primitive model*, M. S. Loth, BS, and B. I. Shklovskii, Phys. Rev. E 82, 056102 (2010).*Capacitance of the Double Layer Formed at the Metal/Ionic-Conductor Interface: How Large Can It Be?*, BS, M. S. Loth, and B. I. Shklovskii, Phys. Rev. Lett. 104, 128302 (2010).

**The "Price of Anarchy" in Congestible Networks**

Describing the routing of traffic through a congestible network -- such as cars in a road network or information through a computer network -- has long been the domain of game theory. Game theoretical ideas were first employed more than a century ago to show that "selfish" choices made by users in networks do not, in general, lead to optimal network flow. The degree of self-interest-driven suboptimality that arises in congsetible networks is dubbed the "price of anarchy" (POA), and predicting its severity is a difficult and in many cases urgently-studied problem.

I have become interested in trying to apply ideas from statistical physics to understand how and when large POA arises in congestible networks. My recent work has shown, in particular, that the POA becomes maximally large in a network when it is poised near a percolation threshold -- i.e., when its most efficient roads just barely connect across the system. Near this percolation point, the properties of the POA can be described using ideas from the theory of phase transitions in statistical physics.

I am interested now in understanding how universally this condition arises in real world networks, and whether a maximally large POA is in fact the most *natural* condition for a many-user network.

Relevant past publications:

*The price of anarchy is maximized at the percolation threshold,*BS, Phys. Rev. E**91**, 052126*The price of anarchy in basketball*, BS, Journal of Quantitative Analysis in Sports, Vol. 6, Iss. 1, Article 3 (2010).

*Understanding the "interaction law" in pedestrian crowds and social systems*

Large collections of humans or other animals often bear a surprising similarity to interacting particle systems. For example, they can exhibit features like vortices, shock waves, jamming transitions, and phase-separation instabilities. These visual similarities suggest the tantalizing possibility that "social" systems can be mapped onto "physical" systems, which would allow one to understand their dynamics by drawing on the huge repository of results and techniques in condensed matter physics.

A basic stumbling block for this idea, however, is that it is unclear how one should think about the "interaction law" between individuals in the group, which is the basic input for many-body theory in physics. In a series of ongoing works, I have been collaborating with researchers in computer science to consider the question of how to describe interactions between pedestrians in a crowd. Our key idea is that the strength of interactions between pedestrians is encoded in the quantitative form of their spatial correlations (as in the world of correlated electron physics). By adapting ideas and analysis techniques from statistical physics, we were able to identify a surprisingly simple and robust result. Namely, that the "interaction energy" between pedestrians in a crowd is proportional to the inverse square of their projected time to collision.

More broadly, the approach of measuring correlations in order to identify and quantify the form of the interaction law is a powerful one, and it has the potential for application across a wide set of social problems.

Relevant past publications:

*Universal power law governing pedestrian interactions*, Ioannis Karamouzas, BS, and Stephen J. Guy, Phys. Rev. Lett.**113**, 238701 (2014).- See also:

*Theory of optimal strategy in basketball*

The past six years or so have seen a huge shift in how quantitative thinking is applied to sports strategy. I have been somewhat involved in this "revolution", authoring a number of papers and giving a couple of (prize-winning) talks at the MIT Sloan Sports Analytics Conference. My works have generally focused on basketball, and have adopted ideas from game theory, statistical mechanics, and the theory of optimal stopping problems. One of my public-level talks is recorded here.

Relevant past publications:

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*Method for Using Player Tracking Data in Basketball to Learn Player Skills and Predict Team Performance*, BS and S. J. Guy, PLoS ONE 10(9): e0136393 (2015). *The price of anarchy -- on the roads and in football*, BS and Bradley P. Carlin, Significance**10**, 3, 25-30 (2013).*The problem of shot selection in basketball*, BS, PLoS ONE 7(1): e30776 (2012).*Scoring Strategies for the Underdog: A General, Quantitative Method for Determining Optimal Sports Strategies*, BS, Journal of Quantitative Analysis in Sports: Vol. 7: Iss. 4, Article 11 (2011).*The price of anarchy in basketball*, BS, Journal of Quantitative Analysis in Sports, Vol. 6, Iss. 1, Article 3 (2010).