On tangents to quadric surfaces

We study the variety of common tangents for up to four quadric surfaces in projective three-space, with particular regard to configurations of four quadrics admitting a continuum of common tangents. We formulate geometrical conditions in the projective space defined by all complex quadric surfaces which express the fact that several quadrics are tangent along a curve to one and the same quadric of rank at least three, and called, for intuitive reasons: a basket. Lines in any ruling of the latter will be common tangents. These considerations are then restricted to spheres in Euclidean three-space, and result in a complete answer to the question over the reals: ``When do four spheres allow infinitely many common tangents?''.Comment: 50 page

Legitimacy and Expertise in Global Internet Governance

Over the course of the past decade or so, attention among Internet policymakers and scholars has shifted gradually from substantive design principles to the structure of Internet governance. The Internet Corporation for Assigning Names and Numbers in particular now faces a new skepticism about its legitimacy to administer the essential Internet Assigned Numbers Authority function. ICANN has responded to these doubts by proposing a series of major governance reforms that would bring nation-states more into the organization\u27s decisionmaking. After all, transnational governance institutions in other substantive areas privilege nation-states as a matter of course. This Symposium Essay shows that these changes reflect a new era in which ICANN and other Internet policymakers no longer view the Internet as uniquely immune from the geopolitics of the physical world

Back to the Future: Economic Self-Organisation and Maximum Entropy Prediction

This paper shows that signal restoration methodology is appropriate for predicting the equilibrium state of certain economic systems. A formal justification for this is provided by proving the existence of finite improvement paths in object allocation problems under weak assumptions on preferences, linking any initial condition to a Nash equilibrium. Because a finite improvement path is made up of a sequence of systematic best-responses, backwards movement from the equilibrium back to the initial condition can be treated like the realisation of a noise process. This underpins the use of signal restoration to predict the equilibrium from the initial condition, and an illustration is provided through an application of maximum entropy signal restoration to the Schelling model of segregation

Large NN limit of irreducible tensor models: O(N)O(N) rank-33 tensors with mixed permutation symmetry

It has recently been proven that in rank three tensor models, the anti-symmetric and symmetric traceless sectors both support a large $N$ expansion dominated by melon diagrams [arXiv:1712.00249 [hep-th]]. We show how to extend these results to the last irreducible $O(N)$ tensor representation available in this context, which carries a two-dimensional representation of the symmetric group $S_3$. Along the way, we emphasize the role of the irreducibility condition: it prevents the generation of vector modes which are not compatible with the large $N$ scaling of the tensor interaction. This example supports the conjecture that a melonic large $N$ limit should exist more generally for higher rank tensor models, provided that they are appropriately restricted to an irreducible subspace.Comment: 17 pages, 7 figure

Probing the scale of New Physics at the LHC: the example of Higgs data

We present a technique to determine the scale of New Physics (NP) compatible with any set of data, relying on well-defined credibility intervals. Our approach relies on the statistical view of the effective field theory capturing New Physics at low energy. We introduce formally the notion of testable NP and show that it ensures integrability of the posterior distribution. We apply our method to the Standard Model Higgs sector in light of recent LHC data, considering two generic scenarios. In the scenario of democratic higher dimensional operators generated at one-loop, we find the testable NP scale to lie within $[10,260]$ TeV at $95\%$ Bayesian credibility level. In the scenario of loop-suppressed field strength-Higgs operators, the testable NP scale is within $[28,1200]$ TeV at $95\%$ Bayesian credibility level. More specific UV models are necessary to allow lower values of the NP scale.Comment: 19 pages, 3 figures, cosmetic changes, matches journal version. Nuclear Physics B (2014