Talks

The idea behind an intersection between loop quantum gravity and noncommutative geometry is to combine elements of unification with a setup of canonical quantum gravity. In my talk I will first review the construction of a semi-finite spectral triple build over an algebra of holonomy loops. Here, the loop algebra is a noncommutative algebra of functions over a configurations space of connections, and the interaction between the Dirac type operator and the loop algebra captures information of the kinematical part of canonical quantum gravity. Next, I will show how certain normalizable, semi-classical states are build which connects the spectral triple construction to the Dirac Hamiltonian in 3+1 dimensions. Thus, these states can be interpreted as one-particle fermion states in an ambient gravitational field. This analysis indicates that the spectral triple construction involves matter degrees of freedom.

Physicists have been working for banks and hedge funds on applied problems in finance for more than two decades, and recently have doing academic research as well. This talk will survey academic research by physicists and contrast it with mainstream economics. I will argue that the difference comes not from the application of alternative techniques or new mathematics, but rather from fundamental differences in what questions are considered interesting and how one should go about solving them. This will be illustrated with a simple model for how systemic risks and extreme price movements are generated by the use of leverage (buying with credit). The current financial crisis illustrates that the economy is indeed a complex system, and that new approaches are needed that properly take this into account.