Talks

In this talk I will review the construction of space starting purely from quantum mechanics and without assuming that the notion of space is attached to a preconceived notion of classical reality. I will show that if one start with the simplest notion of a quantum system encoded into the Heisenberg group algebra one naturally obtain a  notion of space that generalizes the usual notion of Euclidean space. Along the way I will try to illustrate how this notion is in a way going back to the roots of the discovery of QM by Heisenberg-Born-Jordan which never made it past the original papers and giving a critical reading of the subsequent interpretation of space and QM that were put forward by Schrodinger and von Neumann. The notion of space that emerge from quantum mechanics is naturally modular in the sense of Aharonov, it also naturally possess a built-in length scale and renders possible to assign a new notion of locality to non-local superpositions. I will illustrate how  such space can allow reconciliation of relativity with the presence of a fundamental scale.

I will show how to construct such spaces following the original analysis by Mackay and also show that such modular spaces possess a beautiful geometrical structure that generalizes Riemanian geometry to phase space. A geometry we have named Born geometry. I hope this will open wild speculations on the nature of locality in the presence of quantum mechanics and more broadly the nature of classical reality viewed from a quantum perspective.

We study the effective twisted superpotential of 3d N=2 gauge theories compactified on a circle.  This is a rich object which encodes much of the protected information in these theories.  We review its properties, and survey some applications, including the algebra of Wilson loops, computation of supersymmetric partition functions on S^1 bundles, and the reduction of 3d dualities to two dimensions.

We introduce a simple and modern discussion of rotational superradiance based on quantum field theory. We work with an effective theory valid at scales much larger than the size of the spinning object responsible for superradiance. Within this framework, the probability of absorption by an object at rest completely determines the superradiant amplification rate when that same object is spinning. We first discuss in detail superradiant scattering of spin 0 particles with orbital angular momentum l = 1, and then extend our analysis to higher values of orbital angular momentum and spin. Along the way, we provide a simple derivation of vacuum friction—a “quantum torque” acting on spinning objects in empty space. Our results apply not only to black holes but to arbitrary spinning objects. We also discuss superradiant instability due to formation of bound states and, as an illustration, we calculate the instability rate Γ for bound states with massive spin 1 particles.

Quantum groups from character varieties
Abstract: The moduli spaces of local systems on marked surfaces enjoy many nice properties. In particular, it was shown by Fock and Goncharov that they form examples of cluster varieties, which means that they are Poisson varieties with a positive atlas of toric charts, and thus admit canonical quantizations. I will describe joint work with A. Shapiro in which we embed the quantized enveloping algebra U_q(sl_n) into the quantum character variety associated to a punctured disk with two marked points on its boundary. The construction is closely related to the (quantized) multiplicative Grothendieck-Springer resolution for SL_n. I will also explain how the R-matrix of U_q(sl_n) arises naturally in this topological setup as a (half) Dehn twist. Time permitting, I will describe some potential applications to the study of positive representations of the split real quantum group U_q(sl_n,R)

It is a common expectation in quantum gravity that the fundamental nature of space-time would be radically different from the smooth continuum of classical general relativity. In this talk it shall be shown that a quantum modification from loop quantum gravity crucial for singularity resolution is also responsible for deforming the underlying space-time in a manner which cannot be realized using classical geometric structures. With the minimum requirement that the quantum theory satisfies a well-defined notion of covariance explicit midisuperspace models manifesting such non-Riemannian space-times shall be shown to exhibit the physical phenomenon of non-singular signature change. Robustness and implications of this effect shall also be briefly discussed.