A possible solution to the notorious sign problem for systems with non-zero chemical potential is to deform the integration region in the complex plane to a Lefschetz thimble. We introduce an easy to implement Monte Carlo algorithm to sample the dominant thimble, based on a contraction map on a thimble. We point out that manifolds other than Lefschetz thimble could be useful for numerical simulations. We describe a family of such manifolds, using the contraction map, that interpolate between the tangent space at one critical point (where the sign problem could be severe) and the union of relevant thimbles (where the sign problem is mild but a multimodal distribution function complicates the Monte Carlo sampling). We show how this works in a couple of models.

I will discuss nontrivial constraints on the spectrum and structure constants of 2D unitary CFTs from the associativity of OPE and modular invariance, and some implications for non-perturbative completions of gravity in AdS3.

Abstract: Axion stars, gravitationally bound states of low-energy axions, described by a field theory with potential energy f^2 m^2(1-Cos (A/f)) have a maximum mass allowed by gravitational stability. Weakly bound states obtaining this maximum mass have sufficiently large radii such that they are dilute, and as a result, they are well described by a leading-order expansion of the axion potential. Heavier states are susceptible to gravitational collapse. Inclusion of higher-order interactions, present in the full potential, can give qualitatively different results in the analysis of collapsing heavy states, as compared to the leading-order expansion. In this work, we find that collapsing axion stars are stabilized by repulsive interactions present in the full potential, providing evidence that such objects do not form black holes. These dense configurations, which are the endpoints of collapse, have extremely high binding energy, and as a result, quickly decay through number changing interactions.

On September 14, 2015, LIGO detectors picked up a gravitational wave signal coming from the merger of a binary black hole. This is the first direct detection of gravitational waves and the first observation of binary black hole and its merger. In this talk we will go over the key aspects of the discovery, and highlight some its implications for fundamental physics and astrophysics.