School of Natural Sciences

High-Energy Conformal Bootstrap and Tauberian Theory

Baurzhan Mukhametzhanov
Member, School of Natural Sciences, IAS
November 1, 2019

We analyze modular invariance drawing inspiration from tauberian
theorems. Given a modular invariant partition function with a positive
spectral density, we derive lower and upper bounds on the number of
operators within a given energy interval. They are most revealing at high
energies. In this limit we rigorously derive the Cardy formula for the
microcanonical entropy together with optimal error estimates for various
widths of the averaging energy shell. Finally, we identify a new universal

The Continuing Search for Planet Nine

Matthew Holman
Harvard-Smithsonian Center for Astrophysics
October 15, 2019

Several lines of evidence, both theoretical and observational, indicate that additional planets in the outer solar system remain to be discovered.  Most recently, attention has been focused on 'Planet Nine',a few Earth mass planet with a moderate inclination at a distance of a few hundred AU (Trujillo & Sheppard 2014, Batygin & Brown 2016, Brown & Batygin 2016).  I will review this evidence for the existence of this body and will present a variety of approaches that are being used to find it.