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Cosmology in the 21st Century

Revolutionary progress has been achieved in the science of cosmology over the past 30 years. Powerful experiments, made possible by new technologies, have transformed our understanding of the universe. We have unveiled the laws of physics that govern time and space on the grandest scales, from the big bang to present day.

The universe, we’ve learned, is full surprises. For instance, dark matter – the invisible gravitational glue that permeates the vast majority of the universe – remains one of the greatest unsolved puzzles of astrophysics. Nor do we yet fully understand the quantum mechanical nature of the big bang, or the universe’s current transition into a new stage of rapid expansion.

Perhaps most surprising is how remarkably simple these phenomena are to describe, yet so vexing to comprehensively explain.  But as the pace of discovery continues to accelerate, so too will our ability to decode these grandest of puzzles.

During his public lecture, Perimeter Institute cosmologist Kendrick Smith will take the audience on a journey of discovery through the expanding universe, from the big bang to our present-day understanding of dark matter and other cosmic phenomena. He will explore the yet-unsolved mysteries of the universe, and explain how new research aims to shed light on these deep questions.

The Elitzur-Vaidman bomb tester allows the detection of a photon-triggered bomb with a photon, without setting the bomb off. This seemingly impossible task can be tackled using the quantum Zeno effect. Inspired by the EV bomb tester, we define the notion of "bomb query complexity". This model modifies the standard quantum query model by measuring each query immediately after its application, and ends the algorithm if a 1 is measured.

We show that the bomb query complexity is asymptotically the square of the quantum query complexity. Moreover, we will show how this characterization inspires a general theorem relating classical and quantum query complexity, and derive new algorithms from this theorem.

The entanglement spectrum, i.e. the logarithm of the eigenvalues of reduced density matrices of
quantum many body wave functions, has been the focus of a rapidly expanding research endeavor recently.
Initially introduced by Li & Haldane in the context of the fractional quantum Hall effect, its usefulness has been
shown to extend to many more fields, such as topological insulators, fractional Chern insulators, spin liquids,
continuous symmetry breaking states, etc.
After a general introduction to the field we review some of our own contributions to the field, in particular the
perturbative structure of the entanglement spectrum in gapped phases, the entanglement spectrum across the
Mott-insulator transition in the Bose-Hubbard model, and the relation of the entanglement spectrum of
(1+1) dimensional quantum critical systems to the operator content of their underlying CFT.

Recent research has suggested deep connections between geometry and entropy. This connection was first seen in black hole thermodynamics, but has been more fully realized in the Ryu-Takayanagi proposal for calculating entanglement entropies in AdS/CFT. We suggest that this connection is even broader: entropy, and in particular compression, are the fundamental building blocks of emergent geometry. We demonstrate how spatial geometry can be derived from the properties of a recursive compression algorithm for the boundary CFT. We propose a general algorithm for constructing MERA-like tensor networks and elucidate connections to the mathematical field of integral geometry.