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Assuming exotic matter, several models representing static, spherically symmetric wormhole solutions of Einstein's field equations have been considered in the literature. We examine the dynamical stability of such wormholes in one of the simplest model, in which the matter is described by a massless ghost scalar field, and prove that all solutions are unstable with respect to linear fluctuations and possess precisely one unstable, exponentially in time growing mode. Numerical simulations of the nonlinear field equations suggest that these wormholes either expand or collapse and form a black hole. The stability problem for alternative models including electrically charged wormholes is also discussed.

For nearly the past century, the nature of dark matter in the Universe has puzzled astronomers and physicists. During the next decade, experiments will determine if a substantial amount of the dark matter is in the form of non-baryonic, Weakly-Interacting Massive Particles (WIMPs). In this talk I will discuss and interpret modern limits on WIMP dark matter from a variety of complementary methods. I will show that we are just now obtaining sensitivity to probe the parameter space of cosmologically-predicted WIMPs created during the earliest epoch in the Universe. I will discuss the science to extract from a positive signal in different experiments, and the prospects for an era of dark matter astrophysics.

It is well known that the ground state energy of many-particle Hamiltonians involving only 2- body interactions can be obtained using constrained optimizations over density matrices which arise from reducing an N-particle state. While determining which 2-particle density matrices are 'N-representable' is a computationally hard problem, all known extreme N-representable 2-particle reduced density matrices arise from a unique N-particle pre-image, satisfying a conjecture established in 1972. We present explicit counterexamples to this conjecture through giving Hamiltonians with 2-body interactions which have degenerate ground states that cannot be distinguished by any 2-body operator. We relate the existence of such counterexamples to quantum error correction codes and topologically ordered spin systems.

What lies beyond the Standard Model of particle physics? Are there very weakly interacting forms of matter and forces waiting to be discovered? In this talk I will describe some of the efforts underway to detect very weakly interacting particles, from dark matter to new forces. I will discuss recent observations and their theoretical significance as well as the connection to other experimental results. I will conclude with a short summary of the different frontiers and their interrelations.

Traditional condensed matter physics is based on two theories: symmetry breaking theory for phases and phase transitions, and Fermi liquid theory for metals. Mean-field theory is a powerful method to describe symmetry breaking phases and phase transitions by assuming the ground state wavefunctions for many-body systems can be approximately described by direct product states. The Fermi liquid theory is another powerful method to study electron systems by assuming that the ground state wavefunctions for the electrons can be approximately described by Slater determinants. From the encoding point of view, both methods only use a polynomial amount of information to approximately encode many-body ground state wavefunctions which contain an exponentially large amount of information. Moreover, another nice property of both approaches is that all the physical quantities (energy, correlation functions, etc.) can be efficiently calculated (polynomially hard). In this talk, I'll introduce a new class of states: (Grassmann-number) tensor-net states. These states only need polynomial amount of information to approximately encode many-body ground states. Many classes of states, such as Slater determinant states, projective states, string-net states and their generalizations, etc., are subclasses of (Grassmann-number) tensor-net states. However, calculating the physical quantities for these state can be exponentially hard in general. To solve this difficulty, we develop the Tensor-Entanglement Renormalization Group (TERG) method to efficiently calculate the physical quantities. We demonstrate our algorithm by studying several interesting boson/fermion models, including t-J model on a honeycomb lattice.