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Canonical quantization is not well suited to quantize gravity, while affine quantization is. For those unfamiliar with affine quantization the talk will include a primer. This procedure is then applied to deal with three nonrenormalizable, field theoretical, problems of increasing difficulty, the last one being general relativity itself.

Self-learning Monte Carlo (SLMC) method is a general-purpose numerical method to simulate many-body systems. SLMC can efficiently cure the critical slowing down in both bosonic and fermionic systems. Moreover, for fermionic systems, SLMC can generally reduce the computational complexity and speed up simulations even away from the critical points. For example, SLMC is more than 1000 times faster than the conventional method for the double exchange model in 8*8*8 cubic lattice. In addition, SLMC also provides a general framework to naturally integrate the advanced machine learning techniques into Monte Carlo. In this talk, I will give an introduction about the background, basic idea and the design principle of SLMC. Later, I will explicitly show how to use SLMC and its great accelerations in classic systems, free fermions coupled with classical spins systems, and interacting fermion systems. At the end, I will talk our recent developed a new type of neural network, which is motivated by the mean field theory and could be used to represent many physical Hamiltonians. We believe the new structural network would be highly efficient to identify different phases and accelerate the numerical simulations for even complex models.

I’ll discuss the issue of how we can tell which quantum state might be the “right “ one for inflationary quantum fluctuations. I’ll then use a new class of states that entangle curvature fluctuations with those of a spectator scalar field and discuss potential observational signatures of such states.