Physics

We develop a Machine-Learning Renormalization Group (MLRG) algorithm to explore and analyze many-body lattice models in statistical physics. Using the representation learning capability of generative modeling, MLRG automatically learns the optimal renormalization group (RG) transformations from self-generated spin configurations and formulates RG equations without human supervision. The algorithm does not focus on simulating any particular lattice model but broadly explores all possible models compatible with the internal and lattice symmetries given the on-site symmetry representation. It can uncover the RG monotone that governs the RG flow, assuming a strong form of the $c$-theorem. This enables several downstream tasks, including unsupervised classification of phases, automatic location of phase transitions or critical points, controlled estimation of critical exponents, and operator scaling dimensions. We demonstrate the MLRG method in two-dimensional lattice models with Ising symmetry and show that the algorithm correctly identifies and characterizes the Ising criticality.

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Advanced subjects and complicated applications. Applications to the interacting theories. Appelquist and Carazzone theorem in QED. Decupling of massive degrees of freedom in polynomial higher derivative quantum gravity: mixed diagrams. Non-local theories of quantum gravity. On the possibility of the universal IR limit in quantum gravity

Beyond Einstein’s theory. Higher derivative theories of Gravity. Singularities and black holes. Models of Inflation. Consistency checks. Kallen-Lehmann representation. Horava-Lifshitz theories. Infrared problems. Other approaches.

In this talk I will describe recent proposed experimental setups developed to test the quantum nature of gravity and how they can be used to test different quantum theories. After a brief overview of the motivations behind those setups, I will show how, in the context of canonical quantum gravity, one can derive quantum gravitational corrections for an approximate Schrödinger equation for matter fields in a fixed background. The corrections can be non-linear and non-Hermitian, which poses a series of problems. I will focus on the non-Hermitian terms, their interpretation and their possible observational consequences in different scenarios. I will then describe the differences in the pilot-wave approach to quantum gravity, how it offers a natural interpretation for the corrections in terms of the Quantum Equilibrium Hypothesis and a path for deriving the effects of such corrections in tabletop experiments. If there is time, I will comment on the nonlinear modifications of the Schrödinger equations, on a recent attempt to introduce them in the path integral formalism of EFT quantum gravity in a consistent manner (Correlated Worldline Theory) and on their phenomenological consequences.

Basic calculations and basic results. One-loop Feynman diagrams and derivation of the nonlocal form factors for the two-point function. High-energy and low-energy limits. Quadratic decoupling in the IR. Curved-space calculation using the heat-kernel solution. Applications to the fourth-derivative terms in the one-loop effective action of gravity

Presented in collaboration with Navigating Quantum and AI Career Trajectories: A Beginner’s Mini-Course on Computational Methods and their Applications

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Deeptech or science-based innovations often spend more than a decade percolating within academic and government labs before their value is recognized (Park et al., 2022). This development lag time prior to venture formation is only partly due to technological development hurdles. Because science-based inventions are often generic in nature (Maine & Garnsey, 2006), meaning that they have broad applicability across many different markets, the problem of identifying a first application requires the confluence of deep technical understanding with expert knowledge of the practice of commercialization. This process of technology-market matching is a critical aspect of the translation of science-based research out of the lab (Pokrajak 2021, Gruber and Tal, 2017; Thomas et al, 2020, Maine et al, 2015) and is often delayed by a lack of capacity to identify, prioritize and protect market opportunities. Typically, deeptech innovations can take 10-15 years of development, and tens (or even hundreds) of millions of dollars of investment to de-risk before a first commercial application (Maine & Seegopaul, 2016). Academics seeking to commercialize such inventions face the daunting challenge of competing for investment dollars in markets that are ill suited to the uncertainty and timescales of deep tech development. The time-money uncertainty challenge faced by science-based innovators is compounded by the fact that most of the scientists and engineers with the world-leading technical skills required to develop science-based inventions, lack innovation skills training, and so cannot navigate the complexities of early and pre-commercialization development critical to venture success. Some researchers, having developed a mix of technical and business expertise, have demonstrated a long-term ability to serially spin out successful ventures (Thomas et al., 2020). Entrepreneurial capabilities, which can be learned, enable scientistentrepreneurs to play formative roles in commercialising lab-based scientific inventions through the formation of well-endowed university spin-offs. (Park et al, 2022; 2024). Commercialization postdocs, when supported by well designed training, stipends, and de-risking supports, can lead the mobilization of fundamental research along multiple commercialization pathways. Recommendations are provided for scholars, practitioners, and policymakers to more effectively commercialise deeptech inventions.

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Covariant Formalism. Perturbation theory. Gauge fixing. Becchi Rouet Stora Tyutin symmetry and diffeomorphism invariance. One loop and two loop ultraviolet divergencies. Renormalization problems. Euclidean gravity. Gravitational instantons.