A pdf version of my detailed research statement can be found here: research-statement
My research has spanned several major themes of contemporary theoretical physics. These include:
|Quantum many body phenomena||Quantum hall effect, superconductivity, phases of the Hubbard model, DMRG, matrix & tensor product states|
|Classical & Quantum Gravity||Cosmology, holographic superconductors, thermodynamic geometry of black holes, loop quantum gravity (LQG), AdS/CFT|
|Machine Learning||Deep learning & neural networks via PyTorch & Theano|
My primary research interest lies in the field broadly referred to as quantum gravity. I did my graduate training at Pennsylvania State University, under Prof. Stephon Alexander and Prof. Martin Bojowald. My graduate work involved applying ideas from many-body phenomena – in particular, the formation of superconducting fermionic condensates (arXiv:hep-th/0609066, arXiv:hep-th/0702064) – in order to solve the cosmological constant problem.
While at Penn State I was also able to learn about Loop Quantum Gravity, which is considered the main competetitor to String Theory as a candidate theory of quantum gravity. With my collaborator Sundance Bilson-Thompson, I have written an introductory text on LQG, titled LQG for the Bewildered, published in 2017 by Springer Nature.
Other than LQG-inspired approaches to quantum gravity, I am also interested in and have made forays into several other areas of theoretical physics: quantum computation (arXiv:1307.0096), phase transitions in charged anti-deSitter black holes (arXiv:1312.7119, arXiv:1805.11053), tensor networks and matrix product states applied to loop quantum gravity (forthcoming work).
While it may appear that I am interested in many seemingly disjointed areas of theoretical physics, there is a common thread which runs through all my work – the desire to understand how best to formulate a complete, consistent theory of quantum gravity. For this purpose I have employed various tools from quantum information, many body physics and canonical quantum gravity. The shared motivation behind all of my work has been to understand how our smooth, classical spacetime arises from an underlying quantum substrate which might take the form of a tensor network or a Hubbard model on an abstract lattice. Of course, no theory of quantum gravity can be considered complete if it does not incorporate the particles of the standard model and their associated interactions. Therefore my work has also focused on trying to understand how elementary particles can be embedded within loop quantum gravity (arXiv:1002.1462), the relationship between elementary particles and quantum computation (arXiv:1307.0096) and the emergence of non-abelian gauge fields from defects in spin-networks (arXiv:1309.0652).