I am a theoretical, mathematical, and computational physicist. During my PhD, my research focused primarily on quantum gravity. My work included exploring the concept of relative locality in string theory and providing the first rigorous proof of a fundamental relationship between continuous and discrete spacetime geometries in loop quantum gravity. Working on quantum gravity has allowed me to develop a broad expertise in general relativity, quantum mechanics, quantum field theory, and related areas of mathematics.
More recently, my research has focused on the following topics:
Time and causality
I am interested in understanding the nature of time and causality in the context of general relativity and quantum mechanics. My main focus is on scenarios where causality may be violated, such as faster-than-light travel and time travel: are they possible in our universe, how exactly are they related to each other, and how can we resolve the associated paradoxes? My "Lectures on Faster-than-Light Travel and Time Travel", published in the peer-reviewed journal SciPost, provide an up-to-date, comprehensive, and self-contained review of the subject.
The main goal of this research is to enhance humanity's understanding of how time and causality work, which could then be used to expand and improve our fundamental theories of physics, and perhaps even gain a better understanding of quantum gravity. An exciting side effect is the possibility of turning what is usually considered pure science fiction into legitimate science, at least in principle – or given sufficiently advanced technology.
In "Time Travel Paradoxes and Multiple Histories", published in Physical Review D with my student Jacob Hauser, we rigorously proved that time travel paradoxes may be resolved by assuming the existence of multiple histories or timelines, and presented a new paradox resolution which combines the multiple-histories approach with the Novikov self-consistency conjecture.
This paper was the subject of an article in New Scientist magazine, and I also discussed it in an online seminar, available on YouTube. Currently, I am working on generalizing this paradox model with my student Jared Wogan, and on formulating a rigorous mathematical description of a spacetime with multiple histories with my student Michael Astwood.
In addition, with my student Mir Jalal, I explored the possibility of faster-than-light travel in our universe. I am currently working on this question from a new angle with my student Alicia Savelli, and on finding the exact conditions where faster-than-light travel can lead to time travel with my student Katie Curvelo.
Scientific computing
In symbolic computation, I am interested in implementing advanced concepts in mathematics and physics using computer algebra systems. I am the author of OGRe, an object-oriented general relativity package for Mathematica, intended to streamline and simplify symbolic calculations in general relativity and differential geometry, which I update and expand on a regular basis. I am also working on porting this package to Python.
In numerical computation, I am interested in writing high-performance software for scientific research using optimized algorithms, multithreading, cluster computing, GPU programming, and other modern techniques. My C++ thread pool class, which provides a robust, compact, and self-contained interface for enabling multithreading in high-performance scientific software, is one of my most popular open-source projects on GitHub. I am also working on C++ code for high-quality visualization of arbitrary spacetime metrics using relativistic ray tracing, for use in my own research and by other general relativity researchers.
One of my main goals is making scientific computing more user-friendly and accessible to both novice students and established researchers. For this purpose, I write software packages and libraries with special focus on producing clear, lightweight, thoroughly-documented, and easy-to-use code, which is made freely and publicly available on my GitHub page.