Personal page for Nathan Carruth (卢天赐的个人网页)

Welcome! 欢迎光临!

中文

Brief biography

Since November 2024, I have been a postdoc at the Shenzhen International Center for Mathematics at the Southern University of Science and Technology in Shenzhen, China. My advisor is Shijie Dong.

From 2021 through 2024 I was a postdoc at the Yau Mathematical Sciences Center at Tsinghua University in Beijing, China. My advisor was Pin Yu.

I completed my PhD in mathematics under Spyros Alexakis at the University of Toronto in November 2020. My thesis constructed localized solutions to the Einstein vacuum equations in U(1) symmetry. I previously studied physics at UC Berkeley and the Space Sciences Lab, mathematics and physics (Part III Maths) at the University of Cambridge, and mathematics and physics at Utah State University, where I completed a Master's thesis on foundations for a model of quantum time in 2 dimensions under Charles Torre.

More details are in my CV.

Research interests

My main research area at present is mathematical general relativity. In particular, at present I am working on simplifying the use of Demetrios Christodoulou's ‘‘short-pulse ansatz’’ (see, e.g., here), with a goal to make the resultant trapped-surface formation results more easily and broadly applicable. A draft of some early results of this research program is in my recent preprint, in which I was able to show that the involved energy estimates usually associated with applications of the short-pulse ansatz can be avoided entirely and replaced with a simple application of the classical existence and smoothness results of Rendall together with a scaling argument similar to that in my PhD thesis, extended to spherical geometry. I believe that this method should be readily applicable to many new areas. I am interested in particular in extending these methods to apply to nonspherical collapsing shells with an eye towards gaining new insight into the so-called hoop conjecture of Kip Thorne.

I am also interested in mathematical knowledge management (see, e.g., this paper for an introduction). In investigating optimal encodings for Unicode in limited character sets, I obtained some minor results on solid codes which are in here.

In the past I also conducted research in focused ultrasound, mathematical neuroscience, auroral plasma physics, and spacecraft electrical antenna rheometry (see, e.g., this paper: Cassini model rheometry, by Rucker et al.).

A more detailed overview of some of my past research work is available here.

Papers and preprints

Preprints
Trapped surface formation via radial boosts (August 2026)
Error-detecting solid codes (March 2026)
Squeezing a fixed amount of gravitational energy to arbitrarily small scales, in U(1) symmetry (with Spyros Alexakis, June 2024)
Research papers
The Solar Probe Plus Radio Frequency Spectrometer: Measurement requirements, analog design, and digital signal processing (by Marc Pulupa, et al.; my contribution was to estimate the radio properties of the antennas using rheometry, and probably impacted perhaps two lines of the paper)

During my time at Tsinghua I also was responsible for producing interview transcripts and occasional translations from Chinese of articles by S.-T. Yau. While most of these are paywalled, the interview I conducted with Olivia Caramello during the 2023 ICBS, on topos theory (see, e.g., this) and related matters, is available on Professor Caramello's blog here.

Talks and other presentations

A brief summary of my research for a job interview in early September 2026 is available here.

ICGAC 16: Trapped surface formation: physical foundations. Slides.

Teaching

Southern University of Science and Technology
I organized and taught a course in aspects of mathematical general relativity in fall 2025, which gave an introduction to black hole solutions and their geodesics and some background in spinors, among other things. At some point I aim to write up some notes.
Tsinghua University
I organized a discussion course on categorical logic and topos theory in fall 2023. Again, at some point I hope to write up some notes of what was discussed.
University of Toronto
Complex variables (MAT334), summer 2020 (online). A single PDF file containing all lecture notes, homework assignments, and tests is here. A partial typescript of the textbook used for the course, Goursat's Functions of a Complex Variable, is available here.
Partial differential equations (APM346), summer 2019. A single PDF file containing all of the lecture notes, homework assignments, tests, etc., is available here.

Other

My ORCiD is 0000-0001-8026-6084.

In 2024 I worked directly with Bong Lian to help coordinate and run that year's ICBS.

Archives from my time at the University of Toronto are available here.