Samuel Crew
Department of Physics
National Tsing Hua University
Hsinchu
Taiwan
samuel (dot) c (dot) crew (at) gmail (dot) com
Research Interests
I’m an applied mathematician/physicist with broad interests across the physical sciences. My main expertise lie in geometry, asymptotic analysis and numerical methods. Recently, I’ve been particularly interested in problems at the intersection of machine learning and quantum computing: both using ML to study quantum systems and physical approaches to machine learning.
I’ve worked on a wide range of topics in classical and quantum physics—from water waves to holography, quantum field theory to knot theory, and mirror symmetry to lensing in radio astronomy, to give a few examples. I’ve been fortunate to work as a postdoc in mathematics, physics, and computer science departments, and I’m happiest uncovering geometric structures and applying sophisticated mathematical tools to problems that lie across traditional subject divides.
Some more specific examples of past and present research interests include:
- Rough path theory, path signatures and kernels.
- Quantum many body systems.
- Resurgence, Borel resummation and Stokes phenomena.
- 3d N=4 quantum field theory and mirror symmetry.
- Integrability, enumerative geometry and representation theory.
- Free surface flows and water waves.
I also enjoy collaborating with industry. I have worked as a machine learning / data science consultant and worked with Rigetti Computing during my time at Imperial College London.
Publications and Preprints
-
Quantum Path Signatures.
2508.05103 [quant-ph]
S. Crew, C. Salvi, W. F. Turner, T. Cass and A. Jacquier -
Magic Entropy in Hybrid Spin–Boson Systems.
2508.06018 [cond-mat]
S. Crew, Y. L. Li, H. H. Li and P. Y. Chang -
Learning Magic in the Schwinger Model.
2508.09640 [hep-th]
S. Crew and H. H. Lu -
An Algebraic Study of Parametric Stokes Phenomena. (In review)
2410.13690 [hep-th]
I. Aniceto and S. Crew -
AdS4 Holography and the Hilbert Scheme.
JHEP. 2408.10313 [hep-th]
S. Crew, D. Zhang and Z. Zhang -
Exponential Asymptotics Using Numerical Rational Approximation in Linear Differential Equations.
ANZIAM J. 2312.07773 [math.NA]
C. J. Lustri, S. Crew and S. J. Chapman -
Boundaries & Localisation with a Topological Twist.
JHEP. 2306.16448 [hep-th]
S. Crew, D. Zhang and B. Zhao -
Resurgence, Habiro Elements and Strange Identities.
Commun. Number Theory Phys. 2304.07001 [math.NT]
S. Crew, V. Fantini, A. Goswami, R. Osburn and C. Wheeler -
Higher-Order Stokes Phenomenon in Singularly Perturbed ODEs.
SIAM J. Appl. Math. 2303.07866 [math.CA]
S. Crew, J. Shelton and P. Trinh -
Resurgent Aspects of Applied Exponential Asymptotics.
Stud. Appl. Math. 2208.07290 [math.CA]
S. Crew and P. Trinh -
Geometric Aspects of 3d N=4 Gauge Theories.
PhD Thesis
S. Crew -
Boundaries, Vermas and Factorisation.
JHEP. 2010.09741 [hep-th]
M. Bullimore, S. Crew and D. Zhang -
Blocks and Vortices in the 3d ADHM Gauge Theory.
JHEP. 2010.09732 [hep-th]
S. Crew, N. Dorey and D. Zhang -
Factorisation of 3d N=4 Twisted Indices and the Geometry of Vortex Moduli Space.
JHEP. 2002.04573 [hep-th]
S. Crew, N. Dorey and D. Zhang -
New Singularities for Stokes Waves.
J. Fluid Mech. 1510.04254 [physics.fluid-dyn]
S. Crew and P. Trinh
Published in: Journal of High Energy Physics (JHEP), ANZIAM Journal, Communications in Number Theory and Physics, SIAM Journal on Applied Mathematics, Studies in Applied Mathematics and Journal of Fluid Mechanics.
Talks and lectures
2025
- "QML: Signatures, Diffusion, and Resurgent Asymptotics", Seminar, University of Luxembourg. (Sep 2025)
- "Quantum path signatures", Recent advances in rough path theory and signatures, Shanghai Tech. (Sep 2025)
- "Quantum path signatures", ACPMS seminar, Norwegian University of Science and Technology. (Sep 2025)
- "Magic entropy in hybrid systems", NCTS summer school, National Yang Ming Chiao Tong University. (Aug 2025)
- "Parametric resurgence", WKB, Monodromy, and Applications special topic seminar, NCTS, Taiwan. (June 2025)
- "Magic and Gaussianity", Strings seminar, National Taiwan University, Taiwan. (May 2025)
- "Learning quantum magic", Applied math seminar, St Andrew's, UK. (April 2025)
- "Quantum path signatures", CUHK, Hong Kong. (March 2025)
- "The quantum signature kernel", Random matrices and quantum machine learning workshop. NTHU, Taiwan. (Feb. 2025)
- "Matrix models and machine learning", 12th Bangkok hep-th workshop. Chulalonkorn University, Thailand (Jan. 2025)
2024
- "An algebraic approach to parametric resurgence", IHES, Paris (Dec. 2024, cancelled)
- "Matrix models and path signatures", National Tsing Hua University, Taiwan (Nov. 2024)
- "The Quantum Signature Kernel", RIKEN, Japan (Nov. 2024)
- "An algebraic approach to parametric resurgence", Higgs Centre Theoretical Physics, Edinburgh (Oct. 2024)
- "tbc" - Invited conference talk, Eurostrings 24
- "The Quantum Path Signature" - Invited seminar talk at RIKEN, Saitama, Japan (Aug. 2024)
- "An algebraic approach to parametric resurgence" - Seminar talk at Tokyo Metropolitan University (July. 2024)
- "Quantum path signatures" - Invited seminar talk at OIST Okinawa. (July. 2024)
- "Algebraic examples of parametric resurgence" - Invited seminar talk at the University of Birmingham (May. 2024)
2023
- "Analytic continuation for children" - Seminar talk at Exact Asymptotics OIST (Oct. 2023)
- "Parametric resurgence and Borel resummation" - Seminar at National Taiwan University (Oct. 2023)
- "Hemisphere blocks of 3d N=4 gauge theories" - Seminar NCTS at National Tsing Hua University, Taiwan (Oct. 2023)
- "A minimal example of higher order Stokes phenomenon" - Symposium talk at Exact Asymptotics program OIST, Japan (Sept. 2023)
- "A minimal example of higher order Stokes phenomenon" - Seminar at Tokyo Metropolitan University (Sept. 2023)
- "Resurgence for computer scientists" - Seminar talk at RUB (June. 2023)
- "Vortex counting, WKB, and the higher order Stokes phenomenon" - Seminar talk at OIST quantum gravity (Mar. 2023)
2022
- "Resurgence in a toy water wave model" - Seminar talk at UEA (Dec. 2022)
- "Practical parametric resurgence" - Invited talk at INI ARA program (Nov. 2022)
- "Parametric resurgence in nonlinear differential equations" - Seminar at University College Dublin (Oct. 2022)
- "Parametric resurgence and large N vortex counting" - Seminar at OIST Japan (August 2022) - slides
- "Resurgence in quantum field theory" - 3x1 hour lecture series at Tokyo Metropolitan University (August 2022) - outline
- "Resurgence, exponential asymptotics and pathologies in toy water waves problems" - Bath water waves symposium (June 2022)
- "Resurgence and exact WKB" - BAMC, Loughborough (April 2022)
2021
- "Stokes phenomena and Borel resummation" - Lecture at UEA (November 2021)
- "Gauge theory, integrability and curve counting" - Bath algebra, geometry and number theory seminar (May 2021) - slides
- "What is quantum field theory?" - ARA INI Program mini-course
- "Hemisphere blocks in 3d N=4 theories" - Fudan university (Mar. 2021) - watch
pre 2021
- "Factorisation and Vortices in 3d N=4 Theories" - Kavli IPMU (Nov. 2020) - slides
- "Boundaries, Vermas and Factorisation" - Imperial quiver seminar (Nov. 2020)
- "Quivers, Spin Chains and Black Holes" - DAMTP, Cambridge (Jun. 2018)
- "New singularities for Stokes' waves" - BAMC, Oxford (2016)
Teaching
A supervision with me as depicted by a student (artist credit @quantumcutie1228)
NTHU 2025
- Lecturing. Graduate course on quantum machine learning. 8 x 1 hour lectures. Course webpage.
- Supervision. Masters student project supervision. (Learning magic in the Schwinger model with Hsueh-Hao Li.). LMS summer project student supervision. (Resurgence and duality in quantum field theory with Agastyaa Vishvanath and co-supervised with Josh Shelton).
RUB 2023-2024
Led and assessed two student seminar series.
Bath 2021-2022
Co-lectured 2nd year mathematical methods course with Phil Trinh.
- MA30044: Mathematical Methods 1
Cambridge 2016-2021
Small group teaching (15-20 students) and student supervisions (2-3 students). Example classes and assessing student work.
- Classical Dynamics (Part II) Michaelmas 16-17, 17-18, 18-19.
- General Relativity (Part II) Lent 16-17, 17-18.
- Symmetries, Fields and Particles (Part III) Michaelmas 17-18, 18-19, 19-20.
- Mathematical Methods (Part IA Nat. Sci.) 17-18, 18-19, 19-20.
- Mathematical Methods (Part IB Nat. Sci.) 17-18, 18-19, 19-20.
- Quantum Field Theory (Part III) Michaelmas 20-21.
Student reference letters available.
Events
* - served as organiser.
- September 2025 - Invited speaker, workshop on "Recent advances in rough path theory and path signatures". Shanghai Tech.
- August 2025 - NCTS summer school on frontier numerical and analytic approaches to low-dimensional strongly correlated electron systems, NYCU, Taiwan. Invited speaker.
- July 2025 - Research in groups with Ines Aniceto and Job Feldbrugge at ICMS Edinburgh.*
- March 2025 - Visit Omar Kidwai, Chinese University Hong Kong.
- February 2025 - Matrix models and machine learning workshop. NTHU, Taiwan.*
- February 2025 - Visit Masazumi Honda and Akinori Tanaka at RIKEN, Tokyo.
- January 2025 - 12th Bangkok workshop on high-energy theory. Chulalongkorn University, Thailand.
- November 2024 - KIAS-APCTP Frontiers of Theoretical Physics workshop. Jeju Island, Korea.
- November 2024 - Workshop on Applications of Machine Learning and Artificial Intelligence for Physics and Chemistry Problems, National Taiwan University.
- Summer 2024 - Visiting researcher at RIKEN, Japan. Quantum field theory and quantum simulation.
- May 2024 - Workshop on Resurgence and Modularity in QFT and String Theory at GGI, Italy.
- Autumn 2023 - Exact Asymptotics: From Fluid Dynamics to Quantum Geometry. OIST, Japan.*
- October 2023 - Research visit to NTU, Taiwan (Heng-Yu Chen)
- September 2023 - Research visit to YITP, Kyoto (Masazumi Honda)
- September 2023 - Research visit to TMU, Japan (Akira Shudo)
- March 2023 - Quantum Information Theory School. ICMAT, Madrid.
- February 2023 - Quantum Information Processing. Ghent, Belgium.
- September 2022 - Isaac Newton Institute program on applicable resurgent asymptotics (part 2)
- October 2022 - Research visit to UCD Ireland (Robert Osburn)
- July 2022 - University of Bath water waves symposium.
- Various 2022 - Japan: Tokyo metropolitan university, OIST and Kyoto university.
- April 2022 - British Applied Math Conference (Loughborough)
- July 2021 - IHES summer school on enumerative geometry.
- April-June 2021 - Isaac Newton Institute program on applicable resurgent asymptotics (part 1)
CV
I completed my PhD at DAMTP and Trinity college, Cambridge UK in 2021. I studied geometric aspects of quantum field theory and I was supervised by Nick Dorey. Before Cambridge, I was an undergraduate at Lincoln college, Oxford where I studied first for a BA in mathematics (2012-2015) and then an MMathPhys in mathematical and theoretical physics (2015-2016).
Following my PhD, I worked with Phil Trinh as a postdoc in the department of mathematical sciences at the University of Bath. I learnt about resurgence and Borel resummation and worked on a variety of problems in quantum and classical physics and geometry. After my first postdoc, I moved to Bochum, Germany in January 23 to work with Michael Walter and Giulio Malavolta in the computer science department of Ruhr University Bochum and the Max Planck institute for security and data privacy. I worked on a range of exciting problems in quantum information theory and quantum cryptography. I then moved to the mathematics department of Imperial College London where I worked with Cris Salvi and Jack Jacquier on path signatures and quantum machine learning.
I am currently a postdoc in the physics department at National Tsing Hua University, Taiwan mentored by Po-Yao Chang.
