Department of Mathematics

Imperial College London

South Kensington Campus

London SW7 2AZ, UK.

samuel (dot) crew24 (at) imperial (dot) ac (dot) uk

I currently work on machine learning and quantum information theory. I am interested in a variety of problems ranging from path signatures and quantum many body systems to resurgence and holography.

My PhD research was in high energy physics and the geometry of (topological) quantum field theory. In this area, I am particularly interested in connections between supersymmetric gauge theories and geometric structures in the spirit of "physical mathematics".

I am also interested in differential/difference equations and applications of resurgence/Borel resummation in both quantum and classical physics and geometry.

Some more specific examples of past and present research interests include:

- Exact results in 3d N=4 topological QFT and 3d mirror symmetry.
- Integrability, enumerative geometry and geometric representation theory .
- TQFT, knots and resurgence.
- Path signatures, random matrices and quantum algorithms.
- Borel resummation and Stokes phenomenon in differential and difference equations.
- Classical free surface flows.

To summarise, I like using geometry to understand diverse phenomena in classical and quantum physics and I particular enjoy the challenge of working on problems that lie across traditional subject divides.

- S. Crew, D. Zhang and Z. Zhang -
*AdS4 Holography and the Hilbert Scheme*(hep-th/2408.10313) - C. J. Lustri, S. Crew and S. J. Chapman -
*Exponential Asymptotics using Numerical Rational Approximation in Linear Differential Equations.*The ANZIAM journal (2312.07773) - S. Crew, D. Zhang and B. Zhao -
*Boundaries & Localisation with a Topological Twist*(hep-th/2306.16448) - S. Crew, A. Goswami and R. Osburn -
*Resurgence of Habiro elements.*(In review) (math.NT/2304.07001) - S. Crew, J. Shelton and P. Trinh -
*Higher-Order Stokes Phenomenon in Singularly Perturbed ODEs.*(In review SIAP) (math.ca/2303.07866) - S. Crew and P. Trinh -
*Resurgent Aspects of Applied Exponential Asymptotics.*Studies in Appl. Math. (2208.07290) - S. Crew -
*Geometric Aspects of 3d N=4 Gauge Theories.*(PhD Thesis) - M. Bullimore, S. Crew, and D. Zhang -
*Boundaries, Vermas and Factorisation.*JHEP (2021) 263 (2010.09741) - S. Crew, N. Dorey and D. Zhang -
*Blocks and Vortices in the 3d ADHM Gauge Theory.*JHEP (2021) 234 (2010.09732) - S. Crew, N. Dorey and D. Zhang -
*Factorisation of 3d N=4 Twisted Indices and the Geometry of Vortex Moduli Space.*JHEP (2020) 08, 015 (2002.04573) - S. Crew and P. Trinh -
*New singularities for Stokes waves.*J. Fluid Mech. 798, 256-283 (1510.04254)

*"tbc"*- Invited conference talk, Eurostrings 24*"The Quantum Path Signature"*- Invited seminar talk at RIKEN, Saitama, Japan (Aug. 2024)*"An algbraic approach to parametric resurgence"*- Seminar talk at Tokyo Metropolitan University (July. 2024)*"Quantum path signatures"*- Invited seminar talk at OIST Okinawa. (July. 2024)*"Alebraic examples of parametric resurgence"*- Invited seminar talk at the University of Birmingham (May. 2024)*"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)*"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)*"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*"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)

A supervision with me as depicted by a student (artist credit @quantumcutie1228)

- MA30044: Mathematical Methods 1

- 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.

- 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)

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 spent 1.5 years as a postdoc working with Phil Trinh in the department of mathematical sciences at the University of Bath. Here I learnt about resurgence and Borel resummation. I worked on a range of problems in quantum and classical physics and geometry.

Following 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 am currently a postdoc in the department of Mathematics at Imperial College, London.