Dr Joseph Tooby-Smith

Postdoctoral Associate in the high-energy theory group at Cornell University.

 My legal name is: Joseph Smith.


 Useful links to some of my profiles:

Research Interests (summary)

The common theme in all my research is the application of techniques in pure mathematics to solve problems in particle physics. 

The first main area I study is gauge theories, and extensions of the Standard Model gauge algebra. This includes semi-simple extensions or u(1) extensions, and their classification. 

The second main area I study is the application of category theory to particle physics. Unlike e.g. group theory, category theory is not in the standard physicists curriculum. However, just because of this, it does not mean it is not the right language to frame problems in physics.

Academic history

2012-2014: High school, York 6th Form college 

As-level: Biology A. 

A-level: Physics A*, Maths A*, Further Maths A*, Additional Further Maths A*, Chemistry A*. (see here)

2014-2018: Undergrad/Masters, Oxford University, Christ Church College:

MMathPhys (with initial three years on MPhys): Distinction/First Class (double classification)

2018-2021: PhD, Cambridge University, Robinson College and Cavendish Laboratory

Doctor of Philosophy (PhD): Arithmetical, geometrical, and categorical forays into particle physics.

2021-: Postdoc, Cornell University

Hans Bethe Postdoctoral Associate in the high-energy theory group in the Cornell Laboratory for Accelerator-based Sciences and Education (CLASSE)


Recorded seminars



  1. Davighi, J., Gripaios, B.,  and Tooby-Smith, J., Quantum mechanics in magnetic backgrounds with manifest symmetry and locality. Journal of Physics A. arXiv:1905.11999,

  2. Allanach, B., Gripaios, B.,  and Tooby-Smith, J., Solving local anomaly equations in gauge-rank extensions of the standard model. Physical Review D. arXiv:1912.10022,

  3. Allanach, B., Gripaios, B.,  and Tooby-Smith, J., Geometric General Solution to the U(1) Anomaly Equations. arXiv:1912.04804,

  4. Cohen, T., Craig, N., Koren, S., McCullough, M., and Tooby-Smith, J., Supersoft Top Squarks. arXiv:2002.12630,

  5. Allanach, B., Gripaios, B.,  and Tooby-Smith, J., Anomaly cancellation with an extra gauge boson. arXiv:2006.03588, (See also:

  6. Davighi, J., McCullough, M., and Tooby-Smith, J., Undulating Dark Matter. arXiv:2007.03662,

  7. Allanach, B., Gripaios, B.,  and Tooby-Smith, J., Semisimple extensions of the Standard Model gauge algebra. arXiv:2104.14555,

  8. Gripaios, B., and Tooby-Smith, J., Inverse Higgs phenomena as duals of holonomic constraints. arXiv:2103.08923,

  9. Allanach, B., Madigan, M., and Tooby-Smith, J., A nu Supersymmetric Anomaly-free Atlas. arXiv:2107.07926, (see also:


  1. Davighi, J., and Tooby-Smith, J., Electroweak flavour unification. arXiv:2201.07245

Prizes and awards

  • 2014: Principal’s Prize (York College)

  • 2014/2015-2016/2017: Scholarships (Christ Church College, Oxford)

  • 2015/2016: The Scott Prize for performance in the Physics Part A examination (Oxford University)

  • 2016: Collections Prize (Christ Church College, Oxford)

  • 2016/2017: The Scott Prize for best performance in the MPhys Part B examination (Oxford University)

  • 2016/2017 (awarded 2018): Clifford Smith Prize (Christ Church College, Oxford)

  • 2017/2018: Prize for the Best Results on the Oxford MMathPhys (Oxford University)

  • 2018: Honorary Vice-Chancellor’s Award (Cambridge University)

  • 2017/2018: Hooke Prize (Christ Church College, Oxford)

    • ​“This prize is awarded to the most outstanding undergraduate Member of the House [Christ Church College] who achieves the highest mark in the following Honour Schools collectively: Mathematics, Molecular and Cellular Biochemistry, Chemistry, Engineering, Physics and Materials Science.” 

  • ​2017/2018: Roach Prize  (Christ Church College, Oxford)

    • ​“This prize is awarded to the most outstanding undergraduate across the following branches of Science: Mathematics, Biochemistry, Earth Sciences, Engineering, Physics, Materials Science and Biological Science. The most outstanding undergraduate will normally be the person placed proportionately highest in an appropriate Honour School (including in a joint School with Philosophy).”


  • 2016: Undertook a teaching module as part of my undergraduate.

  • 2018 & 2020: Demonstrator for theoretical physics part I (Department of Physics, Cambridge)

  • 2019 & 2020: Supervisor for Gauge Field Theory (Department of Physics, Cambridge)

  • 2019: Supervisor for Quantum Field Theory (DAMTP, Cambridge)

  • 2020: Supervisor for `Symmetries, Fields and Particles’ (DAMTP, Cambridge)

Public Engagement

  • 2016-2018: Oxfords Hands on Science (OxHOS) roadshows and committee member (2017)

  • 2017-2018: Oxford Physics department and Christ Church college open days

  • 2017: Volunteered at Stargazing Oxford event

  • 2019: Volunteered at Cambridge Science Festival

  • 2019: Helped out at Cambridge HEP master classes


Personal bests:

1:59.4 (800m), 3:59.40 (1500m), 8:39.6 (3000m), 9:59.49 (3000m Steeple chase), 15:08.92 (5000m), 30:01 (10k)

Athletic achivements

  • 2019: 3rd team at National 6-stage road relays with Cambridge and Coleridge AC

  • 2019: 2nd team at National Cross Country relays with Cambridge and Coleridge AC

  • 2019: 1st in both the Oxford and Cambridge Town and Gown 10k

  • 2019: Represented Cambridgeshire in track-and-field

  • 2019: 2nd Individual in Oxford Vs Cambridge Blues varsity cross country, and team win

  • 2020: 30th Individual in National Cross Country Championships