John Huerta

Mathematical Physicist

University of Lisbon

john.huerta@tecnico.ulisboa.pt

Office: 2.08A, Pavilhão Matemática.

Department of Mathematics
Instituto Superior Técnico
Avenida Rovisco Pais 1
1049-001 Lisbon, Portugal

ON THE JOB MARKET! Here is my CV.

I am currently a research scientist at CAMGSD at Instituto Superior Técnico, a part of the University of Lisbon.

Research interests

My research concerns mathematical physics via differential geometry and higher structures. Current interests include:

Supergeometry, especially of Lie supergroups.
Super-WZW models and their branes.
Branes in twisted supergravity theories.
Loop groups in supergeometry.
The Cartan geometry of 5-manifolds equipped with "(2,3,5) distributions", the most famous of which is the rolling ball.

Education

PhD in Mathematics, University of California, Riverside, June 2011. Advisor: John Carlos Baez.

Papers

Bundle gerbes on supermanifolds.
How space-times emerge from the superpoint, which appeared in Fortschritte der Physik.
Real ADE-equivariant (co)homotopy and Super M-branes (with Hisham Sati and Urs Schreiber), which appeared in Communications in Mathematical Physics.
M-theory from the superpoint (with Urs Schreiber), which appeared in Letters in Mathematical Physics.
Division algebras and supersymmetry IV, which appeared in Advances in Theoretical and Mathematical Physics.
The magic square of Lie groups: the 2x2 case (with Tevian Dray and Josh Kincaid), which appeared in Letters in Mathematical Physics.
G2 and the rolling ball (with John Baez), which appeared in Transactions of the American Mathematical Society.
Division algebras and supersymmetry III, which appeared in Advances in Theoretical and Mathematical Physics.
Division Algebras, Supersymmetry and Higher Gauge Theory, PhD thesis, UC Riverside.
Division algebras and supersymmetry II (with John Baez), which appeared in Advances in Theoretical and Mathematical Physics.
An Invitation to Higher Gauge Theory (with John Baez, based on his lectures), which appeared in General Relativity and Gravitation.
Division algebras and supersymmetry I (with John Baez), which appeared in Superstrings, Geometry, Topology, and C*-algebras, edited by Doran, Friedman and Rosenberg.
The Algebra of Grand Unified Theories (with John Baez) which appeared in the Bulletin of the American Mathematical Society. Also available as its own webpage.

Popularizations

The Strangest Numbers in String Theory (with John Baez), an expository article about the octonions, which appeared in the May 2011 issue of Scientific American.

Student supervision

I am currently advising the following graduate students:

Nino Scalbi, PhD 2019 - 2023, Instituto Superior Técnico, supported by a fellowship from LisMath. Co-advised with Roger Picken.
Diogo Freire de Andrade, PhD 2021 - 2025, Instituto Superior Técnico, supported by a fellowship from FCT.
Rui Peixoto, MSc 2021 - 2023, Instituto Superior Técnico, supported by a department research fellowship.

I previously supervised Diogo's MSc thesis, which he successfully defended at the beginning of 2021.

If you are interested in doing a PhD with me, please get in touch!

Seminars

This semester (Spring 2023), my student Diogo Andrade and I are organizing a learning seminar on higher categories.

I am one of the organizers of the TQFT Club, with Roger Picken and Marko Stošić.

Teaching

I am not teaching a course this semester, but you can look at my teaching evalutations if you want to.

Recent and Upcoming Talks

Octonions and spinors, 29 May 2023, Spinorial and octonionic aspects of G2 and Spin(7) geometry, Banff International Research Station.
The algebra of grand unified theories, 3 April 2023, Algebra, Particles and Quantum Theory (online seminar).
Body and soul decompositions in supergeometry, 29 March 2023, SuperGeometry and SuperModuli, Simons Center for Geometry and Physics, Stony Brook.
An invitation to higher supergeometry, 25 August 2022, Geometric Structures and Supersymmetry 2022, University of Tromso.
Splitting supermanifolds, 19 April 2022, Geometry and Topology Seminar, Texas Tech University.
Bundle gerbes on Lie supergroups, 19 November 2021, Geometry and Topology Seminar, University of Waterloo.
Bundle gerbes on Lie supergroups, 4 October 2021, Pure Spinors, Superalgebras, and Holomorphic Twists, University of Heidelberg.
Geometric quantization and the Borel--Weil theorem, minicourse, 6-17 September 2021, University of Bologna.
Bundle gerbes on Lie supergroups, 14 June 2021, RIND mathematical physics seminar (online).
The higher algebra of supersymmetry, 29 March 2021, Octonions and the Standard Model, the Perimeter Institute for Theoretical Physics (online).