John Huerta

Mathematician

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, last updated in August 2024.

I have relocated: As of October 2024, I am a visitor at the Mathematical Sciences Institute at the Australian National University in Canberra. If your Australian university is hiring a mathematician, please get in touch!

I remain affiliated with CAMGSD at Instituto Superior Técnico, a part of the University of Lisbon.

Research interests

My research concerns quantum topology and mathematical physics. Current interests include:

Topological quantum field theories (TQFTs) with defects, with connections to the cobordism hypothesis, state sums and factorization homology.
Factorization algebras, with connections to conformal field theories in 2d.
Supergeometry, especially questions related to working in families, and to distributions on supermanifolds.

Education

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

Papers

Poincaré duality for supermanifolds, higher Cartan geometry, and geometric supergravity.
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:

Diogo Freire de Andrade, who will defend sometime in 2025, has been a PhD student since 2021 at Instituto Superior Técnico. His work concerns the general relationship between state sums and topological field theories, especially as suggested by factorization homology. He is supported by a fellowship from FCT.

I previously supervised:

Nino Scalbi, PhD 2019-2024, Instituto Superior Técnico. Nino's thesis establishes a beautiful connection between differential cohomology and diffeological spaces, a generalization of smooth manifolds. He was supported by a fellowship from LisMath, and co-advised with Roger Picken. He now plans to make the transition to industry, so if you're looking for a world-class problem solver, you should recruit Nino!
You can find Nino's thesis on the arXiv.
Rui Peixoto, MSc 2021–2023, Instituto Superior Técnico. Rui's thesis generalized a construction of Costello and Gwilliam from algebras to superalgebras. Specifically, Rui showed how to construct a vertex superalgebra from a holomorphic factorization superalgebra on the complex plane. He defended in December 2023, and received the highest possible grade. He will begin a PhD in mathematics at the University of Massachusetts, Amherst in September 2024.
Diogo Freire de Andrade, MSc 2019–2021, Instituto Superior Técnico. Diogo's thesis concerned a diagrammatic construction of the Drinfeld center of a spherical fusion category. He defended in January 2021, and decided to continue his work as a PhD student.

I am unable to take any new students at this time.

Seminars

In Spring and Summer 2024, Gonçalo Oliveira and I organized a learning seminar on the mathematics of quantum field theory.

In Spring 2023, Diogo Andrade and I organized 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

Vertex superalgebras from prefactorization algebras, 18 October 2024, Algebra Seminar, University of Sydney.
What are the sections of a gerbe? 20 September 2024, Young Researchers Seminar, Instituto Superior Técnico, Lisbon.
The prequantum 2-Hilbert space? 11 July 2024, Categorical Algebra and Geometry, ENSPM24, University of Minho, Braga.
Poincaré duality for families of supermanifolds, 11 April 2024, Geometry Seminar, ICMAT, Madrid.
Poincaré duality for families of supermanifolds, 9 April 2024, Higher Structure Research Group Seminar, the Feza Gursey Center for Physics and Mathematics, Istanbul.
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.
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 Tromsø.
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, RHIND seminar on mathematical physics.
The higher algebra of supersymmetry, 29 March 2021, Octonions and the Standard Model, the Perimeter Institute for Theoretical Physics.