Email: ` jhuerta at math dot tecnico dot ulisboa dot pt `

I'm John Huerta. I'm a mathematical physicist, and currently a postdoc at CAMGSD in Lisbon. Before that, I was a postdoc at Australian National University, dually appointed in mathematics and physics. I earned my PhD in mathematics at UC Riverside under the supervision of John Baez.

My research concerns exceptional structures in mathematics, and their relationship to physical ideas, such as:

- The exceptional Lie group G2 realized as the symmetries of a ball rolling on another ball three times as big.
- The exceptional cocycles of string theory and M-theory, and how they originate with normed division algebras.

I shared the 2013 Levi L. Conant Prize for the paper The Algebra of Grand Unified Theories. It was very humbling to be selected, especially when I think of how many worthy candidates there were. Nonetheless, I'm damn proud of the paper, and I'm glad to see it get more attention. The prize annoucement contains the nicest compliment I have ever received:

The authors are able to maintain an engaging tone throughout the seventy pages it takes to tell this marvelous tale. And as with the stories in theThousand and One Nights, we are left hoping for more.

If you want to teach mathematics, you should
read Lockhart's lament, a
profound plea to teach students the true beauty of mathematics *as a creative
activity*. It was written by Paul Lockhart, a mathematician and grade-school math
teacher. Here is one of my favorite quotes:

There is such breathtaking depth and heartbreaking beauty in this ancient art form [of mathematics]. How ironic that people dismiss mathematics as the antithesis of creativity. They are missing out on an art form older than any book, more profound than any poem, and more abstract than any abstract. And it isschoolthat has done this! What a sad endless cycle of innocent teachers inflicting damage upon innocent students. We could all be having so much more fun.

In June 2011, I earned my PhD in mathematics from the University of California, Riverside, under the advisement of John Baez. My thesis concerns Division Algebras, Supersymmetry and Higher Gauge Theory.

Before all this, I received a bachelor of science with honors (magna cum laude) from Northern Arizona University, where I double majored in mathematics and physics. I also have a master of science in mathematics from UCR.

- M-theory from the superpoint (with Urs Schreiber).
- 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. Text available upon request!
- 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.
- 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.
- 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.

Octonionic windows on physics - a discussion, 3 August 2017, 4th Mile High Conference on Nonassociative Mathematics, University of Denver.

G2 and the rolling ball, 1 June 2017, Geometric Analysis Seminar, Free University of Berlin.

M-theory from the superpoint, 30 May 2017, Quantum Fields and Strings Seminar, University of Surrey.

G2 and the rolling ball, 11 May 2017, Geometry and Topology Seminar, University of Malaga.

L-infinity algebras, cohomology, and physics, 4 May 2017, Geometry and Topology Seminar, University of Malaga.

L-infinity algebras, central extensions, and physics, 29 April 2017, Geometry and Topology Seminar, University of Porto.

M-theory from the superpoint, Iberian Strings 2017, Instituto Superior Tecnico, Lisbon.

M-theory from the superpoint, 18 November 2016, Metodos Categoricos y Homotopicos en Algebra, Geometria y Topologia, University of La Rioja.

L-infinity algebras, cohomology and physics, 17 October 2016, Topology Seminar, University of Oxford.

M-theory from the superpoint, 11 July 2016, Advances in Quantum Gravity 2016, Topos House, San Franciso.

Division algebras and supersymmetry, 24 November 2015, Advances in Quantum Gravity 2015, Los Angeles, CA.

Trigroups and M-theory, 11 July 2015, joint meeting of the AMS-EMS-SPM, Porto, Portugal.

The Octonions, 28 January 2015, Grupo de Fisica Matematica, Universidade de Lisboa, Portugal.

Trigroups and M-theory, 2 September 2014, XXIII International Fall Workshop on Geometry and Physics, University of Granada, Granada, Spain.

G2 and the rolling ball, 14-16 July 2014, Encontro Nacional Sociedade Portuguesa de Matematica, Universidade Nova de Lisboa, Portugal.

Trigroups and M-theory, 9-10 May 2014, Algebra and Representation Theory in the North, University of Sheffield, Sheffield, UK.

Symmetry in mathematics and physics, 18 April 2014, Levi L. Conant Lecture, Worcester Polytechnic Institute, Worcester, MA.

What can higher categories do for physics? 12 March 2014, Faculdade de Ciencia e Tecnologia, Universidade Nova de Lisboa, Portugal.

G2 and the rolling ball, 13 August 2013, 3rd Mile High Conference in Nonassociative Mathematics, University of Denver, Denver, CO.

The functor of points for supermanifolds, 8 July 2013, University of Hamburg, Hamburg, Germany.

G2 and the rolling ball, 4 July 2013, University of Hamburg, Hamburg, Germany.

G2 and the rolling ball, May 2013, Hong Kong University, Hong Kong.

Introduction to higher gauge theory, May 2013, Hong Kong University, Hong Kong.

The categorified Poincare supergroup, 25 March 2013, 94th Peripatetic Seminar on Sheaves and Logic, University of Sheffield, Sheffield, United Kingdom.

The categorified Poincare superalgebra, 10 January 2013, AMS Special Session on Lie Algebras, Algebraic Transformation Groups, and Representation Theory, Joint Mathematics Meeting 2013, San Diego, CA.

G2 and the rolling ball, 12 October 2012, University of Melbourne, Melbourne, Australia.

Superstrings, higher gauge theory and division algebras, 6 December 2011, TQFT seminar, Instituto Superior Tecnico, Lisbon, Portugal.

A higher supergroup for string theory, 2 December 2011, Higher Structures 2011, the Courant Institute, Goettingen, Germany.

Superstrings, higher gauge theory and division algebras, 23 November 2011, theoretical physics seminar, Universitaet Erlangenâ€“Nuernberg, Erlangen, Germany.

A categorified supergroup for string theory, 19 October 2011, Australian category theory seminar, Macquarie University, Sydney, Australia.

G2, the split octonions, and the rolling ball, 18 October 2011, geometry seminar, University of Sydney, Sydney, Australia.

On September 5, 2011, I gave a talk at the IGA workshop on Group-valued moment maps with applications to mathematics and physics at the University of Adelaide. I spoke about a higher supergroup for string theory. Thanks to Pedram Hekmati, Snigdhayan Mahanta, Mathai Varghese, and Craig Westerland for inviting me.

On April 9, 2011, I gave a talk in the AMS Special Session on Physically Inspired Higher Homotopy Algebra, on categorified supergroups for string theory. Thanks to Tom Lada and Jim Stasheff for inviting me.

Feb 7-13, 2011, I participated in a Workshop and School on Higher Gauge Theory, TQFT and Quantum Gravity in Lisbon, Portugal. I gave a minicourse on higher gauge theory for the school, and talked about categorified supergroups for string theory during the workshop. Thanks to Roger Picken and Jeff Morton for inviting me.

On Nov 7, 2010, I gave a talk on division algebra technology for supersymmetry in the AMS Special Session on Quasigroups, Loops and Nonassociative Division Algebras. Thanks to Clifton Ealy for inviting me.

On Nov 5, 2010, I gave a talk in the AMS Special Session on Topology, Geometry and Physics, on L-infinity superalgebras for superstring and M-theory. Thanks to Stephan Stolz for inviting me.

On Nov 4, 2010, I gave a talk in the Geometry/Physics seminar at Northwestern, on L-infinity superalgebras for superstring and M-theory. Thanks to Kevin Costello for inviting me.

On September 27th, 2010, I gave an introductory talk on the quaternions, Introducing the Quaternions, at Fullerton College. In some ways, it is a warm up for this talk on the quaternions, which is much harder. Thanks to Dana Clahane for inviting me!

On June 7th, 2010, I gave a short talk on Lie n-algebras, supersymmetry and division algebras during the workshop on Quantum Fields and Strings: Categorical Aspects at MFO in Oberwolfach, Germany. Thanks go to Christoph Schweigert, Dan Freed and Peter Bouwknegt for inviting me. The slides and the abstract provide a concise summary of my work prior to this meeting.

On June 3rd, 2010, I gave a talk on my work relating Lie n-algebras, supersymmetry and division algebras at Higher Structures IV at the Courant Institute in Goettingen, Germany. Thanks to Chenchang Zhu for inviting me.

On May 21st, 2010, I gave a colloquium talk on the quaternions at Cal State Stanislaus. My friend Jack Bennett spoke earlier in the day on non-unique factorization. Thanks to John Rock for inviting us!

On April 20th, 2010, I gave a talk on my work relating supersymmetry, division algebras and Lie n-algebras at the Claremont topology seminar. Thanks to Sam Nelson for inviting me. I later gave an improved version of this talk at Higher Structures IV in Goettingen, Germany.

On February 22nd, 2010 I gave a talk on addressing on fractals and IFS's in the Dynamical Systems Seminar.

On February 17th, 2010 I gave a talk on Jordan algebras and projective geometry in the mathematics graduate student seminar.

On January 22nd, 2010 I gave a talk titled "A crash course in simplicial methods" in Professor Julie Bergner's Cobordism Seminar.

On November 7th, 2009 I gave a short talk titled Division Algebras and Supermembranes at the Western Sectional AMS meeting, right here at UCR.

On October 23rd, 2009 I gave a talk on the interaction of quantum field theory and topology in Professor Julie Bergner's Cobordism Seminar. Notes available here.

On June 22nd, 2009 I gave a short talk on Supersymmetry and Division Algebras at the 2nd Mile High Conference in Nonassociative Mathematics.

On March 23rd, 2009 I presented a poster on the algebra of grand unified theories at the Algebraic Lie Theory Workshop at the Isaac Netwon Institute in Cambridge, England.

On February 26th, 2009 I took my oral exam and advanced to PhD candidacy. My talk concerned Grand Unified Theories, just like this paper. You can find the slides here, and a more printer-friendly version here. I also gave this talk on February 5th in Professor Michel Lapidus's Mathematical Physics Seminar.

On November 13, 2008 I gave a talk on Grand Unified Theories in
Michel Lapidus's

On June 5th, 2008 I gave a talk on Quantum Mechanics and Representation Theory in
Michel Lapidus's

On April 10th, 2008 I gave a talk on The Octonions in
Michel Lapidus's

In Spring 2008, I gave a series of lectures on grand unified theories in John Baez's Quantum Gravity seminar.

I gave a talk in our departmental seminar on how to get started with LaTeX. Check out my tips here.

During the 2008–2009 school year, John Baez taught a course on Lie theory in his seminar. You can find his notes for the Fall quarter here, and notes for the Winter quarter below:

- John Baez - Lie Theory Through Examples - Winter 2009, Lecture 1.
- John Baez - Lie Theory Through Examples - Winter 2009, Lecture 2.
- John Baez - Lie Theory Through Examples - Winter 2009, Lecture 3.
- John Baez - Lie Theory Through Examples - Winter 2009, Lecture 4.
- John Baez - Lie Theory Through Examples - Winter 2009, Lecture 5.
- John Baez - Lie Theory Through Examples - Winter 2009, Lecture 6.
- John Baez - Lie Theory Through Examples - Winter 2009, Lecture 7.
- John Baez - Lie Theory Through Examples - Winter 2009, Lecture 8.

I have been a teaching assistant for the following courses at UC Riverside:

Math 4 - Precalculus

Math 5 - Precalculus

Math 8B - Introductory Calculus

Math 9ABC - Introductory Calculus

Math 10A - Vector Calculus

Math 10B - Vector Calculus

Math 11/CS 11 - Discrete Math

Math 22 - Business Calculus

Math 46 - Differential Equations

Math 131 - Linear Algebra

Math 132 - Linear Algebra

Math 144 - Set Theory

Math 151C - Advanced Calculus

Math 165AB - Complex Analysis

Math 171 - Abstract Algebra

During the summer I have been the primary instructor for the Topology Qualifying Exam Seminar, taught to help prepare graduate students for their topology qualifier, and for Math 9C, the third quarter of calculus. For this last course, you can read my evaluations here and my student comments here.

During 2008-2009, I was one of the recipients of the Graduate Research Mentorship Fellowship here at UC Riverside. In 2009-2010, I was partially supported by a grant from the Foundational Questions Institue (FQXi).

I am grateful to both UCR and FQXi for their support.

© 2016 John Huerta