# John Huerta

Email: john dot huerta at anu dot edu dot au

Hi. I'm John Huerta. I am a postdoc in mathematics and theoretical physics at Australian National University in Canberra, Australia, working with Peter Bouwknegt. My research concerns the foundations of supersymmetry, applying higher gauge theory to superstrings, supermembranes and supergravity, while taking advantage of the mysterious connection between supersymmetry and division algebras. Lately, I have also been studying the exceptional Lie group G2.

Before this, I earned a PhD in mathematics from UC Riverside. My advisor was John Baez.

I just put my first sole-authored paper on the arXiv, and I would love it if you could give me your comments.

This is the third paper in the "Division algebras and supersymmetry" series, which I began writing with John Baez. The series has come to focus on the `higher symmetries' of the superstring. In the last installment, we described how these higher symmetries take the form of a `Lie 2-superalgebra' extending the Poincare superalgebra in the dimensions where string theory makes sense: 3, 4, 6 and 10. In the new episode, we obtain a more global perspective by integrating this Lie 2-superalgebra to a `Lie 2-supergroup' in the same dimensions. And if all of this sounds really hard, don't worry: the paper takes great pains to explain all of this in an understandable way. And your comments could help to make it even better!

If you want to teach mathematics, you should read Lockhart's lament, a profound plea to teach students the beauty of true 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 is school that 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.

## Education

In June 2011, I earned my PhD in mathematics from the University of California, Riverside, under the advisement of John Baez.

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 UC Riverside.

## Thesis

Now available on the arXiv! Division Algebras, Supersymmetry and Higher Gauge Theory.

## Talks

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, at University of California, Riverside.

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 Mathematical Physics Seminar.

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

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

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 the UCR math department seminar on how to get started with LaTeX. Check out my tips here.

## Notes

### Lie Theory Through Examples

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.

## Teaching

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 46 - Differential Equations
Math 131 - Linear Algebra
Math 132 - Linear Algebra
Math 144 - Set Theory
Math 165AB - Complex Analysis
Math 171 - Abstract Algebra

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.

## Support

During 2008-2009, I was one of the recipients of the Graduate Research Mentorship Fellowship 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.

## LaTeX for Beginners

Look here for my tips on getting started with LaTeX.