Starting September 2011, I am a **Peter M. Curran
Visiting Assistant Professor** at Fordham University.
Previously, I was a postdoctoral fellow at McGill University, mentored by Niky Kamran and funded by an NSF fellowship administered by the MSRI. I earned my PhD in 2009 at Duke University under the direction of Robert Bryant.

My visiting position at Fordham is complete in May 2015, so please keep me in mind if you know of any departments or institutions looking for a mathematician specializing in geometry, analysis, or algebra with a broad interest in science, technology, and education. Download my CV to learn more.

- Math 3010
### Scientific Communications

This is a course on scientific writing and publishing, and it provides credit for the Eloquentia Perfecta 3 requirement.Mondays and Thursdays, 10:00 to 11:15 (Block B) in room JMH 406.Assignments are found on the Course Calendar. To access it, you must be logged into your**@Fordham.edu**Google account.For this course, you will need a laptop. Any modern operating system will work, but you will need to installOne very userful tool is a**version control system**. If you aren't already familiar with one, I suggest trying SourceTree. I won't require its use, but it will make your life easier.I put a short sequence of videos on YouTube about using PGP/GnuPG for message verification. This is not essential or required for our course, but I will sign all of the files I provide for you, so that you can be certain that they are uncorrupted when diagnosing problems. If you tell me “your example file didn't work,” the first thing I'll ask is “did you check the signature?”

All files will be signed with 0x7ECF418F. GnuPG can be downloaded for On most Linux systems, GnuPG is preinstalled by default, as it is used to verify that the system packages are uncorrupted. This is how we maintain trust in open-source software. - Math 1000 Sect 4
### Pre-calculus

This is a course on linear geometry, algebra, and trigonometry for those hoping to move into Math 1203 or 1206 next semester.Mondays and Thursdays, 16:00 to 17:15 (Block E) in room JMH 140.Assignments are found on the Course Calendar. To access it, you must be logged into your**@Fordham.edu**Google account.We will be using Fordham WebWork for online homework. -
### Help Room

The Math Help Room (JMH 410) is a great resource! Feel free to use the Help Room any time. Every teacher in the department has a shift, and*someone*will be there who can help.My shift in Fall 2014 is 12:30--13:30 on Mondays and Thursdays.

My Office Hours in Fall 2014 are 11:30--12:30 on Mondays and Thursdays.

- Linear Algebra II - Math 3001 Section 1. Mondays and Thursdays, 10:00 to 11:15 (Block B) in JMH room 406.
- Applied Calculus I - Math 1203 Section 1. Mondays and Thursdays, 08:30 to 9:45 (Block A) in Freeman Hall room 108.
**Help-Room Hours:**12:30--13:30 and 14:30--15:30 Mondays.

- Pre-calculus - Math 1000 Section 4. Mondays and Thursdays, 10:00 to 11:15 (Block B) in room JMH 140.
- Scientific Communications - Math 3010 Section 1. Mondays and
Thursdays, 11:30 to 12:45 (Block C) in room JMH 406. This is a course on
scientific writing and publishing, and it provides credit for the Eloquentia
Perfecta 3 requirement.
I put a short sequence of videos on YouTube about using PGP/GPG for message verification. This is not essential or required for our course, but I will sign all of the files I provide for you, so that you can be certain that they are uncorrupted when diagnosing problems. If you tell me “your example file didn't work,” the first thing I'll say is “did you check the signature?”

- Finite Mathematics - Math 1100 Section 1. Mondays and Thursdays, 8:30 to 9:45 in room JMH 404.
- Finite Mathematics - Math 1100 Section 2. Mondays and Thursdays, 10:00 to 11:15 in room JMH 404.
- Linear Algebra I - Math 2006 Section 1. Mondays and Thursdays,
11:30 to 12:45 in room JMH 406.

Our textbook is by Hefferon. My end-of-semester notes are available in paper and tablet formats. These are works-in-progress. **Help-Room Hours:**Mondays, 13:30 to 15:30 in room JMH 410.**Office Hours:**Thursdays, 13:30 to 15:30 in room JMH 422B.

- Pre-calculus - Math 1000 Section 1. Mondays and Thursdays, 8:30 to 9:45 in room JMH 342.
- Differential Geometry - Math 4020. Mondays and Thursdays, 10:00 to 11:15 in room JMH 406.
**Help-Room Hours:**Mondays 13:30--15:30.**Office Hours:**Thursdays 12:30--14:30, or email me to arrange a time.

- Pre-calculus - Math 1000 Section 21. Tuesdays, Wednesdays, and Thursdays from 09:00 to 12:00 in room JMH 406.
**NOTE: July 7 through July 13, class will be held in Dealy 302.**

- Multivariable Calculus I - Math 2004 Section 1. Mondays and Thursdays from 14:30 to 15:45.
- Calculus II - Math 1207 Section 2. Mondays and Thursdays from 16:00 to 17:15.
**Help-Room Hours:**Mondays 11:30--13:30.**Office Hours:**Wednesdays 13:00--14:00 and Thursdays 11:30--12:30.

- Pre-calculus - Math 1000 Section 1, Block A on Mondays and Thursdays from 8:30 to 9:45 in Room JMH 132.
- Calculus I - Math 1206 Section 2, Block B on Mondays and Thursdays from 10:00 to 11:15 in Room JMH 132.
- Calculus I - Math 1206 Recitation Sections 1, 4, and 5. Tuesdays.
**Help-Room Hours:**Mondays 12:30--14:30.**Office Hours:**Thursdays 13:00--15:00.

- Fall 2013
### Scientific Communications

A course on scientific and technical writing, for 3rd year science majors.

Students learn LaTeX and prepare presentations and detailed scientific review articles on topics of their choice. - Spring 2012
### Calculus 2

A typical second-semester Calculus course on integration, sequences, and series. We used Stewart's textbook.

Note that responses are significantly better than the departmental average! - Fall 2012
### Differential Geometry

An advanced elective on curves, surfaces, Riemannian geometry, and a little bit of cosmology. - Fall 2012
### Precalculus

An introductory course to prepare freshmen for Calculus.

Covering the algebra of functions.

Polynomials, exponentials, logarithms, and a bit of trigonometry.

I study geometry in the sense of E. Cartan; this means that I examine the intrinsic geometry of PDEs using exterior differential systems, moving frames and representation theory.

In particular, I am currently studying the phenomena of **involutivity** and **hydrodynamic integrability**
using Guillemin normal form and Spencer cohomology. These tools are algebraic tools developed during the 1960s to study formal integrability criteria. Nowadays these formal methods are particularly useful, because they allow us to study PDEs using computer algebra software.

Alongside my theoretical work, I am writing an open-source package for Sage to automatically build, manipulate, classify, and solve PDEs and differential ideals.

Additionally, I am interested in the related frameworks for studying algebroids, pseudo-groups, and distributions. Control theory, mathematical relativity and Finsler geometry are neat, too.

On Dec 9, 2013, I gave a talk about my ongoing work at the Fields Institute in Toronto, as part of the Focused Research Workshop on Exterior Differential Systems and Lie Theory. You can watch a video of the talk to get a sense of my current project. (Be forewarned that my travel schedule meant it was my least-prepared talk ever.)

Beyond this particular specialty, my interest in science is quite broad, and I try to stay abreast of developments in many branches of science. I try to read the weekly issues of Science and Nature, but I've also found that podcasts are an amazingly efficient way to learn new ideas. If you also have a general interest in science, I recommend these resources, which I follow religiously:

Source | News | Podcast | Topic |
---|---|---|---|

RadioLab | blog | podcast | Awesome presentation of contemporary science and the boundaries of human knowledge, for a general audience. |

The Guardian's Science Weekly | news | podcast | The Guardian's science reporters talk with experts in science and science policy. This is a nice median between the popular discussion of RadioLab and the technical intricacies of the Nature and AAAS/Science podcasts. |

Nature News | news | podcast | Newest articles from probably the most prestigious journal in the world. Excellent podcast! |

Science/AAAS | news | podcast | Newest articles from probably the second most prestigious journal in the world. Excellent podcast and good coverage of AAAS meetings. |

Inside Science | info | podcast | BBC Radio 4's new weekly science show, with Adam Rutherford. Discussions focus on the life of working scientists today. |

Material World | blog | podcast | BBC Radio 4's old weekly general science show, with Quentin Cooper. Refreshingly sophisticated compared to a science show that airs on Fridays in the US. |

Planet Money | blog | podcast | NPR's great production analyzing modern global economics in a thoughtful and reasonably scientific way. Unfortunately, most of the content never reaches the airwaves; you have to follow the podcast. |

Relatively Prime | info | podcast | A really thoughtful project outlining the role of modern research mathematics. |

DisasterCast | info | podcast | A fascinating series about systems engineering and safety. |

Additionally, aside from their good coverage of consumer technology and Internet policy, Ars Technica has a fantastic science blog known as The Scientific Method.

The most insightful commentaries I have seen about research are The Importance of Stupidity in Scientific Research by Martin A. Schwartz
and You and Your Research by Richard Hamming. Regarding mathematics as a social activity, everyone should read On Proof and Progress in Mathematics and this short essay by William Thurston. On a lighter note, a fantastic description of how it *feels* to do mathematics was recently written by
Yasha Berchenko-Kogan.

Recently, I've also started using Twitter to follow other scientists and science journalists.

- 2014-11
*Generalized Hydrodynamic Integrability for Exterior Differential Systems*(In preparation for Fall 2014 submission. Private pre-print available on request.) - 2014-10
*Constructing Involutive Tableaux with Guillemin Normal Form*(Available at arXiv:1410.7593 [math.AP].) - 2014-10
*Degeneracy of the Characteristic Variety*(Available at arXiv:1410.6947 [math.AP].) - 2014-08
*WHAT IS... Guillemin normal form?*(Under review at Notices of the American Mathematical Society. Private pre-print available on request.) - 2010-10
*Integrable GL(2) Geometry and Hydrodynamic Partial Differential Equations*(Communications in Analysis and Geometry, vol 18 no 4 2010. pdf, maple code) - 2009-05
*Integrability of Second-Order Partial Differential Equations and the Geometry of GL(2)-Structures*. PhD Dissertation, Duke University. (pdf)

Have you ever wanted to build and manipulate differential ideals and symbols of PDEs on an open-source computer algebra system?

You're in luck! I'm developing >Symbol, a package for Sage. You can help at BitBucket.

I am the administrator for the Fordham University **Research Computing
Cluster**, a service offered through the Academic
Computing Environment. This is a modern Linux environment, provided and
maintained to support the ongoing research of Fordham faculty.

If you would like an account, please fill out this questionairre to make the process as fast as possible. I am happy to meet and talk with anyone about how the Research Computing Cluster can serve your research.

Over time, I have spent an unreasonable number of hours learning the intricacies of Linux system administration. I have submitted patches and (properly documented) bug reports to various open-source programs, and I see the world of open-source software as another branch of the academic discipline. We all build on each-others' work, and it is scientifically unethical to rely on tools that you cannot ultimately deconstruct, understand, and modify.

Currently, for my own research, I am developing an Exterior Differential Systems package for Sage, the python-based, open-source math engine that is quickly taking over the world. My package will be modeled on Jeanne Clelland's excellent Cartan package for Maple, whose only problem is that it is a package for Maple.

My current and recent undergraduate research students have worked on problems in computer vision, including analyzing Spline curves in Randers geometry and developing moving-frame methods for image recognition and signal analysis.

Regarding Linux, I have used all the major distributions at one time or another, going back a long way, but for the moment I am settled on Debian. I recently found this, containing this disc and more, while going through an old box of books. I guess I really have been using linux a long time! (Actually, I think my brother bought that CD, but I do clearly recall running "make config" to build my kernel in RedHat 4.2 (Biltmore) in 1997.)

I have tinkered with things like IPv6 and other networking technologies. (I am curious what mathematical modeling and control theory can reveal about network catastrophes due to the Bufferbloat problem that has recently been brought to light.)

- Email: asmith122@fordham.edu or adsmith@member.ams.org
**(email is always preferred!)** - For secure communication, use my PGP/GnuPG public key: B8709DBD
- Office:

422B John Mulcahy Hall

Mathematics Department, Fordham University

Bronx, New York 10458-5165 USA

USA - Office Phone: +1 (718) 817-5926
**(rarely answered)** - Skype (only online if pre-arranged) abrahamsmith