Differential geometry reading group
The aim is to improve our geometric intutition and learn the language of diff. forms, metrics, exteriour derivative, Lie derivative, covariant derivative, etc. and to generalize vector calculus to calculus on manifolds. Application areas to be considered include geometric mechanics, geometry of phase space of dynamical systems, fluid mechanics on curved surfaces, general relativity and other applications in physics, diff. geometry of surfaces, discrete differential geometry.
About
The group consists of 4-5 people ranging from undegrad. students to seniour academics. Meetings are held every Tuesday, 3pm in room 448, Erskine Building (School of Mathematics and Statistics Library). We normally read Frankel’s “Geometry of physics” and solve the problems therein. Many other textbooks are available as references. Occasionally we embark on a special fast-reading program to prepare ourself towards a specific topic, e.g., a talk by an invited speaker. 2012S1: we put aside Frankel once again and align our reading with MATH426 "Differential geometry".
Resources
A shared folder is used and regularly updated to store notes, whiteboard scans, latex files, books, articles, seminar slides, and web links, -- currently amounting to 260MB.
Please use our SVN repository at https://svn.math.canterbury.ac.nz/repos/dg/ for contributing or editing the LaTeX source of the problems and solutions, and pictures.
News
- We resume reading Frankel from the Chapter 3 for the remainder of 2012 and welcome back Chen-Yang to the group: 3 postdocs in attendance, the student members having a break.
- Some of us are auditing MATH427 'Lie Groups and Lie Algebras' and MATH416 'Exterior Differential Systems' in S2. The group is turned into a two hour weekly tutorials for the MATH416.
- Meetings resume Tuesday, February 28th or March 6th.
- Good news: MATH426 is running in 2012S1. The group switches to the course's recommended books.
- The last meeting this year is the next Tuesday, 13th.
- There is an opinion that it would be nice to produce some lecture notes centered around problems & solutions to be used by students preparing to take the formal 400 level course on diffgeometry. Therefore some of us will be trying to typeset as we go.
- Meetings continue over the summer break.
- Back to the normal slow reading of Frankel's, Chapter 2.
- We welcome Klas Modin, our first invited speaker, supported by the School, who will talk to the group about Arnold-Euler equations on Friday Oct 28th following his seminar to the School on Thursday Oct 27th.
- Frankel’s “Geometry of physics” is suspended temporarily to study topics from Geometric mechanics using the books of Arnold, Khesin, “Topological Methods in Hydrodynamics” and Marsden, Ratiu, “Introduction to Mechanics and Symmetry”.
Inquiries: Igor Rychkov
