LTCC Advanced Course:
Applications of Differential Geometry to Mathematical Physics
The courses on Applications of Differential Geometry to Mathematical
Physics will place at the University of Kent (Canterbury) on
Wednesday, 30 January 2013 and Wednesday, 13 February 2013. The courses
are part of the advanced courses of the London taught course centre
(LTCC). A draft syllabus can be found
here. This advanced course first
took place
in November 2008
and again in November
2010
(click links for details).
For further information please contact
Dr
Steffen
Krusch.
(Could you please also email
me
if you are
intending to attend the course, and are not from the University of
Kent, so that I can get a rough idea of numbers.)
Lecturers
Location
The lectures will take place in
PS110
in the Ingram Building, also known as the SPS Conference Room. Click here for an
interactive map of the University of Kent. (To be confirmed)
Preliminary Schedule
On Wednesday, 30 January, the schedule is
- 11.00-12.00 Lecture 1
(Steffen Krusch)
(manifolds, fibre bundles, vector and principal bundles, sections in
fibre bundles, metric, connection, general relativity, Yang-Mills field
theory)
- 12.00-13.00 Lunch break
- 13.00-14.00 Lecture 2 (Andy Hone)
(tensors and forms, metrics)
- 14.00-14.45 Tutorial 1
- 14.45-15.15 Tea
- 15.15-16.15 Lecture 3 (Andy Hone)
(Lagrangian mechanics, Hamiltonian mechanics, symplectic and Poisson
geometry)
- 16.15-17.00 Tutorial 2
On Wednesday, 13 February, the schedule is
- 11.00-12.00
Lecture 4 (Steffen Krusch)
(Homotopy theory, Ginzburg-Landau vortices, moduli space, vortex
dynamics, vortices in different geometries)
- 12.00-13.00 Lunch break
- 13.00-14.00 Lecture 5 (Andy Hone)
(Hamiltonian PDEs and field theory, integrable systems)
- 14.00-14.45 Tutorial 3
- 14.45-15.15 Tea
- 15.15-16.15
Lecture 6
(Steffen Krusch)
- 16.15-17.00 Tutorial 4
Assessment
The assessment consists of written work which should be scanned in
and emailed to either Andy Hone or Steffen Krusch by Friday, 31 May
2013. There are
two
options:
- two section A questions and one section B question
- one section C question
Section A, B, and C questions are given as follows:
- Section A questions are all questions on
Exercise sheet 1, question 2 on
Exercise sheet 2,
questions 1, 2, 3, and 6 on
Exercise sheet 3,
and questions 1, 2, 3, 4, 5, 6 and 7 on
Exercise sheet 4.
- Section B questions are
questions 1, 3 and 4 on
Exercise sheet 2,
questions 4 and 5 on
Exercise sheet 3,
and question 8 on
Exercise sheet 4.
- Section C questions are question 9 on
Exercise sheet 4,
and questions 2 and 3 on
Exercise sheet 5.
Recommended Reading
We found the following literature quite useful, when preparing the course.
- M Nakahara, Geometry, Topology and Physics, Second
Edition, Graduate Student Series in Physics, Institute of Physics
Publishing, 2003
- R Bott and LW Tu, Differential Forms in Algebraic
Topology, Springer Verlag, New York, 1982
- NS Manton and PM Sutcliffe, Topological Solitons,
Cambridge University Press, 2004
- VI Arnold, Mathematical Methods of Classical Mechanics,
Second Edition, Graduate Texts in Mathematics, Springer Verlag, New York,
1997
- O Babelon, D Bernard and M Talon, Introduction to Classical
Integrable Systems, Cambridge Monographs on Mathematical Physics,
Cambridge University Press, 2003
- D Huybrechts, Complex geometry,
Springer-Verlag, Berlin, 2005
Back to
Steffen Krusch's Home Page
Last updated 14 March, 2013.