Workshop on Differential Geometry
& Applications
La Trobe University
June 13 - 16, 2006
Aims
The principal aim is to provide the necessary cross-fertilisation for attacking some open problems. The workshop will bring together differential geometers broadly sharing a background in differential equations but working in a wide variety of areas. Many of the speakers have not worked together before. The format of the meeting will be one of exposing outstanding problems in lectures and working on them in open session. These problems include the inverse problem in the calculus of variations and the geometric integration of PDE’s. The participants are encouraged to spend 2 or 3 weeks at La Trobe. In the week of the workshop Tom Ivey (“Cartan for Beginners”) and Keizo Yamaguchi (Hokkaido University) will both give informal courses (see below) suitable for postgraduates and Early Career Researchers (ECR's). These courses will provide background for the business of the workshop proper. There will also be a couple of introductory lectures on geometric numerical integration and the geometry of difference equations.
- Basic notions:
Differential ideals, Pfaff & Frobenius theorems, jet spaces and standard contact systems
- Involutivity:
Integral elements, the Cartan-Kahler theorem, Cartan's Test
- Geometric examples:
The Euclidean frame bundle, Frenet equations & vortex filament flow, surfaces in R^3 (CMC, Weingarten, canal surfaces); triply orthogonal systems; minimal hypersurfaces in S^4
- Prolongation:
General theory; linear Pfaffian systems & tableaux; more geometric examples, including Hopf hypersurfaces
- Characteristics:
The characteristic variety, Darboux's method, Hopf hypersurfaces in CH^2
Geometry of linear differential systems - Towards the contact geometry of second order
- Geometry of jet spaces:
Linear differential systems (Pfaffian systems); Grassmannian construction of geometric jet spaces; Strong and weak derived systems; Cauchy characteristic systems; Backlund Theorem
- Tanaka theory of linear differential systems:
Symbol algebras of regular differential systems; (algebraic) Prolongation of symbol algebras; Proof of Backlund Theorem
- PD manifolds of second order:
Realization Lemma; Characterization of submanifolds in second order jet spaces; Reduction Theorems; Higher order contact manifolds; Goursat flags
- Differential systems associated with simple graded Lie algebras:
Semi-simple graded Lie algebras; Gradations in terms of root space decompositions; Gradation in terms of matix representations; Theorem on prolongations
- G2 – geometry of overdetermined systems of second order:
Low dimensional (local) classification of regular differential systems; Cartan’s G2-model on 5-dimensional space; G2-model of overdetermined systems of second order; Other examples
Call for Papers
Participants are requested to submit an abstract for their presentation. The duration of these presentations will be 30 minutes with 10 minutes for questions/discussion. The organisers have a strong preference for talks addressing open problems.
- Abstracts can be submitted in any version of TeX, but we request authors to minimise the complexity of their code,
- submit an abstract via the registration page. The deadline for abstracts has been extended to June 1st.
Registration fees
- Australian residents
- base fee $A100
- student/unemployed $A70
- Australian Mathematical Society/ANZIAM/AMSI members 50% discount on the above categories.
- International registration fee $US100.
Accommodation
Limited apartment accommodation near campus in the form of single and twin rooms is available on a "first come first served" basis. See the registration form.
Motel accommodation is available at the "Parkside Motor Inn" on the north western boundary of the University.
We would advise booking early. Click on link for contact details (including email).
Conference Dinner
The conference dinner will held at a local restaurant (exact venue to be arranged) on Thursday June 18th. Approximate cost is $40 - 45. Vegetarian food will be available.
Travel Grants
We particularly encourage graduate students to give presentations on their work. All interstate graduate students, ECR's and unemployed mathematicians, regardless of their intention to give a talk, are entitled to apply to the organisers for an AMSI funded travel grant. Victorian participants in financial need may also apply for smaller grants. Participants should indicate on the registration form if they wish to apply for assistance.
Sponsors
Invited Speakers
- Ian Benn (Newcastle)
- Mike Crampin (Ghent)
- Tom Ivey (Charleston)
- Jonathan Kress (UNSW)
- Demeter Krupka (Olomouc, Czech Rep.)
- Olga Krupkova (Olomouc, Czech Rep.)
- Tom Mestdag (Michigan/Ghent)
- Geoff Prince (LaTrobe)
- Willy Sarlet (Ghent)
- David Saunders (EBS, UK)
- Gerard Thompson (Toledo)
- Peter Vassiliou (Canberra)
- Keizo Yamaguchi (Hokkaido)
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