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Applications to Geometry

18th December 2000 to 22nd December 2000

Original URL:

Isaac Newton Institute for Mathematical Sciences

Singularity Theory

July to December 2000

Organisers: VI Arnold (Moscow and Parix IX), JW Bruce (Liverpool), V Goryunov (Liverpool), D Siersma (Utrecht)

A Newton Institute Workshop


 University of Liverpool, 16 - 21 December 2000

Committee: Bill Bruce, James Damon, Peter Giblin, Terry Wall

Local Organiser: Peter Giblin

Much of Singularity Theory was inspired by geometrical problems. Thom’s early work on differential geometry via families of functions has borne enormous fruit in a richer understanding of the higher geometry of surfaces, and this in turn has found application in other fields such as computer vision. Projections of surfaces to planes, giving apparent contours, and the general theories of caustics and wavefronts, are other examples where new techniques were motivated by geometrical problems. Remarkable duality connections have been found between some of these problems, and there are applications to algebraic geometry and other fields of mathematics.

This workshop will take as its theme interactions between singularity theory and geometry in its many modern guises. Besides the topics mentioned above one could mention Gauss mappings, the geometry of discriminants and bifurcation diagrams, coadjoint orbits, billiards, arrangements and the global geometry of singular waves and varieties.

Possible participants include: P Akhmetiev, SS Anisov, JW Bruce, SIR Costa, JN Damon, A  Davydov, E Ferrand, TJ Gaffney, P Giblin, VV Goryunov, S Izumiya, S Janeczko, M Kazarian, D Mond, G Mikhalkin, O Neto, V Nikulin, T Nowik, D Siersma, M Teicher, B Teissier, MM Tibar, DJA Trotman, VA Vassiliev, O Viro, CTC Wall, V Zakalyukin.

Updates of the progamme will be posted at:

Working Sessions Arrival is planned for Saturday afternoon, 16 December, with working sessions Sunday to Thursday lunchtime. Departure Thursday afternoon, 21 December.

Location The Workshop will be held at the University of Liverpool Liverpool is situated 200 miles north-north-west of London. There is an hourly train service (3 hours journey time) from Euston station in London. There are also more-or-less direct trains from Cambridge (possibly a change at Ely) which give a cheaper fare. There is a local airport (Liverpool, Speke Airport: cheap fares with Easyjet to some European destinations!) but the nearest large airport is Manchester (40 miles).

Accommodation will be in a University hall of residence and sessions of the Workshop will be held in the Mathematics Building of the University. Transport between the two will be provided.

The Workshop is sponsored by grants from the London Mathematical Society and from the Newton Institute. It is hoped that these grants will cover all local expenses of participants (from dinner Saturday through to lunch Thursday). Participants are expected to obtain travel expenses from elsewhere. Application is particularly welcomed from research students. The workshop will be limited to about 40 participants.

For enquiries contact Peter Giblin.

Completed applications should be sent to Peter Giblin.

The closing date for applications is: 30 September 2000.

University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons