Askold Khovanski (University of Toronto)
The theory of fewnomials
Fields Institute, Stewart Library
October 2, 2-3:30 pm
October 5, 11:30 -1 pm
October 8, 10- 11:30 am
1. What the theory is about.
2. Generalizations of Rolle's Theorem and two simple versions
of the theory
3. Theorems on Real and Complex Fewnomials (with proofs)
Fields Institute, Stewart Library
October 14, 11:30 am- 1 pm
October 16, 2-3:30 pm
Saul Schleimer (University of Warwick)
Introduction to three-manifolds, triangulations, and normal
surfaces
Fields Institute, Room 230
November 6, 9, 13, 23 (2-3:30 pm)
*November 27 (1-2:30 pm)*
1. Three-manifolds, important examples (S^3, T^3, PHS^3, Seifert-Weber
space, handlebodies), the fundamental group, incompressible
surfaces, Haken manifolds, the loop theorem, sphere decomposition
and connect sum, torus decomposition
2. Thurston geometries, examples (Seifert fibred spaces, quotients
of S^3, E^3, H^3), the geometrization theorem and the Poincare
conjecture, implications for the homeomorphism problem, recognition
of: three-sphere, unknot, Haken manifolds, H^3/\Gamma (Jason
Manning's algorithm)
3. (Pseudo) Triangulations of three-manifolds, ideal triangulations,
examples, Weeks' SnapPea program, normal and almost normal surfaces,
Haken sum and geometric consequences, incompressible surfaces
normalize, Jaco-Tollefsen algorithm (sphere decomposition),
finding compressions, unknot recognition lies in NP, Jaco-Oertel
algorithm
(Haken recognition)
4. Sweep-outs, normalization of almost normal surfaces, Rubinstein-Thompson
algorithm for three-sphere recognition
5. Crushing triangulations along two-spheres, Casson's algorithm
to recognize the three-sphere, Agol-Hass-Thurston algorithm,
Three-sphere
recognition lies in NP
