Thursdays 10:00-11:30 in room 7218.
Organisers: Justin Roberts, Peter Teichner
This term our reading seminar makes the leap from super to hyper: we
intend to learn something about hyperbolic manifolds.
Thurston's discovery in the late 70s that almost all 3-manifolds ought
to have hyperbolic structures led to an exponential boom in the theory
of hyperbolic geometry, and not just in three dimensions. In the early
80s Gromov revolutionised combinatorial group theory with his theory
of hyperbolic groups. Both schools are still going strong, and a
knowledge of hyperbolic geometry seems more than ever a valuable piece
of mathematical background to have.
Both Thurston and Gromov are famous for the density of ideas in their
work rather than its accessibility. Fortunately, there are now many
good expositions available. We plan to work through Benedetti and
Petronio's Springer book "Lectures on Hyperbolic geometry" - we will
probably try to get through chapters A-C, covering the basics of
hyperbolic geometry, geometric structures on manifolds, Teichmueller
space and Mostow rigidity, perhaps augmented by additional topics from
other references (such as Thurston's Princeton book "Three-dimensional
geometry and topology vol.1", Ratcliffe's Springer book, Casson and
Bleiler's LMS book on automorphisms of surfaces, or Thurston's
original notes.) If there is sufficient interest and stamina we could
perhaps continue with a reading seminar on geometric group theory in
the spring.
No specific background will be assumed of the audience. We invite all
interested grad students, visitors and faculty to attend.
Provisional schedule:
January 8: Justin Roberts Overview/organisational
meeting
We will try to divide up and assign the term's talks to
willing participants!
Jan 15: Justin Roberts Hyperbolic space
Jan 22: Mike Gurvich Geometric structures on manifolds
Jan 29: Graham Hazel Teichmuller space
Feb 5: Tom Fleming Hyperbolic simplexes and the
figure-eight knot
Feb 12: Wee Teck Gan Quasi-isometries
Feb 19: Henning Hohnhold The Gromov norm
Feb 26: Sean Raleigh Mostow rigidity
March 4: Jana Comstock Classification of 3-dim. geometries,
Part I
March 11: Peter Teichner Classification of
3-dim. geometries, Part II
justin@math.ucsd.edu
