NZ Mathematics Research Institute 2006
Workshop on Geometric Methods in the Topology of 3-Dimensional Manifolds
Taipa
8 - 15 January 2006
For more photographs of the area around Taipa taken, like that above, by Louise Gauld click
here.
Speakers
| Timetable
| Registration
| Support
| Sponsors
| Preliminary Reading
| Recommended Related Activities
| Organisers
**NEW**
Hopefully everyone expected to attend received an email message in mid-December
confirming that they were expected and that accommodation is arranged for them.
If you did not receive that email message then email
David Gauld for confirmation.
Similarly if you asked for help with transport then an email message will have been sent to you
on 20 December proposing which ride you have been allocated. Again if you did not receive such
an email message then you should email David Gauld urgently to make arrangements. Note that if
you have been assigned a ride in a minibus and miss it then you will have to travel to Taipa some
other way. There is one bus going to Taipa the
next day, Monday 9th, leaving Auckland between 8 and 9 and getting to Taipa at about 3pm. I do
not know whether there are any spare seats on that bus.
If you are travelling separately then you should go to the Taipa Bay Resort first; there you
will be allocated a room.
**END NEW**
The focus of the 2006
NZMRI Summer
Workshop is Geometric Topology and Differential Geometry:
The Poincare Conjecture
The meeting is one of the key events of the Thematic Programme
funded by the
New Zealand Institute of Mathematics and its Applications
(NZIMA).
The meeting will consist of a preliminary workshop in which the necessary
tools for the understanding of the recent work on the Poincare conjecture by
Perelman will be developed. Subsequently more specialised lectures will be
given by invited researchers
The principal speakers are:
-
Timetable and format
Arrival: by the evening of Sunday 8 January, 2005.
Departure: the afternoon of
Sunday 15 January.
Talks will start on the morning of Monday 9 January,
and finish by lunchtime Sunday 15 January.
Thursday 12 January and the remaining afternoons are free.
Accommodation
Accommodation is booked at:
the Taipa Bay Resort
Please follow the links to obtain the relevant address and other
contact information. Some participants will be housed in the very nearby Blue Pacific Motel and some
in the Taipa Sands Motel, about 5 minutes walk away.
Your final allocation will be made by the organisers after discussion with staff at the resort.
Other activities
On Thursday, 12 January, David
Gauld will lead an organised excursion to the top of some nearby high hill.
Accommodation costs are covered for New Zealand based participants in
the workshop.
However, the budget for the meeting is limited. Hence if a New
Zealand based participant is accompanied
by a non-participating partner (or by family), then we will ask you
to cover all related expenses.
Catering will cost about $250 per person for the week.
We also ask that participants who have research grants make
additional contributions towards costs.
We can provide GST receipts or invoices for this purpose.
Alternatively, participants may wish to make tax-deductible donations
to the NZMRI
in support of its mission of enhancing mathematical research in New
Zealand and to enable
it to continue running these sorts of meetings in the future.
Accommodation and meals are normally provided
free to all NZ-based student
participants.
We urge you to seek travel support from your home
institution.
Graduate students based in Australia who are
student members of the
Australian Mathematical Society are eligible to receive a subsidy
of up to
AUD$300 each which will cover all of
your local accommodation and catering costs.
This support is generously provided by the Australian Mathematical
Society,
with the total grant in any one year not exceeding AUD$2,100.
We encourage you to seek travel support from your local institution.
The NZMRI's funding for the workshop does not permit support
for participants based outside of New Zealand.
Room costs are NZ$150 per night twin share
Catering will cost about NZ$250 per person for the week.
If you need additional information on related costs, please
contact us.
Lunch and dinner will be provided for participants
and their families from
Monday to Saturday (except on the free Thursday).
Catering will
cost about $250 per person for non participants and
those based
outside of New Zealand.
Taipa is at the head of Doubtless Bay on the east coast about 350 km drive north
of Auckland. The Taipa Bay Resort website leads to some maps. The Automobile Association is another good source of
maps: click on the
Northland Region in that map to get more detail, including Taipa.
Land
Information New Zealand is an excellent source of maps of New Zealand. If you accept their terms and
conditions then you will be given a map of New Zealand. Select a part which straddles the 35 degree line and extends south
to Auckland. Where the 35 degree line crosses the map you should see a large north-facing bay bounded on
the west by a headline shaped rather like a capital gamma: this is Doubtless Bay. Select a small box on
the map near the southern shore of the bay and Taipa is located at the mouth of the western and smaller
of two estuaries entering the bay. Once you have enlarged enough place names and contours will appear.
If you have not visited Northland before then you are strongly urged to drive yourself there: the drive
through the Waipoua Forest on the longer, western, route is especially
beautiful, but so is the eastern drive past the Bay of Islands.
If you do need a ride from Auckland then you are invited to indicate this on the registration form.
A minivan will be organised if needed to take participants from Auckland.
The meeting is one of the key events of the Thematic
Programmes funded by the
New Zealand Institute of Mathematics and its Applications (NZIMA).
Australian students attending the meeting may also be eligible to receive
support from the Australian Mathematical Society.
Registration closed on 5th September: if you have not yet registered and wish to attend email David
Gauld to see whether there is still space available.
Here is a list of those registered.
At the University of Auckland we are having a series of preliminary lectures aimed at helping people
prepare, beginning 18 November 2005 and running Monday, Wednesday, Friday for maybe six lectures
total. These lectures are being given by David Gauld, Richard Evans
and Rod Gover. We will try to scan handwritten notes taken by those attending the lectures and put
them on the web. Two versions of the first lecture appear there, the
second version was scanned in the wrong order but it still works!
Two versions of the second lecture are
available now too. Here are two versions of notes from the third
lecture. and from the fourth
lecture, but just one from the fifth lecture
and finally two versions of notes from the sixth
lecture. We have now completed those lectures.
There is a range of good introductory material that you can read to prepare for the workshop. The
book "The shape of space" by Jeffrey R Weeks, Volume 96 of the series of monographs and textbooks
in Pure and Applied Mathematics published by Marcel Dekker, while somewhat old, has numerous helpful
pictures and discusses all of the three relevant geometries in dimension 2 then the eight in
dimension 3. David Gauld prepared some geometry notes for his graduate
topology class which are somewhat imperfect but give a start. Email corrections and improvements to
David Gauld. Those notes give some useful further
sources. One particularly rich source is the website
Notes and commentary on Perelman's Ricci flow papers, maintained by Bruce Kleiner and John Lott.
Also look at the Clay Mathematics
Institute announcement of its Summer School 2005. For good overall surveys in the style we
expect of the Notices of the American Mathematical Society look at the articles by
Milnor and
Anderson. The AMS Bulletin
article by
Morgan
is another good one to look at.
Here are some sources for relevant Differential Geometry (thanks to Rod Gover for this advice):
Bennett Chow and Dan Knopf, "The Ricci flow: an introduction", Mathematical Surveys and Monographs,
110. American Mathematical Society.
For basic differential geometry the first chapters of
S Helgasson, "Differential Geometry, Lie Groups and symmetric spaces"
is a classical source.
Also S.W. Hawking and G.F.R. Ellis
"The large scale structure of space-time"
gives a good summary treatment of differential geometry (although toward
applications in theoretic physics).
Someone recommended
S.I. Goldberg
"Curvature and Homology"
I haven't looked at this myself.
John M Lee, "Riemannian manifolds. An
introduction to curvature", Graduate Texts in Mathematics, 176.
Springer-Verlag.
I have often used Michael Spivak's "A Comprehensive introduction to
differential geometry" -- but these are lengthy and not ideal I would
say. (I use them because I have them!)
A book I really like is:
Ib Madsen and Jurgen Tornehave, "From calculus to cohomology. de Rham cohomology and
characteristic classes", Cambridge University Press.
This is very efficient at starting from elementary beginnings and getting
to some serious results.
The
NZ-Japan Knot Theory Conference will take place in Auckland immediately before the Workshop from
4 to 7 January. Immediately after the Workshop the Workshop
Manifolds at Melbourne will take place.
The organisers are
Jeff Cheeger
Roger Fenn
David Gauld
Cameron Gordon
Vaughan Jones
Additional information
This page will be updated regularly. To obtain further information,
email David Gauld
Last updated 21 December 2005.
