The main speakers will each give three talks on their recent work. It is hoped that this will allow them to go into rather more depth and detail than is possible at most conferences. There will be, in addition, several other speakers, including Caroline Series, Marc Lackenby, Mary Rees and Jake Rasmussen.

This event is open to any mathematician who wishes to attend. There is no registration fee. Some travel support is available for graduate students at UK universities or at Princeton.

This workshop is part of a new initiative by Oxford and Princeton to strengthen links between the two universities. It is funded in part by the London Mathematical Society and the Oxford University Press.

1. Your arrival & departure dates.

2. Your choice of accommodation (room with ensuite bathroom
in Keble College; room with shared bathroom in Keble College; other)

3. Whether or not you wish to come to the conference dinner.

4. If you are graduate student, whether you wish to
apply for financial support. If so, you should send an
estimate of your travel expenses, and also give details
of any other sources of funding available to you.

5. Whether you wish to reserve a parking space at Keble
College.

You also need to send a reservation fee for
the accommodation (if you wish to stay in Keble College)
and conference dinner (if you wish to come; see below for costs). This
should be made payable to the Mathematical Institute,
University of Oxford. THIS NEEDS TO ARRIVE BY **6 MAY**
to guarantee your accommodation. It should be
sent to:

Marc Lackenby,

Mathematical Institute,

University of Oxford,

24-29 St Giles'

Oxford OX1 3LB

United Kingdom

There is no registration fee.

Single room with ensuite bathroom: 51 pounds per night, plus 17.5% taxes. These lie in the historic part of the college.

Both prices include the cost of breakfast. These rooms are nice, but they are students rooms during term-time, and so are not the height of luxury.

Keble College has no double rooms. So, if you will be accompanied, then we suggest you try some of the alternative accommodation suggested in the websites below.

If you wish to stay in Keble College, you need
to reserve your accommodation by ** 6 MAY** . The reservation
fee is 10% of the total cost and is non-refundable.
The remainder needs to be paid by ** 23 JULY**.

Participants with a UK, US or Euro bank account may pay by cheque, made payable to the Mathematical Institute, University of Oxford. In the case of US dollars or Euros, please be sure to use the correct rate of exchange (ie the one used for converting to pounds). In addition, you need to add 4.18 pounds to cover our bank charges. Those without a UK, US or Euro bank account should use an international money order. Since these usually incur a bank charge, you may wish to pay the full cost of your accommodation at the time of reservation, in order to avoid two sets of charges. Unfortunately, credit cards are not accepted.

IF YOU MISS THE 6 MAY DEADLINE, then we cannot guarantee that accommodation will be available for you at Keble College. However, the chances are that there will still be rooms free after that date. Contact Marc Lackenby under these circumstances.

There is plenty of other accommodation in Oxford, although much of it is quite expensive. See www.visitoxford.org or www.touristnetuk.com/wm/oxford for more information. Oxford is quite a large city (about 7 miles across) and so you should ensure that if you do organise your own accommodation, then it is within easy reach of the Mathematical Institute: you should choose a hotel that either in the city centre or just north of it.

**By car:** Driving time is about an hour outside of
the rush hour, but it can take considerably longer
at peak times. Cars can be rented at Heathrow
Airport or in Oxford. If you do drive to Oxford,
and are staying at Keble College, there are a few
parking spaces available. Contact
Marc Lackenby if you wish to reserve one of these.

**By rail:** The easiest route is to take the Heathrow
Express from Heathrow to London Paddington (journey time 15 minutes)
and then a fast train from Paddington to Oxford
(journey time one hour). This is a good way to get
from the airport to Oxford. But the trains in the
UK are, alas, unreliable and so we do not advise
that you depend on them to get you back to the
airport on time! Train timetables are available
here.

** By coach:** A cheap, regular and reliable coach service is
available directly between Oxford and Heathrow.
Journey time is usually about 1.5 hours, but may be
longer in the rush hour. More information about
coaches between Oxford and Heathrow is available
here.

** By taxi:** This is certainly the most hassle-free but
also the most expensive: about 70 pounds one way.

Maps of Oxford are available here and here.

Zoltan Szabo (Princeton) - 3 talks

Marc Lackenby (Oxford)

Jake Rasmussen (Princeton)

Mary Rees (Liverpool)

Caroline Series (Warwick)

Juan Souto (Bonn)

Vivien Easson (Oxford)

See below for titles and abstracts.

Jim Anderson (Southampton)

Javier Aramayona (Southampton)

Stevie Budden (Sussex)

Jack Button (Cambridge)

Olivier Collin (UQAM)

Marston Conder (Auckland)

Edward Crane (Oxford)

Chunrong Feng (Loughborough)

Alastair Fletcher (Warwick)

Stefano Francaviglia (Pisa)

Vaibhav Gadre (Brandeis)

James Giblin (Warwick)

Tim Haire (Cambridge)

Maxim Hendriks (Leiden)

Joonhyung Kim (Seoul)

Hyunsuk Kang (Cambridge)

Misha Kapovich (Davis)

Steve Kerckhoff (Stanford)

Inkang Kim (Seoul)

Sadayoshi Kojima (Tokyo Institute of Technology)

Thilo Kuessner (Siegen)

Cyril Lecuire (UMPA)

Raymond Lickorish (Cambridge)

Andrew Lobb (Harvard)

Cormac Long (Southampton)

Joseph Maher (Caltech)

Sylvain Maillot (Strasbourg)

Vlad Markovic (Warwick)

Bruno Martelli (Pisa)

Yoav Moriah (Technion)

Hugh Morton (Liverpool)

Oliver Nash (Oxford)

Junalyn Navarra-Madsen (Dallas, Texas)

Walter Neumann (Columbia)

Max Neumann-Coto (National University of Mexico)

Ken'ichi Ohshika (Osaka)

Jonathon Parker (Durham)

Kate Petersen (Austin, Texas)

Joan Porti (Barcelona)

Kasra Rafi (UCSB)

Alan Reid (Austin, Texas)

Tim Riley (Yale)

Martin Scharlemann (UCSB)

Irene Scorza (Warwick)

Ken Shackleton (Southampton)

Jennifer Schultens (Davis)

Ivan Smith (Cambridge)

Michal Stukow (Gdansk)

John Sullivan (TU Berlin)

Blazej Szepietowski (Gdansk)

Yasemin Talu (METU)

Akira Ushijima (Warwick)

Genevieve Walsh (Austin, Texas)

Matthew Weston (Sussex)

Jonathon Williams (Southampton)

9.15 - 10.00: Tea & coffee

10.00 - 11.00: Dave Gabai - Shrinkwrapping and the taming of hyperbolic 3-manifolds, I

11.00 - 11.30: Tea & coffee

11.30 - 12.30: Zoltan Szabo - Heegaard diagrams and holomorphic disks, I

12.30 - 2.30: Lunch

2.30 - 3.30: Juan Souto - Volume of hyperbolic manifolds and distances of Heegaard splittings

3.30 - 4.15: Tea & coffee

4.15 - 5.15: Mary Rees - The Ending Laminations Theorem direct from Teichmuller geodesics

** Tuesday**

9.30 - 10.30: Dave Gabai - Shrinkwrapping and the taming of hyperbolic 3-manifolds, II

10.30 - 11.15: Tea & coffee

11.15 - 12.15: Zoltan Szabo - Heegaard diagrams and holomorphic disks, II

12.15 - 2.30: Lunch

2.30 - 3.30: Jake Rasmussen - Khovanov Homology and the slice genus

3.30 - 4.15: Tea & coffee

4.15 - 5.15: Vivien Easson - Surface subgroups and handlebody attachment

7.00: Workshop dinner in Keble College

** Wednesday **

9.30 - 10.30: Dave Gabai - Shrinkwrapping and the taming of hyperbolic 3-manifolds, III

10.30 - 11.15: Tea & coffee

11.15 - 12.15: Zoltan Szabo - Heegaard diagrams and holomorphic disks, III

12.15 - 2.30: Lunch

2.30 - 3.30: Caroline Series - Thurston's bending measure conjecture for
quasifuchsian once punctured torus groups

3.30 - 4.15: Tea & coffee

4.15 - 5.15: Marc Lackenby - Large groups and thin position

We will discuss a new technique for finding Cat(-1) surfaces in hyperbolic 3-manifolds. We will use this to prove "If M is a complete hyperbolic 3-manifold with finitely generated fundamental group, then M is topologically and geometrically tame".

** Zoltan Szabo - Heegaard diagrams and holomorphic disks**

The lectures will give a quick introduction to the Heegaard Floer homology groups for closed oriented three-manifolds. These invariants are constructed by using Heegaard diagrams and studying Lagrangian Floer homology in the symmetric product of the Heegaard surface.

** Marc Lackenby - Large groups and thin position **

A group is known as "large" if it has a finite index subgroup that admits a surjective homomorphism onto a non-abelian free group. Such groups have many interesting properties, for example super-exponential subgroup growth. Possibly the strongest form of the virtually Haken conjecture asserts that any hyperbolic 3-manifold has large fundamental group. This is known to be true in the cusped case, by a theorem of Cooper-Long-Reid. In my talk, I will give a necessary and sufficient condition for a finitely presented group to be large, in terms of the existence of a nested sequence of finite index subgroups where successive quotients are abelian groups with sufficiently large rank and order. The proof is topological in nature, using a version of thin position for Cayley graphs of finite groups. I will then show how the Cooper-Long-Reid result follows as a corollary.

** Jake Rasmussen - Khovanov Homology and the slice genus **

I'll describe an invariant of knots defined using Khovanov's Jones polynomial homology. This invariant is defined in a similar way to Ozsvath and Szabo's tau-invariant (defined using the knot Floer homology), and shares many of its properties. In particular, it gives a lower bound on the four-ball genus of a knot. As a corollary, one gets a purely combinatorial proof of the Milnor conjecture.

** Mary Rees - The Ending Laminations Theorem direct from Teichmuller Geodesics.
**

I shall discuss a direct proof [3] of the Ending Laminations Theorem, in the incompressible boundary case, and when the ending laminations data is a pair of minimal laminations. The proof follows the general strategy of Minsky's approach to the Ending Laminations Conjecture, both in his special case proofs over the last 10 years or so, and in his proof with Brock and Canary, announced in 2002, and since partially disseminated, of the whole conjecture. But there are significant differences in detail. My proof uses directly a theory of Teichmuller geodesics which was developed [2] for quite a different purpose. The basic idea of this theory, and of the proof of [3], is that, after suitable decomposition, one can exploit methods valid for geodesics through the thick part of Teichmuller space. I shall try to bring this out in my talk. In fact, another key tool is some results of Minsky which he proved [1] concerning elementary-move-related pleated surfaces in a hyperbolic manifold. Although used to prove the case of bounded geometry laminations data, the results in question do not require bounded geometry.

[1] Minsky, Yair: Bounded Geometry for Kleinian Groups. Invent. Math. 146 (2001) 143-192.

[2] Rees, Mary: Views of Parameter Space: Topographer and Resident. Asterisque 288, 2003. See especially Chapters 14-15.

[3] Rees, Mary: The geometric model and coarse Lipschitz equivalence direct from Teichmuller geodesics. http://www.liv.ac.uk/~maryrees/maryrees.homepage.html (Also in the arxiv.)

** Caroline Series - Thurston's bending measure conjecture for
quasifuchsian once punctured torus groups **

We prove Thurston's bending measure conjecture for quasifuchsian once punctured torus groups. The conjecture states that the bending measures of the two components of the convex hull boundary uniquely determine the group. The proof uses a number of recent results about bending measures which we will review.

** Juan Souto -
Volume of hyperbolic manifolds and distaces of Heegaard splittings **

Let M be a hyperbolic manifold, M = H \cup H' a Heegaard splitting and d_P(H,H') the distance in the pants-complex between the handlebody sets corresponding to H and H'. We prove that the volume of M is bounded from above and below by linear functions in d_P(H,H'). The appearing constants depend only on the genus of the Heegaard splitting. (This is a joint work with J. Brock).

** Vivien Easson - Surface subgroups and handlebody attachment **

Let M be a 3-manifold (not a 3-ball) containing no essential small surface (sphere, torus, disc or annulus). If M has non-empty boundary it is Haken and hence can be given a complete hyperbolic structure with totally geodesic boundary. Moreover, its fundamental group contains surface subgroups each corresponding to a virtually embedded surface in M. Attach handlebodies (and solid tori) to the boundary of M. We show that each surface subgroup as above survives most such operations. (arXiv:math.GT/0403077)

Return to Marc Lackenby's homepage.