The workshop and seminars on "Invariants of Knots and 3-Manifolds" took place
at the Research Institute for Mathematical Sciences (RIMS), Kyoto University,
in September 2001.
The workshop was held over the period September 17-21.
Seminars were held on the Tuesdays, Wednesdays and Thursdays of the other
weeks of September, including "Goussarov day" on September 25.

Since the interaction between geometry and mathematical physics in the 1980s,
many invariants of knots and 3-manifolds have been discovered and studied:
polynomial invariants such as the Jones polynomial,
Vassiliev invariants, the Kontsevich invariant of knots,
quantum and perturbative invariants, the LMO invariant
and finite type invariants of 3-manifolds.
The discovery and analysis of the enormous number of
these invariants yielded a new area:
the study of invariants of knots and 3-manifolds
(from another viewpoint, the study of the sets of knots and 3-manifolds).
There are also developing topics related to other areas such as
hyperbolic geometry via the volume conjecture and
the theory of operator algebras via invariants arising from 6j-symbols.
On the other hand, recent works have almost completed
the topological reconstruction of the invariants
derived from the Chern-Simons field theory.

An aim of the workshop and seminars was to discuss
future directions for this area.
To discuss these matters fully, we planned 1 month of activities,
relatively longer than usual.
Further, to encourage discussions among the participants,
we arranged a short problem session after each talk,
and requested the speaker to give his/her open problems there.
Many interesting problems were presented in these problem sessions and,
based on them, we had valuable discussions
in and between seminars and the workshop.
Open problems discussed there were edited and formed into a problem list,
which, I hope, will clarify the present frontier of this area and
assist readers when considering future directions.

The workshop and seminars were organized by
T. Ohtsuki, H. Murakami, J. Murakami, and T. Kohno.
This proceedings volume was edited by
T. Ohtsuki, T. Kohno, T. Le, J. Murakami, J. Roberts, and V. Turaev.
The workshop and seminars were partially supported by
Grand-in-Aid for Scientific Research,
Ministry of Education, Culture, Sports, Science and Technology, Japan:
Kiban(C)13640064 (T. Ohtsuki), Kiban(B)12440014 (T. Kohno),
Kiban(B)12440015 (S. Kojima), Kiban(B)12440018 (H. Murakami),
and partially supported by the Inoue Foundation for Science.
The workshop and seminars were held as partial activities of
the 2001 RIMS project research
"Low-dimensional topology in the twenty-first century",
organized by H. Murakami, T. Kobayashi, J. Murakami, T. Ohtsuki, K. Saito,
M. Sakuma, and K. Taniyama. The logo was designed by N. Okuda.

*T. Ohtsuki, September 2002*

1. Pages 1-12 :

- Dror Bar-Natan

2. Pages 13-28 :
**
QHI, 3-manifolds scissors congruence classes and the volume conjecture
**

- Stephane Baseilhac, Riccardo Benedetti

3. Pages 29-41 :
**
A homological definition of the Jones polynomial
**

- Stephen Bigelow

4. Pages 43-54 :
**
Periodicity of Goussarov-Vassiliev knot invariants
**

- Stavros Garoufalidis

5. Pages 55-68 :
**
On the quantum sl_2 invariants of knots and integral homology spheres
**

- Kazuo Habiro

6. Pages 69-87 :
**
Quantum invariants of Seifert 3-manifolds and their asymptotic expansions
**

- Soren Kold Hansen, Toshie Takata

7. Pages 89-101 :
**
Polynomial invariants and Vassiliev invariants
**

- Myeong-Ju Jeong, Chan-Young Park

8. Pages 103-117 :
**
Knot invariants derived from quandles and racks
**

- Seiichi Kamada

9. Pages 119-141 :
**
p-Modular TQFT's, Milnor torsion and the Casson-Lescop invariant
**

- Thomas Kerler

10. Pages 143-160 :
**
Loop spaces of configuration spaces and finite type invariants
**

- Toshitake Kohno

11. Pages 161-181 :
**
A surgery formula for the 2-loop piece of the LMO invariant of a pair
**

- Andrew Kricker

12. Pages 183-199 :
**
On configuration space integrals for links
**

- Christine Lescop

13. Pages 201-214 :
**
Matrix-tree theorems and the Alexander-Conway polynomial
**

- Gregor Masbaum

14. Pages 215-233 :
**
Cubic complexes and finite type invariants
**

- Sergei Matveev, Michael Polyak

15. Pages 235-244 :
**
Power sums and Homfly skein theory
**

- Hugh R. Morton

16. Pages 245-261 :
**
Asymptotics and 6j-symbols
**

- Justin Roberts

17. Pages 263-279 :
**
Generalisations of Rozansky-Witten invariants
**

- Justin Roberts, Justin Sawon

18. Pages 281-294 :
**
(2+1)-dimensional topological quantum field theory with a Verlinde basis and Turaev-Viro-Ocneanu invariants of 3-manifolds
**

- Nobuya Sato, Michihisa Wakui

19. Pages 295-302 :
**
Torsions of 3-manifolds
**

- Vladimir Turaev

20. Pages 303-311 :
**
On the potential functions for the hyperbolic structures of a knot complement
**

- Yoshiyuki Yokota

21. Pages 313-335 :
**
Skein module deformations of elementary moves on links
**

- Jozef H Przytycki

22. Pages 337-362 :
**
The algebra of knotted trivalent graphs and Turaev's shadow world
**

- Dylan P. Thurston

23. Pages 363-376 :
**
Some computational results on mod 2 finite-type invariants of knots and string links
**

- Ted Stanford

24. Pages 377-572 :
**
Problems on invariants of knots and 3-manifolds
**

- T. Ohtsuki (Editor)

**These pages are not updated anymore.
They reflect the state of
.
For the current production of this journal, please refer to
http://msp.warwick.ac.uk/.
**