CIMPA-UNESCO-VIETNAM School and Workshop on
Braids in Algebra, Geometry and Topology
(Hanoi, January 17-28, 2011)



Braid groups are a key tool in several parts of algebra, geometry and topology. Representative examples include the theory of quantum groups, hyperplane arrangements and knot theory. The school will introduce participating students to some important new developments in each of these very active areas of mathematics, focusing on the unifying role of braid group. In adopting this approach, we aim to present a large picture of mathematics to students and counteract a trend towards early specialization and exclusive focus on one narrow research topic. In addition, we hope that the school will boost interdisciplinary research as well as help promoting exchanges and collaborations between mathematicians in the region and experts from Europe, Japan and the United States .


Organizing committee:

  • Nguyen Viet Dung ( Institute of Mathematics, Hanoi, Vietnam)

  • Martin Lorenz (Temple University, Philadelphia, USA)

  • Phung Ho Hai (Institute of Mathematics, Hanoi, Vietnam)

Date and location:

The school will be held from January 17 to January 28, 2011, at the Institute of Mathematics, Vietnamese Academy of Science and Technology, 18 Hoang Quoc Viet Road, CauGiay District, 10307 Hanoi, Vietnam

Scientific program:

Braids, originally introduced in the context of low-dimensional topology, have since developed into a theme that permeates large parts of mathematics, thereby providing a link between many different areas of current mathematical research. The main topics of the CIMPA school in Hanoi will include knot theory, quantum groups and hyperplane arrangements, three thriving branches of mathematics where braid groups play an essential role. The school is primarily aimed at postgraduate students and young researchers in the region. After providing an introduction to the theory of braid groups, further lecture courses will lead up to some current problems in the aforementioned areas and related topics. The school will be followed by a 3-day workshop for specialists that will be devoted to a discussion of recent advances and perspectives for future research.

List of courses:

The school will be essentially centered on six courses. The lecture notes and slides of courses will be updated along the school. Please visit this page regularly to download them.

List of courses:

  • Corrado De Concini (Univ. Rome I, Italy) : Hyperplane arrangements and partition functions

  • Christian Kassel (Univ. de Starsbourg et CNRS, France) : Braid Groups and Hecke Algebras

  • Toshitake Kohno (Tokyo Univ., Japan) : Braid groups, configuration spaces and iterated integrals

  • Luis Paris (Univ. de Bourgogne, France) : An invitation to braid groups

  • Claudio Procesi (Univ. Rome I, Italy) : From splines to the index theorem

  • Le Tu Quoc Thang (Georgia Inst. of Technology, USA) : Braid groups and knot invariants


Abstracts of the Courses

Schedule of the Lectures

Workshop Talks

List of Participants


Lecture Notes: