This award supports the participation of a group of US-based researchers and graduate students at a training school on ``Braids in Algebra, Geometry and Topology'', to be held January 17-28, 2011 in Hanoi. Lorenz is one of the organizers of the workshop while Le is one of the principal lecturers. The training school is primarily aimed at graduate students and young researchers. A series of six mini-courses by some of the world's leading experts will cover topics ranging from an introduction to the theory of braid groups to some current research in knot theory, quantum groups, and hyperplane arrangements, three thriving branches of mathematics where braid groups play an essential role. Immediately following the training school, there will be a 3-day workshop for specialists that will be devoted to a discussion of recent advances and perspectives for future developments.
Braids, originally introduced in the context of low-dimensional topology, have since developed into a theme that permeates large parts of mathematics and mathematical physics, thereby providing a link between many different areas of current research. The Institute of Mathematics at the Vietnam Academy of Science and Technology in Hanoi is the center of mathematical research in Vietnam; it has a strong tradition of research in several areas of algebra, geometry, and topology that are closely tied to braid groups. The training school in Hanoi will introduce participating students to some important new developments in a broad range of mathematical subjects, focusing on the unifying role of braid group. In adopting this approach, the organizers aim to present a panoramic view of current research in mathematics and counteract a trend towards specialization and exclusive focus on one narrow topic. In addition, the organizers expect that the school and its accompanying workshop will boost interdisciplinary research as well as help promoting exchanges and collaborations between mathematicians in the region of Southeast Asia and experts from Europe and the United States.
'' which was held at the Vietnam Academy of Science and Technology (VAST) in Hanoi during January 17-28, 2011. The conference had two parts: A training school from January 17 through January 25; it consisted of six mini-courses that were presented by leading experts in the field and primarily aimed at junior mathematicians. The principal aim was to introduce participants to some important new developments in a broad range of mathematical subjects, focusing on the unifying role of braid group. The school was followed by a two-day workshop devoted to recent progress in the field. It gave young researchers the opportunity to present some of their results to an expert audience. The organizing committee of the conference consisted of Nguyen Viet Dung, Phung Ho Hai (both VAST Institute of Mathematics, Hanoi, Vietnam) and Martin Lorenz (Temple University, Philadelphia, USA; PI of this grant). The grant continued to run under a no-cost extension for a second year, until 8/31/2012, in order to spend a small amount of remaining funds on travel expenses for invited speakers visiting Temple University and for a trip of a graduate student from Temple University to a workshop in Seattle. List of participants supported by this grant during the conference in Hanoi Martin Lorenz (US citizen, senior faculty at Temple University): PI of this grant, co-organizer of the conference, and a lecturer at the workshop; Thang Le (US citizen, senior faculty at Georgia Tech): lecturer of one of the mini-courses given at the training school; Michael Brandenbursky: postdoc from Israel working at Vanderbilt University; he gave a lecture at the workshop; Kei Nakamura: postdoc from Japan working at Temple University; he was a lecturer at the workshop; Meridith Perrie (US citizen): participating graduate student from Georgia Tech; Anh Tran: participating graduate student from Georgia Tech; Thao Vuong: participating graduate student from Georgia Tech; Tung Hoang: participating graduate student at the University of Illinois in Chicago. Other support The conference was also supported by a major grant from the Centre International de Mathe´matiques Pures et Applique´es (CIMPA, France) and by several smaller grants from the International Mathematical Union, the National Foundation for Science and Technology Development of Vietnam (VAST), and the Institute of Mathematics in Hanoi. The training school was held under the auspices of CIMPA and followed their organizational format. CIMPA was represented on location by Claude Cibils, the director of CIMPA. Mini-courses given at the training school Each course comprised five 50-minute lectures. The daily schedule of the training school consisted of five lectures, three in the morning and two in the afternoon. The contents of the mini-courses ranged from the basic notions in the theory of braid groups to a thorough discussion of very recent progress in the field, primarily concerning applications of braid groups to hyperplane arrangements, knot invariants, Hecke algebras, iterated integrals and other areas. Here is the list of mini-courses given during the training school. Corrado De Concini (Univ. of Rome I, Italy): Hyperplane arrangements and partition functions Christian Kassel (Univ. of Strasbourg and CNRS, France): Braid groups and Hecke algebras Toshitake Kohno (Univ. of Tokyo, Japan): Braid groups, configuration spaces and iterated integrals Luis Paris (Univ. de Bourgogne, Dijon, France): An invitation to braid groups Claudio Procesi (Univ. of Rome I, Italy): From splines to the index theorem Thang Le (Georgia Inst. of Technology, USA): Braid groups and knot invariants Other activities During the training school and workshop, joint lunches at a restaurant near the Mathematics Institute in Hanoi were offered to all participants so as to encourage interaction, mathematical and otherwise. The local organizers also organized a city tour of Hanoi, a conference banquet, and a day trip to Halong Bay. All these activities were well attended. They presented an excellent opportunity for many young mathematicians, mainly from Vietnam and neighboring countries, to learn recent developments in an exciting area of mathematics with numerous ramifications from outstanding experts, to discuss their research with each other, and to make valuable international connections. Broader impacts Due to the fact that some senior Vietnamese mathematicians were in attendance, the conference will undoubtedly have an impact on the teaching as well as on the research level of mathematics in Vietnam. All materials of the training school and the workshop, such as complete lecture notes of the mini-courses, abstracts of all workshop talks and the list of conference participants, are available to the public on the conference web site: www.math.ac.vn/conference/cimpa2011/cimpa2011.htm .
