The focus of the conference is on the modern methods in 3-manifold and knot theory, and their interactions with other areas of mathematics. Of particular interest are the relations between quantum topology and, for example, gauge theory, quantum computing, non-commutative algebra, representation theory, and other adjacent areas in geometry and topology. The conference shall both give an overview over the current state of modern algebraic and combinatorial methods in 3-dimensional topology and provide an opportunity for participants to educate themselves along the borderlines of overlapping areas of research. The conference is continuing the annual geometry and topology conference that was held at Ohio State from 1989 to 2000 in a different format. Most of the funding is for the support of doctoral students and recent PhD's, who are at the beginnings of their academic careers. The conference exposes them to a variety of new developments and interrelations in 3-dim topology from which they can develop their future research directions and projects as well as gives them an opportunity to introduce themselves to the topology community with presentations of their own work.

Topology of 3-manifolds is the study of the possible shapes in a 3-dimensional space. In two dimensions such shapes can be discs, spheres or also the surfaces of doughnuts and pretzels. They were of obvious interest and discussion among scientists and philosophers before 1492 when they asked what the shape of (the 2-dim surface of) the earth is. Remarkably, a similar discussion about the possible 3-dimensional shape of our cosmos is taking place right now among modern astronomers and astrophysicists. Yet, 3-dimensional shapes are much harder to describe and to distinguish. Conversely, physics heavily influenced 3-dimensional topology. The models that theoretical physicists use to describe elementary particles turned out to be highly insightful guidelines to develop new theories about the abstract 3-dimensional spaces in topology, from which eventually the areas of "quantum topology" and "gauge theory" emerged as purely mathematical disciplines. Furthermore, the algebraic tools and methods that are being developed along with the topology prove to be of much more universal interest. They serve, for example, as theoretical models for quantum computers, which - if constructed - would be able to break all known public encryption codes, such as those used, e.g., in the military and in the world of finance.

National Science Foundation (NSF)
Division of Mathematical Sciences (DMS)
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Joanna Kania-Bartoszynska
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Ohio State University
United States
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