Topological structures in mathematics, physics and biology

The Laboratory of Topology and Dynamics of the Novosibirsk State University and international research unit «Center Poncelet» organize the multidisciplinary workshop «Topological structures in mathematics, physics and biology». The workshop will be held from September 14 (day of arrivals) to September 18 (day of departures) in the picturesque surroundings of Novosibirsk in resort hotel Sosnovka.
Poster of the workshop
Map of the resort hotel Sosnovka

By this event, we would like to highlight and promote some common faces of topology, statistical physics, condensed matter theory and biology, which jointly constitute the new interdisciplinary branch of mathematical physics, emerging at the edge of knot theory and statistics of fluctuating non-phantom string-like objects of different nature. Besides the traditional fundamental topological issues, there exists a set of important, but much less studied problems dealing with various incarnations of the "knot entropy" problem in soft matter physics and biology.

A number of problems in statistical and condensed matter physics, as well as in biology have straightforward interpretation in terms of the topology of fluctuating extended one- dimensional objects embedded in surfaces or in 3D spaces. Abstract images of entangled random trajectories have a variety of manifestations and include knotted polymer chains, random walks, chaotic processes, topology of Feynman diagrams, Wilson loops in topological field theories etc.

From a physical perspective, emergence of extended topological objects leads to a bunch of new nonperturbative phenomena in soft matter, and in biopolymer statistics. The workshop is aimed in communicating and exchanging the modern theoretical and numerical investigations carried out on low-dimensional topology in mathematics, soft matter physics and biophysics (protein folding and genomics). Our hope is that scientists from different fields, who might not ordinarily interact, will have an opportunity for cross- fertilization of ideas. In particularly, we expect to translate the topological ideas elaborated in high energy and topological field theory to soft mater physics. Thus, the unifying strands, which tie together the event, are the generic cross-disciplinary methods, rather than the particular applications.

The main topics of the conference are tentatively split in the following subjects:

1. New general mathematical trends in low-dimensional topology
2. Topology in physics: from field theories to soft matter and disordered systems
3. Statistical topology of biopolymers and beyond

During the conference public lectures of generic interest are expected.

Program committee

Louis Kauffman (University of Illinois at Chicago, USA and Novosibirsk State University, Russia)

Sergei Nechaev (Center Poncelet, Moscow, Russia)

Iskander Taimanov (Novosibirsk State University, Russia)

Andrei Vesnin (Novosibirsk State University, Russia)

Organizing committee

Nikolay Abrosimov (Novosibirsk State University, Russia)

Konstantin Gotin (Novosibirsk State University, Russia)

Meiramgul' Ermentay (Novosibirsk State University, Russia)

Andrei Vesnin (Novosibirsk State University, Russia)