Thematic program "New Trends in Topology"
February 1 – June 30, 2022
There were several far-reaching conceptual developments in topology at the turn of the century. In the late 1980’s – early 1990’s, a spectacular progress in the theory of knots and 3-dimensional manifolds was made by the Fields medalists E. Witten and V. Jones followed by the work of N. Reshetikhin, V. Turaev, O. Viro and others who related this area of topology to the theory of quantum groups. As a result, a new mathematical field was born, the topological quantum field theory.
In parallel to the appearance of the topological quantum field theory, there emerged a theory of Gromov-Witten invariants, under the influence of implantation of pseudo-holomorphic curve technique into symplectic geometry by M. Gromov and the holomorphic curve counting into quantum 2-dimensional gravity by E. Witten. This had led, in particular, to the Kontsevich-Manin theory of quantum cohomology and a breakthrough in enumerative geometry.
These new research areas are not only linked by the time of their appearance and the string theory as a common root, but also by deep relations between the techniques and underlying algebraic structures. The very recent developments in Gromov-Witten theory brought to light direct bridges between enumerative geometry of open strings and the theory of knot invariants. This program is devoted to a number of the most active areas of these research fields.
The following activities will be organized during the program:
- introductory school “Classical and Quantum Topology in dimension three”, April 11 – 15, 2022
- introductory school “New Methods in Enumerative Geometry”, April 25 – 29, 2022
- conference “Low-Dimensional Topology”, June 6 – 10, 2022
- conference “On the Crossroad of Topology and Enumerative Geometry”, June 13 – 17, 2022
- a weekly research seminar.
- Evgeny Fominykh, St. Petersburg University
- Ilia Itenberg, Sorbonne University
- Viatcheslav Kharlamov, Université de Strasbourg
- Vladimir Turaev, Indiana University
- Oleg Viro, Stony Brook University
Institutions participating in the organization of the event:
- St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
- Leonhard Euler International Mathematical Institute in Saint Petersburg
- Chebyshev Laboratory at St.Petersburg State University
The program is supported by a grant from the Government of the Russian Federation, agreements 075-15-2019-1619 and 075-15-2019-1620, and by a grant from Simons Foundation.