A Panorama of Quantum Topology - Recent Progress in Quantum Algebra, Low-Dimensional Topology, and Mathematical Physics (26w5582)

The Banff International Research Station will host the "A Panorama of Quantum Topology - Recent Progress in Quantum Algebra, Low-Dimensional Topology, and Mathematical Physics" workshop in Banff from July 17 to 24, 2026.

This workshop highlights new results at the interface of quantum topology with a wide range of vibrant areas of modern mathematics, including quantum algebra, Lie theory, knot theory, geometric topology, mathematical physics and computation. Quantum topology studies the global properties of geometric spaces in low dimensions -- 3-dimensional space, space-time, and knotted strings and surfaces in these spaces -- using tools inspired by quantum physics. These powerful tools are known as invariants: quantities which help distinguish spaces and shapes from one another. The ground-breaking Jones polynomial of the 1980's opened the door to a host of new invariants including the knot homology theories of the 21st century, revolutionising knot theory and low-dimensional topology.

This event will facilitate a broad overview of the state of the art in quantum invariants, including fast computations, universal invariants and their relationships to famous equations arising from quantum physics and algebra, and the interplay between topological and geometric properties of spaces. The participant list features many of the leading world experts in this area, and provides opportunities for young researchers to become involved through an early career showcase, problem sessions, mentoring, and informal interactions.

This event is organized by Associate Professor Zsuzsanna Dancso of the University of Sydney, Australia (quantum topology), Professor Hans Boden of McMaster University, Canada (low-dimensional topology), and Assistant Professor Iva Halacheva of Northeastern University, USA (representation theory and quantum algebra).

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF) and Alberta's Technology and Innovation.