Perspectives on Knot Homology

External homepage


Banff International Research Station

Audience: Researchers in the topic
Conference dates: 17-May-2021 to 21-May-2021
Organizer: BIRS Programme Coordinator*
*contact for this listing

Quantum polynomial invariants of links and tangles, such as the Jones polynomial and the HOMFLY-PT polynomial, have played a central role in many areas of mathematics and physics over the last 3 decades. Knot homology is a far reaching generalization of polynomial invariants, which is still being developed. Homological knot invariants are referred to as categorification of the polynomial invariants -- polynomial invariants arise as the (graded) Euler characteristic of a homology theory. There are deeper structures which become manifest at the categorified level -- just like in transition from the Euler characteristic to homology in basic algebraic topology. In particular, one can speak of maps between vector spaces, but not between numbers or polynomials. The appropriate notion of a “map” between two knots is a surface cobordism in 4-space. In several cases, these give rise to maps on homology of the boundary links - a feature not available at the level of the Euler characteristic.

Many examples of homological invariants of knots and links were constructed over the last two decades, using a wide variety of methods: diagrammatic and geometric representation theory, gauge theory, and symplectic geometry. String theory and quantum field theories have led to influential predictions about the structure of the homological invariants, and provide general outlines of how they should arise from physics. While there is a uniform mathematical construction of quantum link and three-manifold invariants, we are yet to discover a uniform approach to their homological generalization. The aim of this workshop is to bring together experts on many developing perspectives on knot homology (physical, geometric and algebraic) to draw connections between them, and to explore applications.

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), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT).

Upcoming talks
Past talks
Your timeSpeakerTitle
FriMay 2119:00Ina PetkovaAnnular link Floer homology and gl(1|1)
FriMay 2117:30Sergei GukovFrom knot homology to 3-manifold homology
FriMay 2116:00Paul WedrichInvariants of 4-manifolds from Khovanov-Rozansky link homology
ThuMay 2019:00Ben WebsterKnot homology from coherent sheaves on Coulomb branches
ThuMay 2017:30Michael WillisTBA
ThuMay 2016:00Louis-Hadrien RobertFoam evaluation, link homology and Soergel bimodules
WedMay 1917:30Mina AganagicTBA
WedMay 1916:00Robert LipshitzKhovanov stable homotopy type and friends
TueMay 1819:00Eugene GorskyTautological classes and symmetry in Khovanov-Rozansky homology
TueMay 1817:30Edward WittenKnot Homology From Gauge Theory
TueMay 1816:00Tobias EkholmSkein valued curve counts, basic holomorphic disks, and HOMFLY homology
MonMay 1719:00Ciprian ManolescuKhovanov homology and the search for exotic 4-spheres
MonMay 1717:30Melissa ZhangUpsilon-like invariants from Khovanov homology
MonMay 1716:00Tudor DimofteQFT's for non-semisimple TQFT's
Embed this schedule
Export series to