Topology Seminar

The Topology Seminar has talks on a variety of topics in topology, including algebraic geometry, chromatic homotopy theory, configuration spaces, continuum theory, functor calculus, graph cohomology, homotopical algebra, Nielsen fixed-point theory, operads, simplicial sets, spaces of knots and links, span theory, and topological groups.

Spring 2026

For the Spring 2026 semester we will meet 1:00 - 2:00 on Fridays in 208 Maxim Doucet Hall or on Zoom.

For more information or connection details contact Robin Koytcheff.

• 23 January 2026, 2:00 - 3:00 (note time change)
  From Khovanov homology to its stable homotopy refinement
  Nilangshu Bhattacharyya (LSU)
  Abstract: Khovanov homology assigns a knot or a link to a bigraded homology theory that categorifies the Jones polynomial. It has concrete applications, for instance Rasmussen’s s-invariant, extracted from Lee’s deformation, which gives a lower bound on the smooth slice genus. At the same time, while the theory is very combinatorial and closely tied to the representation theory of U_q(sl₂), it can be hard to see the underlying geometric picture directly from the homology groups. The stable homotopy refinement, introduced by Lipshitz and Sarkar, upgrades Khovanov homology to a space level invariant: a spectrum whose cohomology recovers Khovanov homology while supporting additional structure that is invisible in homology. In this talk, I will start with the construction of Khovanov homology and then gradually move toward its stable homotopy refinement. My work uses this viewpoint to build and study stable homotopy types beyond classical links, including planar trivalent graphs with perfect matchings, and to connect these refinements with themes from contact geometry and Floer theoretic settings.
  

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