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Takeshi Saito : Singular Supports in Equal and Mixed Characteristics
4 videos

Takeshi Saito : Singular Supports in Equal and Mixed Characteristics

Summer School 2024 - Low dimensional Topology
42 videos

Summer School 2024 - Low dimensional Topology

Summer School 2023 - New trends in mathematical fluid dynamics
31 videos

Summer School 2023 - New trends in mathematical fluid dynamics

Emergent phenomena in many-body quantum systems / Phénomènes émergents des systèmes quantiques a plusieurs corps
5 videos

Emergent phenomena in many-body quantum systems / Phénomènes émergents des systèmes quantiques a plusieurs corps

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Summer School 2024 - Low dimensional Topology

Collection Summer School 2024 - Low dimensional Topology

Organizer(s) Scientific Committee: Greg Kuperberg, Christine Lescop, Gwénaël Massuyeau, Jean-Baptiste Meilhan / Organization Committee: Christine Lescop, Gwénaël Massuyeau, Jean-Baptiste Meilhan
Date(s) 17/06/2024 - 05/07/2024
linked URL https://if-summer2024.sciencesconf.org
00:00:00 / 00:00:00
13 42

Khovanov invariants via immersed curves 4

By Liam Watson

Both Heegaard Floer homology and Khovanov homology admit relative versions associated with surface decompositions. In the case of a manifold with torus boundary, the Heegaard Floer invariant can be Both Heegaard Floer homology and Khovanov homology admit relative versions associated with surface decompositions. In the case of a manifold with torus boundary, the Heegaard Floer invariant can be interpreted in terms of immersed curves in a punctured torus; and in the case of a 4-ended tangle, the Khovanov invariant can be interpreted in terms of immersed curves in the 4-punctured sphere. While these invariants have different origins, this point of view highlights common algebraic underpinnings. Using mutation as a point of departure, this series will focus on Khovanov invariants in order to tell some of the algebraic and the geometric parts of this story.Lecture 1 (1 hour): Conway's mutation problemLecture 2 (1.5 hours): Bar-Natan's category from a bordered perspectiveLecture 3 (1.5 hours): Tangle invariants as immersed curvesLecture 4 (1 hour): Linearity: towards mutation invariance over any field

Information about the video

  • Date of recording 28/06/2024
  • Date of publication 07/01/2026
  • Institution Institut Fourier
  • Licence CC BY NC ND
  • Language English
  • Format MP4

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