Geometry and physics of knot homology

introduction

• knot homology
• A-polynomial
• quantization
• categorification

lectures by Gukov

• 4 lectures at MPI by Gukov
  • 4/17, 4/22, 4/24, 4/25
• notes taken at https://docs.google.com/file/d/0B8XXo8Tve1cxYzlJUk5aU21EZTA/edit

lecture 1

• knot polynomials
  • Jones
  • Alexander
  • HOMFLY-PT

lecture 2

• knot homology
  • Khovanov homology - Jones
  • knot Floer homology - Alexander
  • triply graded homology - HOMFLY

memo

• http://www.birs.ca/events/2014/5-day-workshops/14w5073

related items

• A-polynomial, B-model, and Quantization
• Knot invariants from exactly solvable models and representation theory

expositions

• Edward Witten, Two Lectures on Gauge Theory and Khovanov Homology, http://arxiv.org/abs/1603.03854v1
• Nawata, Satoshi, and Alexei Oblomkov. “Lectures on Knot Homology.” arXiv:1510.01795 [hep-Th, Physics:math-Ph], October 6, 2015. http://arxiv.org/abs/1510.01795.
• Piotr Sułkowski physics and geometry of knot homologies
• Gukov, Sergei, and Ingmar Saberi. 2012. “Lectures on Knot Homology and Quantum Curves.” arXiv:1211.6075 [hep-Th] (November 26). http://arxiv.org/abs/1211.6075.
• Sergei Gukov, Quantization and Categorification, Lecture 4. 2012. http://www.youtube.com/watch?v=e4ETGWgaZDY&feature=youtube_gdata_player.

articles

• Stavros Garoufalidis, Aaron D. Lauda, Thang T. Q. Lê, The colored HOMFLYPT function is \(q\)-holonomic, arXiv:1604.08502 [math.GT], April 28 2016, http://arxiv.org/abs/1604.08502
• Hee-Joong Chung, Tudor Dimofte, Sergei Gukov, Piotr Sułkowski, 3d-3d Correspondence Revisited, http://arxiv.org/abs/1405.3663v2
• Elliot, Ross, and Sergei Gukov. ‘Exceptional Knot Homology’. arXiv:1505.01635 [hep-Th], 7 May 2015. http://arxiv.org/abs/1505.01635.
• Chung, Hee-Joong, Tudor Dimofte, Sergei Gukov, and Piotr Sułkowski. “3d-3d Correspondence Revisited.” arXiv:1405.3663 [hep-Th], May 14, 2014. http://arxiv.org/abs/1405.3663.