Series:Advances in Physics Research
Proceedings of the International Conference on Knots, Quivers and Beyond (ICKQB 2025)
Conference: Proceedings of the International Conference on Knots, Quivers and Beyond (ICKQB 2025)
Date: 18-21 February 2025
Location: Mumbai, India (Hybrid)
Website: https://sites.google.com/view/knots-quivers-beyond/home From February 18 to 21, 2025, the Indian Institute of Technology, Bombay, hosted an international workshop “Knots, quivers and beyond”, sponsored by the Government of India under the “Scheme for Promotion of Academic and Research Collaboration” (SPARC) of the Ministry of Human Resource Development. The main aim of the workshop was to present a selection of recent advances related to the structure and calculation of homological knot invariants, centered around the celebrated knots-quivers correspondence first proposed by Kucharski-Reineke-Stosic-Sulkowski in 2017. The workshop featured 17 invited speakers from around the world including India, Europe, North America, and China as well as numerous local and online participants. It provided in particular an opportunity for IIT graduate students to be exposed to a highly active research area and to connect with potential international collaborators. This volume contains eight summaries of talks written by the workshop speakers, with several contributions being collaborative. Subjects include relations between topological field theory and problems of graph coloring; a review of the knots-quivers correspondence which relates motivic Donaldson-Thomas invariants of symmetric quivers to quantum invariants of knots; the representation theory of the spherical double affine Hecke algebra using brane quantization; exponential networks and their relation to enumerative combinatorics, specifically the Hilbert scheme of points in the plane via string dualities; 3d Chern-Simons theory as a playground for the calculation of entanglement entropy, with a focus on multi-component torus links; the existence of certain incompressible surfaces as a geometric question about knots that can be addressed with Heegaard Floer homology; the advantages of multiply-graded link homologies associated with the general linear Lie algebra over its specialization. This sample gives a faithful cross-section of the topics covered at the workshop. Further information, including slides and video recordings of all talks given at the workshop, are available at the website sites.google.com/view/knots-quivers-beyond/home. We are grateful to SPARC for the generous funding of the project that led to this workshop and the speakers and participants for their contributions to a lively atmosphere of discussions and collaboration. We also wish to thank Priya Vyas from Springer Nature for her patience and professional handling of the expedited editorial process that led to this volume. Ramadevi Pichai
Johannes Walcher
On behalf of the Organizers May 2025
Date: 18-21 February 2025
Location: Mumbai, India (Hybrid)
Website: https://sites.google.com/view/knots-quivers-beyond/home From February 18 to 21, 2025, the Indian Institute of Technology, Bombay, hosted an international workshop “Knots, quivers and beyond”, sponsored by the Government of India under the “Scheme for Promotion of Academic and Research Collaboration” (SPARC) of the Ministry of Human Resource Development. The main aim of the workshop was to present a selection of recent advances related to the structure and calculation of homological knot invariants, centered around the celebrated knots-quivers correspondence first proposed by Kucharski-Reineke-Stosic-Sulkowski in 2017. The workshop featured 17 invited speakers from around the world including India, Europe, North America, and China as well as numerous local and online participants. It provided in particular an opportunity for IIT graduate students to be exposed to a highly active research area and to connect with potential international collaborators. This volume contains eight summaries of talks written by the workshop speakers, with several contributions being collaborative. Subjects include relations between topological field theory and problems of graph coloring; a review of the knots-quivers correspondence which relates motivic Donaldson-Thomas invariants of symmetric quivers to quantum invariants of knots; the representation theory of the spherical double affine Hecke algebra using brane quantization; exponential networks and their relation to enumerative combinatorics, specifically the Hilbert scheme of points in the plane via string dualities; 3d Chern-Simons theory as a playground for the calculation of entanglement entropy, with a focus on multi-component torus links; the existence of certain incompressible surfaces as a geometric question about knots that can be addressed with Heegaard Floer homology; the advantages of multiply-graded link homologies associated with the general linear Lie algebra over its specialization. This sample gives a faithful cross-section of the topics covered at the workshop. Further information, including slides and video recordings of all talks given at the workshop, are available at the website sites.google.com/view/knots-quivers-beyond/home. We are grateful to SPARC for the generous funding of the project that led to this workshop and the speakers and participants for their contributions to a lively atmosphere of discussions and collaboration. We also wish to thank Priya Vyas from Springer Nature for her patience and professional handling of the expedited editorial process that led to this volume. Ramadevi Pichai
Johannes Walcher
On behalf of the Organizers May 2025