All of the articles in this proceedings volume have been presented at the [knots,quivers and beyond conference] during [18–21, Feb 2025] in [IIT Bombay]]. These articles have been approved by the Editor-in-Chief, who affirms that this document is a truthful description of the conference.

We begin with a review of the modern perspective on graph coloring, which appeared in the work of many people, including Penrose. Next, we outline how the work of Treuman-Zaslow and Caslas-Zaslow led to graph coloring being seen as topological defects labeled by the elements of the Klein-Four Group....

This note is an overview of the knot-quiver correspondence, which relates symmetric quivers and their partition functions, a.k.a. motivic Donaldson-Thomas generating series, to quantum invariants of knots and links in S(For the reader unfamiliar with knot theory, we refer to a classic book by Dale Rolfsen...

In this proceeding, we briefly summarize the results of [1], which investigates the representation theory of the spherical double affine Hecke algebra (DAHA) of type C∨C1, using brane quantization. Our analysis establishes a bijective correspondence between compact Lagrangian A-branes in the SL(2,C)...

We give an introduction and brief review of the “exponential networks approach” to counting BPS states in local Calabi-Yau threefolds. We begin by illustrating the basic ideas in the celebrated correspondence between the BPS spectrum of 4d N = 2 pure SU(2) gauge theory, finite geodesics on the Seiberg-Witten...

We investigate the reduced density matrices obtained for the quantum states in the context of 3d Chern-Simons theory with gauge group SU(2) and Chern-Simons level k. We focus on the quantum states associated with the Tp,p torus link complements, which is a p-party pure quantum state. The reduced density...

This chapter briefly describes the motivation behind asking geometric questions regarding topological invariants of knots and links, and ends with an open question in that direction involving Heegaard Floer homology for links. This is based on the talk presented at ‘Knots, Quivers and Beyond’ conference...

The article describes a construction of a knot homology theory for knots in RP3. This is achieved by defining a map from projective knots to virtual knots and importing the virtual Khovanov theory through this map. Structural features of knots in RP3 is analyzed in detail for the construction of the...

This expository note outlines why it is sometimes useful to consider the bigraded type A link homology theories as associated with the Lie algebras glN instead of slN.