A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Holographic principle matches deformed Liouville theory action.
Study uses holography to analyze entanglement entropy in deformed CFTs.
The paper connects knot homology, quantum 6j-symbols, and complements of knots.
The paper connects quivers to knot complements and studies their BPS states and 3d N=2 theories.
Reshetikhin-Turaev (a.k.a. Chern-Simons) TQFT is a functor that associates vector spaces to two-dimensional genus g surfaces and linear operators to automorphisms of surfaces. The purpose of this paper is to demonstrate that there exists a Macdonald q,t-deformation -- refinement -- of these operators that preserves the…
Study of knot complements yields quantum modularity insights.
Simplified KR polynomial for bipartite links reduces to tensor products of vector spaces.
New quantum invariant is asymptotically multiplicative under cyclic covers.
We conjecture explicit evolution formulas for Khovanov polynomials for pretzel knots in some regions in the windings space. Our description is exhaustive for genera 1 and 2. As previously observed, evolution at T != -1 is not fully smooth: it switches abruptly at the boundaries between different regions. We reveal that…
We review a construction of a new class of algebraic curves, called super-A-polynomials, and their quantum generalizations. The super-A-polynomial is a two-parameter deformation of the A-polynomial known from knot theory or Chern-Simons theory with SL(2,C) gauge group. The two parameters of the super-A-polynomial encod…
The generalized volume conjecture relates asymptotic behavior of the colored Jones polynomials to objects naturally defined on an algebraic curve, the zero locus of the A-polynomial . Another "family version" of the volume conjecture depends on a quantization parameter, usually denoted or ; this quan…
We consider braids with repeating patterns inside arbitrary knots which provides a multi-parametric family of knots, depending on the "evolution" parameter, which controls the number of repetitions. The dependence of knot (super)polynomials on such evolution parameters is very easy to find. We apply this evolution meth…
The paper generalizes knot invariants and their connections to quivers and ideals.
We introduce and compute a 2-parameter family deformation of the A-polynomial that encodes the color dependence of the superpolynomial and that, in suitable limits, reduces to various deformations of the A-polynomial studied in the literature. These special limits include the t-deformation which leads to the "refined A…