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.
Worldsheet skein D-module for Hopf link conormal uniquely determines partition functions.
Solves a recursion for Gromov-Witten invariants of the unknot.
The paper calculates a formula for knot complements using holomorphic curves.
Researchers compute dimensions of GLN-skein modules for genus-one mapping tori.
The meridian maps of the full Homfly skein of the annulus are linear endomorphisms induced by the insertion of a meridian loop, with either orientation, around a diagram in the annulus. The eigenvalues of the meridian maps are known to be distinct, and are indexed by pairs of partitions of integers p and n into k and k…
We introduce new skein invariants of links based on a procedure where we first apply the skein relation only to crossings of distinct components, so as to produce collections of unlinked knots. We then evaluate the resulting knots using a given invariant. A skein invariant can be computed on each link solely by the use…
Geometrically, Legendrian surfaces related by surgery have related skein-valued cluster spaces.
A map from 3-manifold skein to Lagrangian skein via holomorphic curve counting.
The expectation value of Wilson loop operators in three-dimensional SO(N) Chern-Simons gauge theory gives a known knot invariant: the Kauffman polynomial. Here this result is derived, at the first order, via a simple variational method. With the same procedure the skein relation for Sp(N) are also obtained. Jones polyn…
The paper improves bounds on skein tree depth and delta-crossing numbers for knots and links.
New identities lift q-dilogarithm to a more complex algebra.
New findings show the Gilmer-Masbaum map isn't always one-to-one.
Study of Chern-Simons theory and link invariants using gauge fields and skein relations.
The paper defines a new algebra structure on skein modules of 3-manifolds and shows it's isomorphic to a known algebra.
The Hecke algebra H_n contains well known idempotents E_λ which are indexed by Young diagrams with n cells. They were originally described by Gyoja. A skein theoretical description of E_λ was given by Aiston and Morton. The closure of E_λ becomes an element Q_λ of the skein of the annulus. In this skein, they are known…
Symmetrizes 4d and 3d BPS quivers for Argyres-Douglas theories.
The paper improves bounds on the complexity of computing link polynomials.
Sliced skein algebras and geometric Kauffman bracket study algebraic structures and their properties.
Proposes SPFB method for optimizing partition functions in stochastic learning.
Traditionally introduced in terms of advanced topological constructions, many link invariants may also be defined in much simpler terms given their values on a few initial links and a recursive formula on a skein triangle. Then the crucial question to ask is how many initial values are necessary to completely determine…
The study analyzes decision trees on real and categorical features, deriving bounds on their VC dimension and proposing improved pruning algorithms.
We study partition functions of random Bergman metrics, with the actions defined by a class of geometric functionals known as `stability functions'. We introduce a new stability invariant - the critical value of the coupling constant - defined as the minimal coupling constant for which the partition function converges.…
New categorifications of biquandle brackets defined.
We extend some results of Bonahon, Bullock, Turaev and Wong concerning the skein algebras of closed surfaces to L^e's stated skein algebra associated to open surfaces. We prove that the stated skein algebra with deforming parameter +1 embeds canonically into the centers of the stated skein algebras whose deforming para…
Carrega has shown that the Kauffman bracket skein module of the 3-torus over the field of rational functions in the variable A can be generated by 9 skein elements. We show this set of generators is linearly independent.
Study skein modules via gauge theory, finding non-TQFT dimensions.
Study introduces indecomposability for varifolds, leading to geometric consequences.
LA-MCTS learns search space partition for black-box optimization using Monte Carlo Tree Search.
For every oriented surface of finite type, we construct a functorial Khovanov homology for links in a thickening of the surface, which takes values in a categorification of the corresponding gl(2) skein module. The latter is a mild refinement of the Kauffman bracket skein algebra, and its categorification is constructe…
Let k be a subring of the field of rational functions in α, s which contains α^{1}, α^{-1}, s^{1}, s^{-1}, . Let M be a compact oriented 3-manifold, and let K(M) denote the Kauffman skein module of M over k. Then K(M) is the free k-module generated by isotopy classes of framed links in M modulo the Kauffman skein relat…
The paper calculates a specific weight system for chord diagrams with a particular graph structure.
Policy gradient methods with aggregated states can achieve better performance than approximate policy iteration.
In this paper the properties of the Kauffman bracket skein module of are investigated. Links in lens spaces are represented both through band and disk diagrams. The possibility to transform between the diagrams enables us to compute the Kauffman bracket skein module on an interesting class of examples consisti…
3D gauge theories link knot polynomials to vortex partition functions.
Let be a surface with negative Euler characteristic, genus at least one and at most one boundary component. We prove that the skein algebra of over the field of rational functions can be algebraically generated by a finite number of simple closed curves that are naturally associated to certain generators of the…
Algorithms learn and test variable partitions in various groups and error metrics.
Study on skein module dimensions at irreducible representations.
Defines map from skein module to Habiro ring for quantum modularity.
The main goal is to find the Homfly polynomial of a link formed by decorating each component of the Hopf link with the closure of a directly oriented tangle. Such decorations are spanned in the Homfly skein of the annulus by elements Q_λ, depending on partitions λ. We show how to find the 2-variable Homfly invariant <λ…
We prove a finiteness property of the values of the skein polynomial of homogeneous knots which allows to establish large classes of such knots to have arbitrarily unsharp Bennequin inequality (for the Thurston-Bennequin invariant of any of their Legendrian embeddings in the standard contact structure of R^3), and a gi…
We define an invariant of graphs embedded in a three-manifold and a partition function for 2-complexes embedded in a triangulated four-manifold by specifying the values of variables in the Turaev-Viro and Crane-Yetter state sum models. In the case of the three-dimensional invariant, we prove a duality formula relating …
Researchers prove positivity of skein algebra structure constants for specific surfaces.
We show that for the Kauffman bracket skein module over the field of rational functions in variable A, the module of a connected sum of 3-manifolds is the tensor product of modules of the individual manifolds.
We study the algebraic and geometric properties of stated skein algebras of surfaces with punctured boundary. We prove that the skein algebra of the bigon is isomorphic to the quantum group providing a topological interpretation for its structure morphisms. We also show that its sta…
The Murphy operators in the Hecke algebra H_n of type A are explicit commuting elements whose sum generates the centre. They can be represented by simple tangles in the Homfly skein theory version of H_n. In this paper I present a single tangle which represents their sum, and which is obviously central. As a consequenc…
The paper explores basic properties of knot skein invariants.
Let Sigma be a closed oriented surface of genus g. We show that the Kauffman bracket skein module of Sigma x S^1 over the field of rational functions in A has dimension at least 2^{2g+1}+2g-1.
In this paper we propose a novel Bayesian methodology for Value-at-Risk computation based on parametric Product Partition Models. Value-at-Risk is a standard tool to measure and control the market risk of an asset or a portfolio, and it is also required for regulatory purposes. Its popularity is partly due to the fact …