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.
New Lehmer constants computed for free groups, improving bounds.
Guts determine the leading coefficients of -Alexander torsions for 3-manifolds.
We study properties of a generalization of the Mahler measure to elements in group rings, in terms of the Lueck-Fuglede-Kadison determinant. Our main focus is the variation of the Mahler measure when the base group is changed. In particular, we study how to obtain the Mahler measure over an infinite group as limit of M…
It is shown that in a tower of coverings the regularized determinant of a generalized Laplacian converges to the -determinant. This shows generic nontriviality of analytic torsion or regularized determinants since the -counterparts are easier to compute. We further have an "Euler product expansion" for regula…
We investigate the Gram determinant of the bilinear form based on curves in a planar surface, with a focus on the disk with two holes. We prove that the determinant based on curves divides the determinant based on curves. Motivated by the work on Gram determinants based on curves in a disk and curves in an an…
Determinant modulo 8 classifies virtual knots based on polynomial coefficients.
Abstract: Determinants and formulas for operators on various spaces.
Paper computes link determinants using Fourier-Hadamard transforms.
Study on Laplacian determinant in isosceles triangles, finding equilateral triangle minimizes determinant.
Study shows exponential growth of Laplacian determinant on random hyperbolic surfaces.
An algorithm determines knot colorability and determinants from petal projections.
Study Gram determinants in knot theory, focusing on a Möbius band determinant.
Identifies images of determinant morphism for specific co-Higgs bundles.
We study the zeta determinant of global boundary problems of APS-type through a general theory for relative spectral invariants. In particular, we compute the zeta determinant for Dirac-Laplacian boundary problems in terms of a scattering Fredholm determinant over the boundary.
Paper introduces VDE, a variance-reduced determinant estimator.
Unified determinants via a single equation.
We give definitions of cohomology determinants for compact, connected, orientable 3-manifolds. We also give formulae relating cohomology determinants before and after gluing a solid torus along a torus boundary component. Cohomology determinants are related to Turaev torsion, though the author hopes that they have othe…
The Gram determinant of type was introduced by Lickorish in his work on invariants of 3 - manifolds. We generalize the theory of the Gram determinant of type by evaluating, in the annulus, a bilinear form of non-intersecting connections in the disc. The main result provides a closed formula for this Gram determ…
We compute the relative zeta-function metric on the determinant line bundle for a family of elliptic boundary value problems of Dirac-type. To do this we prove a general formula relating the zeta-determinant to a Fredholm determinant over the boundary for a class of higher-order elliptic boundary value problems.
The paper connects Chebyshev polynomials and Gram determinants on Möbius bands.
New Gram determinant from Möbius band connects to annulus case.
Study on pseudo-Einstein 3-manifolds, calculating determinant changes under conformal transformations.
Topologies on algebraic and equational theories are used to define germ determined, near-point determined, and point determined rings of smooth functions, without requiring them to be finitely generated. It is proved, that any commutative algebra morphism (without requiring continuity) between near-point determined rin…
Determinants of theta curves and symmetric graphs are studied.
The purpose of this paper is to present the construction of a canonical determinant functional on elliptic pseudodifferential operators associated to the Guillemin-Wodzicki residue trace. The resulting functional is multiplicative, a local invariant, and not defined by a regularization procedure. The residue determinan…
We study the asymptotic behaviour of regularized determinants of certain Laplace type operators with respect to singular deformations of the underlying manifold which are obtained by stretching a tubular neighborhood of an embedded separating hypersurface to a cylinder of infinite length. Using the asymptotic expansion…
Stochastic representation for determinants derived from Brownian loop soups.
Researchers compute zeta-determinants and analytic torsion for metric mapping tori.
Formula found for knot determinant in 3-braid weaving.
We compute the curvature of the determinant line bundle on a family of Dirac operators for a noncommutative two torus. Following Quillen's original construction for Riemann surfaces and using zeta regularized determinant of Laplacians, one can endow the determinant line bundle with a natural Hermitian metric. By using …
We obtain generalizations of some results of Turaev relating leading order terms of the Turaev torsion of closed, oriented, connected 3-manifolds to certain ``determinants'' derived from cohomology operations such as the alternate trilinear form on the first cohomology group given by cup product. These determinants unf…
The volume density of a hyperbolic link is defined as the ratio of hyperbolic volume to crossing number. We study its properties and a closely-related invariant called the determinant density. It is known that the sets of volume densities and determinant densities of links are dense in the interval [0,v_{oct}]. We cons…
We study the geometry and partial differential equations arising from the consideration of Frobenius determinants, also called-group-determinants. This leads us to address some aspects of twistor theory as well as some extensions of Bessel functions.
Paper discusses gluing formula for zeta-determinants with Robin boundary condition.
New proof limits Jones polynomial values for quasi-alternating links.
Algorithms for Gaussian process, marginal likelihood methods or restricted maximum likelihood methods often require derivatives of log determinant terms. These log determinants are usually parametric with variance parameters of the underlying statistical models. This paper demonstrates that, when the underlying matrix …
We construct a determinant of the Laplacian for infinite-area surfaces which are hyperbolic near infinity and without cusps. In the case of a convex co-compact hyperbolic metric, the determinant can be related to the Selberg zeta function and thus shown to be an entire function of order two with zeros at the eigenvalue…
We explain the bundle structures of the {\it Determinant line bundle} and the {\it Quillen determinant line bundle} considered on the connected component of the space of Fredholm operators including the identity operator in an intrinsic way. Then we show that these two are isomorphic and that they are non-trivial line …
Study uniquely determines Riemannian metric derivatives from boundary data.
In \cite{BR1}, \cite{BR2}, a parabolic determinant line bundle on a moduli space of stable parabolic bundles was constructed, along with a Hermitian structure on it. The construction of the Hermitian structure was indirect: The parabolic determinant line bundle was identified with the pullback of the determinant line b…
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…
Researchers found counterexamples to a 2-jet determination theorem in higher codimension.
On compact surfaces with or without boundary, Osgood, Phillips and Sarnak proved that the maximum of the determinant of the Laplacian within a conformal class of metrics with fixed area occurs at a metric of constant curvature and, for negative Euler characteristic, exhibited a flow from a given metric to a constant cu…
We prove an adiabatic decomposition formula of the zeta-determinant of the Laplace type operator with respect to Dirichlet boundary condition. We allow the non-invertible tangential operator. As a result, our adiabatic decomposition formula involves the scattering matrix over the manifold with cylindrical end. We also …
Study proves spectral determination of triangles and quadrilaterals, with restrictions on higher-order polygons.
Novel algorithm speeds up log-determinant estimation for large matrices.
Study uses renormalized area to determine metric expansion from minimal surfaces.
We express the colored Jones polynomial as the inverse of the quantum determinant of a matrix with entries in the -Weyl algebra of -operators, evaluated at the trivial function (plus simple substitutions). The Kashaev invariant is proved to be equal to another special evaluation of the determinant. We also discus…