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.
Formulates integrals for hypersphere arrangements using cohomology and Cayley-Menger determinants.
The aim of this text is to establish some relations between Markov chains in Dirichlet Environments on directed graphs and certain hypergeometric integrals associated with a particular arrangement of hyperplanes. We deduce from these relations and the computation of the connexion obtained by moving one hyperplane of th…
New identities for simplex volume in Euclidean space.
Unified method for computing modular curvature on toric noncommutative manifolds using hypergeometric functions.
New harmonic Hadamard manifolds defined via hypergeometric equations.
Study spherical Fourier transform on hypergeometric type harmonic manifolds.
New proof of rearrangement lemma for noncommutative tori using hypergeometric functions.
Study functional relations on noncommutative tori using transformations.
New lattices are linked to higher hypergeometric functions.
It is well-known to the experts that multi-dimensional state integrals of products of Faddeev's quantum dilogarithm which arise in Quantum Topology can be written as finite sums of products of basic hypergeometric series in q=e^{2πiτ} and \tilde{q}=e^{-2πi/τ}. We illustrate this fact by giving a detailed proof for a fa…
Harmonic manifolds of hypergeometric type have entropy bounds related to real hyperbolic spaces.
Proposes a differentiable hypergeometric distribution for learning group importance.
New method identifies graph structure from data using generalized hypergeometric distributions.
Develops tropical geometry for weighted Hurwitz numbers, generalizing previous results.
Estimates unknown population sizes using the hypergeometric distribution.
We extend projectively equivariant quantization and symbol calculus to symbols of pseudo-differential operators. An explicit expression in terms of hypergeometric functions with noncommutative arguments is given. Some examples are worked out, one of them yielding a quantum length element on .
This paper establishes certain existence and classification results for solutions to Toda systems with three singular sources at 0, 1, and . First, we determine the necessary conditions for such an Toda system to be related to an th order hypergeometric equation. Then, we construct solutions …
We investigate the pricing of financial options under the 2-hypergeometric stochastic volatility model. This is an analytically tractable model that reproduces the volatility smile and skew effects observed in empirical market data. Using a regular perturbation method from asymptotic analysis of partial differential eq…
Study of line congruences for Appell's rank-4 hypergeometric functions.
Although this article can be read independently, it is a continuation of the introduction to integrable systems aspects of quantum cohomology given in part 1 (math.DG/0104274). In the same elementary style, i.e. assuming basic properties of quantum cohomology and concentrating on the simplest nontrivial examples, the q…
Survey of early complex analysis and topology, highlighting Euler's influence on Riemann's work.
We derive a factorization of the Alexander polynomial of the 4-strand Turk's head knot using hypergeometric representations.
We present a global representation for surfaces in 3-dimensional hyperbolic space with constant mean curvature 1 (CMC-1 surfaces) in terms of holomorphic spinors. This is a modification of Bryant's representation. It is used to derive explicit formulas in hypergeometric functions for CMC-1 surfaces of genus 0 with thre…
Formula derived for special q-hypergeometric series at roots of unity.
New groups discovered with unique properties in a specific space.
Paper proves BGW tau-function can be represented as Q-polynomials.
The paper introduces new methods for Asian option pricing using Laguerre quadrature.
Constructs explicit nontrivial cycles in Habiro cohomology of smooth varieties.
Differential Galois theory connects connections with parameters to isomonodromic deformations.
Paper constructs new identities linking quantum invariants and modular forms.
Paper proves a Cohen-Dimca-Orlik type theorem for Z-local systems of hyperplane arrangements.
Unified framework for differentiable graph partitioning with probabilistic cuts.
Explicit computation of Kontsevich weights for symplectic Poisson structures.
In the genus one case, we make explicit some constructions of Veech on flat surfaces and generalize some geometric results of Thurston about moduli spaces of flat spheres as well as some equivalent ones but of an analytico-cohomological nature of Deligne-Mostow, which concern the monodromy of Appell-Lauricella hypergeo…
New quasi-Einstein metrics found on a sphere.
New formulas for colored Jones polynomials of double twist knots generalize series and duality.
This work presents an exact solution to the generalized Heston model, where the model parameters are assumed to have linear time dependence The solution for the model in expressed in terms of confluent hypergeometric functions.
We propose localization techniques for computing Gromov-Witten invariants of maps from Riemann surfaces with boundaries into a Calabi-Yau, with the boundaries mapped to a Lagrangian submanifold. The computations can be expressed in terms of Gromov-Witten invariants of one-pointed maps. In genus zero, an equivariant ver…
New formulas for colored Jones polynomials of double twist knots and related series.
Classical solvable stochastic volatility models (SVM) use a CEV process for instantaneous variance where the CEV parameter takes just few values: 0 - the Ornstein-Uhlenbeck process, 1/2 - the Heston (or square root) process, 1- GARCH, and 3/2 - the 3/2 model. Some other models were discovered in \cite{Labordere2009…
When using Traizet's regeneration technique to construct minimal surfaces, the simplest nontrivial configurations are given as the roots of polynomials that satisfy a hypergeometric differential equation. We exhibit examples of simple minimal surfaces exhibiting the same behavior.
We draw a handlebody picture of the Hacon-Pardini surface. This is a complex surface obtained by taking the quotient of a product of two surfaces of genus 2 and 3, under the product of two involutions: the hypergeometric and a fixed point free involution.
We draw a handlebody picture of the Catanese-Ciliberto-Mendes Lopes surface. This is a complex surface obtained by taking the quotient of a product of two surfaces of genus 2 and 3, under the product of two involutions: the hypergeometric and a fixed point free involution.
The SABR model is shortly presented and the volatility swap explained. The fair value for a volatility swap is then computed using the usual theory in financial mathematics. An analytical solution using confluent hypergeometric functions is found. The solution is then verified using Rama Cont's functional calculus.
After introducing the sub-Riemannian geometry of the Heisenberg group Hn, n \geq 1, we recall some basics about hypersurfaces endowed with the H-perimeter measure and horizontal Green's formulas. Then, we describe a class of compact closed hypersurfaces of constant horizontal mean curvature called "Isoperimetric Profil…
Proposes a new uncertain volatility model with worst-case scenario analysis.
Researchers create a fundamental domain for all Deligne-Mostow lattices in PU(2,1).
For the Möbius spheres , we give alternative elementary proofs of the recursive formulas for GJMS-operators and -curvatures due to the first author [Geom. Funct. Anal. 23, (2013), 1278-1370; arXiv:1108.0273]. These proofs make essential use of the theory of hypergeometric series.