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.
Study finds u-plane integral equals full correlator at strong coupling and matches Donaldson invariants.
We analyze the u-plane contribution to Donaldson invariants of a four-manifold X. For , this contribution vanishes, but for , the Donaldson invariants must be written as the sum of a u-plane integral and an SW contribution. The u-plane integrals are quite intricate, but can be analyzed in great det…
We generalize the analysis by Moore and Witten in [arXiv:hep-th/9709193], and consider integration over the u-plane in Donaldson theory with surface operators on a smooth four-manifold X. Several novel aspects will be developed in the process; like a physical interpretation of the "ramified" Donaldson and Seiberg-Witte…
Universal functions derived for topological correlators in Yang-Mills theory.
We compute the Moore-Witten regularized u-plane integral on CP^1 x CP^1 directly in a chamber where the elliptic unfolding technique fails to work. This allows us to determine explicit formulas for its SU(2) and SO(3)-Donaldson invariants in terms of Mock modular forms.
We compute the Moore-Witten regularized u-plane integral on CP^2, and we confirm their conjecture that it is the generating function for the SO(3)-Donaldson invariants of CP^2. We prove this conjecture using the theory of mock theta functions and harmonic Maass forms. We also derive further such generating functions fo…
There are two families of Donaldson invariants for the complex projective plane, corresponding to the SU(2)-gauge theory and the SO(3)-gauge theory with non-trivial Stiefel-Whitney class. In 1997 Moore and Witten conjectured that the regularized u-plane integral on the complex projective plane gives the generating func…
Eguchi, Ooguri, and Tachikawa recently conjectured a new moonshine phenomenon. They conjecture that the coefficients of a certain mock modular form H(tau), which arises from the K3 surface elliptic genus, are sums of dimensions of irreducible representations of the Mathieu group M24. We prove that H(tau) surprisingly a…
Study shows non-convergence of short-maturity expansion in SABR model.
Revisits SYM theory to compute Donaldson invariants using mock modular forms.
We generalise the analysis in [arXiv:0904.1744] to superspace, and explicitly prove that for any embedding of surface operators in a general, twisted N=2 pure abelian theory on an arbitrary four-manifold, the parameters transform naturally under the SL(2,Z) duality of the theory. However, for nontrivially-embedded surf…
The study examines stability of Hamiltonian Poisson integrators on both integrable and non-integrable systems.
Geometrically interprets integrability of geodesic flow using web theory.
Proof shows volume equals integral points for certain manifolds.
Integrates rough geometric forms on manifolds.
The paper defines and analyzes set-valued stochastic integrals for Lévy processes.
New integration theory on topological spaces, including fractals.
We discuss a recurrent geometrical method, due to Élie Cartan and von Weber ([1],[11]) enabling us to determine, step by step, the maximal integral manifolds of a not necessarily integrable nor regular Pfaffian system. The dimensions of such integral manifolds can, of course, vary from point to point but more so can va…
We define a non-absolutely convergent integration on integral currents of dimension 1 in Euclidean space. This integral is closely related to the Henstock-Kurzweil and Pfeffer Integrals. Using it, we prove a generalized Fundamental Theorem of Calculus on these currents. A detailed presentation of Henstock-Kurzweil Inte…
The paper defines and proves the existence of decompositions of integral varifolds.
Counterexample shows Ito integrand needn't be locally square integrable.
Study integrable geodesic flows on 2-surfaces with high-degree polynomial first integrals.
TQ separates sampling and integration for high-dimensional integrals.
We introduce renormalized integrals which generalize conventional measure theoretic integrals. One approximates the integration domain by measure spaces and defines the integral as the limit of integrals over the approximating spaces. This concept is implicitly present in many mathematical contexts such as Cauchy's pri…
The article constructs stochastic integration in Riemannian manifolds.
Method finds differential equations for integrable billiard tables.
Constructs Lie groupoid integrating elliptic tangent bundles and Poisson structures.
Investigates integrable systems with linear periodic integral for e(3) Lie algebra.
We use neural networks as control variates with geometric integration techniques.
Integral foliated simplicial volume is a version of simplicial volume combining the rigidity of integral coefficients with the flexibility of measure spaces. In this article, using the language of measure equivalence of groups we prove a proportionality principle for integral foliated simplicial volume for aspherical m…
This paper is an exposition of heuristics related to Witten's functional integral, relating it to Vassiliev invariants and to the Kontsevich integrals that can be used to produce Vassiliev invariants of knots and links.In particular, we give a simplified version of the appearance of the Kontsevich integrals in the pert…
Surveying integrability of Lie algebroids and structures.
This paper provides an existence-and-uniqueness theorem characterizing the stochastic integral with respect to a Wiener process. The integral is represented as a mapping from the space of measurable and adapted pathwise locally integrable processes to the space of continuous adapted processes. It is characterized in te…
We construct an infinite-dimensional symplectic 2-groupoid as the integration of an exact Courant algebroid. We show that every integrable Dirac structure integrates to a "Lagrangian" sub-2-groupoid of this symplectic 2-groupoid. As a corollary, we recover a result of Bursztyn-Crainic-Weinstein-Zhu that every integrabl…
Integrable LCK manifolds characterized as Kähler Lie algebras.
The linking integral is an invariant of the link-type of two manifolds immersed in a Euclidean space. It is shown that the ordinary Gauss integral in three dimensions may be simplified to a winding number integral in two dimensions. This result is then generalized to show that in certain circumstances the linking integ…
New integrable deformations for topological hierarchies from Frobenius manifolds.
Sharp lower bound found for integral varifolds' mean curvature.
Proves a theorem for normal distributions on manifolds with boundary.
The paper proves conditions for Darboux integrability in diagonal hydrodynamic systems.
A new method integrates forms on Riemann surfaces, leading to modular forms.
Researchers prove integrability of magnetic systems on spheres up to dimension 6.
A new adaptive binarization technique using fuzzy integrals improves image quality.
Starting from a homogeneous polynomial in momenta of arbitrary order we extract multi-component hydrodynamic-type systems which describe 2-dimensional geodesic flows admitting the initial polynomial as integral. All these hydrodynamic-type systems are semi-Hamiltonian, thus implying that they are integrable according t…
A new geometric definition of integration for differential forms.
We prove that a holomorphic Lie algebroid is integrable if, and only if, its underlying real Lie algebroid is integrable. Thus the integrability criteria of Crainic-Fernandes do also apply in the holomorphic context without any modification. As a consequence we give another proof of the following theorem: a holomorphic…
Integral filling volume of mapping tori grows sublinearly with complexity.
New integral theorems improve density function estimations.