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.
Geometrically interprets integrability of geodesic flow using web theory.
We review localization techniques for functional integrals which have recently been used to perform calculations in and gain insight into the structure of certain topological field theories and low-dimensional gauge theories. These are the functional integral counterparts of the Mathai-Quillen formalism, the Duistermaa…
Derives path-integrals for superstrings on curved backgrounds using string geometry theory.
Proof shows volume equals integral points for certain manifolds.
Derives path integrals for perturbative strings on various backgrounds.
This paper is an exposition of the relationship between Witten's Chern-Simons functional integral and the theory of Vassiliev Invariants of knots and links in three dimensional space. We conceptualize the functional integral in terms of equivalence classes of functionals of gauge fields and we do not use measure theory…
3D BF theory on certain 3-manifolds evaluated via residues and large k limits.
These notes were inspired by the course ''Quantum Field Theory from a Functional Integral Point of View'' given at the University of Zurich in Spring 2017 by Santosh Kandel. We describe Feynman's path integral approach to quantum mechanics and quantum field theory from a functional integral point of view, where the mai…
Polytopes connect Lie theory to physics, integrating integrable systems.
Symmetries in shell theory lead to multiple deformation possibilities.
In this paper we develop an integration theory for zero sets of polyfold Fredholm sections. The results are needed in the application of the polyfold theory. We use it for example in the construction of symplectic field theory.
In this short note we show how Dubrovin's integrable hierarchies, defined using the Gromov-Witten theory of a closed symplectic manifold, generalizes to Hamiltonian Floer theory. In particular, we show how the required generalization of the PSS isomorphism, relating Gromov-Witten theory and Hamiltonian Floer theory, ca…
In this paper we develope, in a geometric framework, a Hamilton-Jacobi Theory for general dynamical systems. Such a theory contains the classical theory for Hamiltonian systems on a cotangent bundle and recent developments in the framework of general symplectic, Poisson and almost-Poisson manifolds (including some appr…
We present the theory of tensors with Young tableau symmetry as an efficient computational tool in dealing with the polynomial first integrals of a natural system in classical mechanics. We relate a special kind of such first integrals, already studied by Lundmark, to Beltrami's theorem about projectively flat Riemanni…
Integrates singular subalgebroids using diffeological groupoids.
Analyzes string topology operations using Chen's integrals and homotopy transfer.
These are notes on the theory of supermanifolds and integration on them, aiming to collect results that are useful for a better understanding of superstring perturbation theory in the RNS formalism.
In this lecture delivered at the Integrable and Quantum Field Theory at Peyresq sixth meeting, we review the Lychagin's Monge-Ampere operators theory and exhibit the link it establishes between the classical problem of local equivalence for non linear partial differential equations and the problem of integrability of s…
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…
The paper studies cohomological Donaldson-Thomas theory for local systems on a 3-torus.
We continue the study of the spectral theory associated to integrable metrics, started in our previous paper arXiv:1301.1793 [math.SP]. We introduce the notion of 1-integrable metric on line-bundles on a compact Riemann surface. We extend the spectral theory of generalized Laplacians to line-bundles equipped with 1-int…
We provide a draft of a theory of geometric integration of rough differential forms which are generalizations of classical (smooth) differential forms to similar objects with very low regularity, for instance, involving Hölder continuous functions that may be nowhere differentiable. Borrowing ideas from the theory of r…
The paper analyzes frameworks for integrating sustainability into investment decisions.
The purpose of this paper is to connect two subjects: the theory of quantum integrable systems (complete commutative rings of differential operators), and differential Galois theory. We define quantum completely integrable systems (QCIS), algebraically integrable QCIS, the differential Galois group of a QCIS. We show t…
Identifies all perturbative vacua in bosonic string theory.
We extend the spectral theory of generalized Laplacians to integrable metrics on compact Riemann surfaces. As a consequence, we attach in a direct way, a holomorphic analytic torsion to any integrable metrics. We also provide a different approach to define the holomorphic analytic torsion. We prove that both approaches…
Geometric theory of integration developed in SDG.
Geometric approach uses Bäcklund transformations to create integrable discrete analogs of surface nets.
This paper establishes three relations between the Toda field theory associated to a simple Lie algebra and the integral curves of the standard differential system on the corresponding complete flag variety. The motivation comes from the viewpoint on the Toda field theories as Darboux integrable differential systems as…
Develops a new integration theory for financial markets.
The notion of integrability will often extend from systems with scalar-valued fields to systems with algebra-valued fields. In such extensions the properties of, and structures on, the algebra play a central role in ensuring integrability is preserved. In this paper a new theory of Frobenius-algebra valued integrable s…
We derive general Novikov-Morse type inequalities in a Conley type framework for flows carrying cocycles, therefore generalizing our results in [FJ2] derived for integral cocycle. The condition of carrying a cocycle expresses the nontriviality of integrals of that cocycle on flow lines. Gradient-like flows are distingu…
Review of sigma models on flag manifolds, linking to spin chains and integrable theories.
Study wave functions in complex Chern-Simons theory, finding integrality and rational points.
Unified asymptotic theory and tests for ACD models reveal infinite-mean durations in cryptocurrency trading.
Remarkable parallelism between the theory of integrable systems of first-order quasilinear PDE and some old results in projective and affine differential geometry of conjugate nets, Laplace equations, their Bianchi-Baecklund transformations is exposed. These results were recently applied by I.M.Krichever and B.A.Dubrov…
Introduces a massive variant of Ray-Singer Torsion to avoid zero modes in topological field theories.
A new method integrates forms on Riemann surfaces, leading to modular forms.
Extends Campanato theory to multi-valued functions for geometric variational problems.
Study of defects in gauge theories connects quantum field theory to classical integrability.
Unified method proves integrality of LMOV invariants for framed unknot.
Paper develops Lie theory for Rota-Baxter operators on Lie algebras and groups.
We investigate an equivariant generalization of Morse theory for a general class of integrable models. In particular, we derive equivariant versions of the classical Poincaré-Hopf and Gauss-Bonnet-Chern theorems and present the corresponding path integral generalizations. Our approach is based on equivariant cohomology…
We introduce a theory of stochastic integration with respect to a family of semimartingales depending on a continuous parameter, as a mathematical background to the theory of bond markets. We apply our results to the problem of super-replication and utility maximization from terminal wealth in a bond market. Finally, w…
We consider the problem of computing the integrable sub-distributions of the non-integrable Vessiot distribution of multi-dimensional second order partial differential equations (PDEs). We use Vessiot theory and solvable structures to find the largest integrable distributions contained in the Vessiot distribution assoc…
We review quantum field theory approach to the knot theory. Using holomorphic gauge we obtain the Kontsevich integral. It is explained how to calculate Vassiliev invariants and coefficients in Kontsevich integral in a combinatorial way which can be programmed on a computer. We discuss experimental results and temporal …
The paper establishes a correspondence between normal distributions and neat foliations on manifolds with boundary.
Researchers calculate the Ray-Singer Torsion for bundles.