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.
Unified description of Weierstrass-type representations.
Singular fiber resolution does not describe the spontaneous breaking of gauge symmetry in F-theory, as the corresponding branch of the moduli space does not exist in the theory. Accordingly, even non-abelian gauge theories have not been fully understood in global F-theory compactifications. We present a systematic disc…
Non-classification result for wild knots complicates structure analysis.
Study shows LLC correlates with neural network compressibility.
Geometrically describes Jacobi equations for field theories with dissipation.
This paper describes differential K-theory using Hilbert bundles and superconnections.
New matrix describes knots with 'warping degree'.
A new multiagent model of the stock market is formulated that contains four states in which the agents may be located. Next, the model is reformulated in the language of the functional integral containing fluctuations of prices and quantities of cash flows. It is shown that in the functional integral of that type descr…
The aim of this paper is to propose an unambiguous intrinsic formalism for higher-order field theories which avoids the arbitrariness in the generalization of the conventional description of field theories, which implies the existence of different Cartan forms and Legendre transformations. We propose a differential-geo…
The paper characterizes boundaries in Turaev-Viro TQFTs and Dijkgraaf-Witten theories.
This paper reviews three types of probabilistic models: discriminative, descriptive, and generative.
The Rusk-Skinner formalism was developed in order to give a geometrical unified formalism for describing mechanical systems. It incorporates all the characteristics of Lagrangian and Hamiltonian descriptions of these systems (including dynamical equations and solutions, constraints, Legendre map, evolution operators, e…
In this paper we study the local description of spaces of forms on transitive Lie algebroids. We use this local description to introduce global structures like metrics, -Hodge operation and integration along the algebraic part of the transitive Lie algebroid (its kernel). We construct a Čech-de Rham bicomplex wit…
We develop an approach to Khovanov homology of knots via gauge theory (previous physics-based approches involved other descriptions of the relevant spaces of BPS states). The starting point is a system of D3-branes ending on an NS5-brane with a nonzero theta-angle. On the one hand, this system can be related to a Chern…
Using properties of the determinant line bundle for a family of elliptic boundary value problems, we explain how the Fock space functor defines an axiomatic quantum field theory which formally models the Fermionic path integral. The 'sewing axiom' of the theory arises as an algebraic pasting law for the determinant of …
Researchers describe a Morse theoretic coproduct for Goresky-Hingston.
Explains solution space of Toda equations using Lie theory.
SageMath package diffstrata calculates intersection theory on abelian differentials.
The twisted face-pairing construction of our earlier papers gives an efficient way of generating, mechanically and with little effort, myriads of relatively simple face-pairing descriptions of interesting closed 3-manifolds. The corresponding description in terms of surgery, or Dehn-filling, reveals the twist construct…
The paper describes Calabi-Yau metrics on complex flag manifolds using Lie theory.
Study develops time-continuous models and probabilistic descriptions for agent-based economic market models.
Extended Riemannian geometry aids in DFT formulations.
Summary of para-Hermitian geometry for T-duality in string theory.
The paper reveals a property of chromatic homology for complete graphs.
Develops a new framework for anomaly description in quantum field theories.
Combinatorial method computes Legendrian knot invariant.
Let be a finitely generated free group. By using Bestvina-Handel theory, as well as some further improvements, the eigengroups of a given automorphism of (and its fixed subgroup among them) are globally analyzed and described. In particular, an explicit description of all subgroups of which occur as the fix…
New risk bounds for Lasso derived using MDL principle.
We consider the geometric formulation of the Hamiltonian formalism for field theory in terms of {\em Hamiltonian connections} and {\em multisymplectic forms}. In this framework the covariant Hamilton equations for Mechanics and field theory are defined in terms of multisymplectic --forms, where is the dimens…
We review the basic elements of the geometrical formalism for description of gauge fields and the theory of invariant connections, and their applications to the coset space dimensional reduction of Yang-Mills theories. We also discuss the problem of classification of principal fibre bundles, which is important for the …
Study finite type invariants for knots in rational homology 3-spheres.
We generalize the notion of parallel transport along paths for abelian bundles to parallel transport along surfaces for abelian gerbes using an embedded Topological Quantum Field Theory (TQFT) approach. We show both for bundles and gerbes with connection that there is a one-to-one correspondence between their local des…
Unified description of adjoint knot polynomials for various knots.
Ph.D. thesis on complex Brunn-Minkowski theory using Hilbert bundles.
We treat the vakonomic dynamics with general constraints within a new geometric framework which will be appropriate to study optimal control problems. We compare our formulation with Vershik-Gershkovich one in the case of linear constraints. We show how nonholonomic mechanics also admits a new geometrical description w…
New bracket unifies nonholonomic dynamics and Hamilton-Jacobi theory.
Revives Vogel's diagrammatic technique for universal Lie algebra computations.
We present a uniform description of -structures in dimension as well as -structures in dimension in terms of a characterising spinor and the spinorial field equations it satisfies. We apply the results to hypersurface theory to obtain new embedding theorems, and give a general recipe for bu…
This paper uses a path integral approach to model complex economic systems with many agents.
Survey of global geometry for double field theory.
Moduli spaces of doubly periodic monopoles, also called monopole walls or monowalls, are hyperkähler; thus, when four-dimensional, they are self-dual gravitational instantons. We find all monowalls with lowest number of moduli. Their moduli spaces can be identified, on the one hand, with Coulomb branches of five-dimens…
Paper introduces Ddim, a new measure of model complexity, for MDL-based learning and change detection.
Field theories help describe twisted bundles on orbifolds.
Categorifies Hopf fibration using category theory.
Survey of spectral theory and dynamics for infinite volume hyperbolic manifolds.
Formulae for 1-3 handle attachments in 4-manifolds.
In this paper, we examine Kitaev's lattice model for an arbitrary complex, semisimple Hopf algebra. We prove that this model gives the same topological invariants as Turaev-Viro theory. Using the description of Turaev-Viro theory as an extended TQFT, we prove that the excited states of the Kitaev model correspond to Tu…
We construct a cohomology theory for oriented links using singular cobordisms and a special type of 2-dimensional Topological Quantum Field Theory (TQFT), categorifying the quantum sl(2) invariant. In particular, we give a description of the universal dot-free sl(2) foam cohomology for links via a TQFT.