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.
This study explores the index theory of Heisenberg elliptic and transversally Heisenberg elliptic operators using -theory.
Study pin manifolds using Clifford linear Dirac operator and KO-theory.
The paper proves homotopy equivalences for spaces of unbounded Fredholm operators.
Paper develops Lie theory for Rota-Baxter operators on Lie algebras and groups.
Defines operations in non-Archimedean metrics theory.
New operations defined on moduli spaces for bundles with orientations.
Local index theorem for chiral geometric operators proved using heat kernel.
We give an overview of the generalized Calderón-Zygmund theory for "non-integral" singular operators, that is, operators without kernels bounds but appropriate off-diagonal estimates. This theory is powerful enough to obtain weighted estimates for such operators and their commutators with $\BMO$ functions. of…
Study hypoelliptic operators on Carnot manifolds, extending index theory results.
Local index formula for Lorentzian Dirac operators on spacetimes.
Operator on tangles derived from knot 2-cabling.
Mathematical proof of index equality for lattice Dirac operators and continuum operators.
We study the geometry and partial differential equations arising from the consideration of group-determinants, and representation theory. The simplest and most striking such example is undoubtedly that of the Humbert operator, associated with the cyclic group Z/3Z. This operator appears as a natural extension of the La…
We introduce two -theories, one for vector bundles whose fibers are modules of vertex operator algebras, another for vector bundles whose fibers are modules of associative algebras. We verify the cohomological properties of these -theories, and construct a natural homomorphism from the VOA K-theory to the associa…
Study Schiffer operators on Riemann surfaces, linking conformal and topological invariants.
We factorize the Dirac operator on the Connes-Landi 4-sphere in unbounded KK-theory. We show that a family of Dirac operators along the orbits of the torus action defines an unbounded Kasparov module, while the Dirac operator on the principal orbit space -an open quadrant in the 2-sphere- defines a half-closed chain. W…
This is an expository paper which gives a proof of the Atiyah-Singer index theorem for elliptic operators. Specifcally, we compute the geometric K-cycle that corresponds to the analytic K-cycle determined by the operator. This paper and its companion ("K-homology and index theory II: Dirac Operators") was written to cl…
Develops connections between operator K-theory and positive scalar curvature.
We investigate index theory in the context of Dirac operators coupled to superconnections. In particular, we prove a local index theorem for such operators, and for families of such operators. We investigate eta-invariants and prove an APS-theorem, and construct a geometric determinant line bundle for families of such …
A commuting -tuple of bounded linear operators on a Hilbert space $\clh$ associate a Hilbert module over in the following sense: \[\mathbb{C}[z_1, \ldots, z_n] \times \mathcal{H} \rightarrow \mathcal{H}, \quad \quad (p, h) \mapsto p(T_1, \ldots, T_n)h…
We give a survey on the Weierstrass representations of surfaces in three- and four-dimensional spaces, their applications to the theory of the Willmore functional and on related problems of spectral theory of the two-dimensional Dirac operator with periodic coefficients.
The paper proposes a method to sample quantum field configurations using neural operators and flows.
Research resolves sign conventions in Floer theory for Morse-Bott case.
The main result of this paper is a new and direct proof of the natural transformation from the surgery exact sequence in topology to the analytic K-theory sequence of Higson and Roe. Our approach makes crucial use of analytic properties and new index theorems for the signature operator on Galois coverings with boundary…
Scattering theory for harmonic one-forms on Riemann surfaces.
Constructs index for elliptic operators using rapidly decaying kernels.
A general theory of quantum spinor structures on quantum spaces is presented, within the conceptual framework of the formalism of quantum principal bundles. Quantum analogs of all basic objects of the classical theory are constructed and analyzed. This includes Laplace and Dirac operators, quantum versions of Clifford …
In the paper we consider the theory of elliptic operators acting in subspaces defined by pseudodifferential projections. This theory on closed manifolds is connected with the theory of boundary value problems for operators violating Atiyah-Bott condition. We prove an index formula for elliptic operators in subspaces de…
It is a classic result that the geometry of the total space of a principal bundle with reference to the action of the bundle's structure group is codified in the bundle's operation, a collection of derivations comprising the de Rham differential and the contraction and Lie derivatives of all vertical vector fields and …
This is an expository paper which gives a proof of the Atiyah-Singer index theorem for Dirac operators, presenting the theorem as a computation of the K-homology of a point. This paper and its follow up ("K-homology and index theory II: Elliptic Operators") was written to clear up basic points about index theory that a…
The notion of pseudo-differential operators with coefficients in a continuous trace algebra over a manifold are introduced and their index theory is studied. The algebra of principal symbols in this calculus provides an abstract Poincaré dual to the continuous trace algebra. Index formulas for pseudo-differential opera…
Proves elliptic operator images are closed on Hilbert bundles.
We study twisted N=2 superconformal gauge theory on a product of two Riemann surfaces Sigma and C. The twisted theory is topological along C and holomorphic along Sigma and does not depend on the gauge coupling or theta-angle. Upon Kaluza-Klein reduction along Sigma, it becomes equivalent to a topological B-model on C …
Proves a lattice version of the Atiyah-Singer index theorem.
The spectral flow theorem is applied to operators on finite intervals.
An index theory for projective families of elliptic pseudodifferential operators is developed when the twisting, i.e. Dixmier-Douady, class is decomposable. One of the features of this special case is that the corresponding Azumaya bundle can be realized in terms of smoothing operators. The topological and the analytic…
Develops trace class operators and inverse Laplacian theory for infinite dimensions.
New proof confirms operations on constructible functions match theory.
New theory allows simultaneous block-diagonalization of commuting operator fields.
A families index theorem in K-theory is given for the setting of Atiyah, Patodi and Singer of a family of Dirac operators with spectral boundary condition. This result is deduced from such a K-theory index theorem for the calculus of cusp, or more generally fibred cusp, pseudodifferential operators on the fibres (with …
We present the theory of pseudodifferential operators acting on a vector orbibundle over an orbifold, construct the zeta function of an elliptic pseudodifferential operator and show the existence of a meromorphic extension to the complex plane with at most simple poles. We give formulas for generalized densities on the…
The geometry of the total space of a principal bundle with regard to the action of the bundle's structure group is elegantly described by the bundle's operation, a collection of derivations consisting of the de Rham differential and the contraction and Lie derivatives of all vertical vector fields and satisfying the si…
We generalize Roe's Index Theorem for operators of Dirac type on open manifolds to elliptic pseudodifferential operators. To this end we introduce a class of pseudodifferential operators on manifolds of bounded geometry which is more general than similar classes defined by other authors. We revisit Spakula's uniform K-…
Koopman operator theory simplifies complex systems analysis.
Study constructs transverse metrics using transformations commuting with elliptic operators.
This research develops approximation theory for OOMs of infinite-dimensional processes.
The paper explores the index theory of sub-Laplacians on higher nilpotent Carnot manifolds.
In this paper we introduce a notion of scattering theory for the Laplace-Beltrami operator on non-compact, connected and complete Riemannian manifolds. A principal condition is given by a certain positive lower bound of the second fundamental form of angular submanifolds at infinity. Another condition is certain bounds…