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.
Proves a general connected sum formula for families Seiberg-Witten invariants.
We prove two tropical gluing formulae for Gromov-Witten invariants of exploded manifolds, useful for calculating Gromov-Witten invariants of a symplectic manifold using a normal-crossing degeneration. The first formula generalizes the symplectic-sum formula for Gromov-Witten invariants. The second formula is stronger, …
G2SAT learns to generate SAT formulas from real-world examples.
Note on new cancellation formulas for manifolds.
Derives Selberg trace formula on Riemann surfaces and generalizes to other spaces.
Proves a formula for a special invariant of 4-manifolds.
For even dimensional manifolds, we prove some twisted anomaly cancellation formulas which generalize some well-known cancellation formulas. For odd dimensional manifolds, we obtain some modularly invariant characteristic forms by the Chern-Simons transgression and we also get some twisted anomaly cancellation formulas.
It has been shown that the Alvarez-Gaum-Witten miraculous anomaly cancellation formula in type IIB superstring theory and its various generalizations can be derived from modularity of certain characteristic forms. In this paper, we show that the Green-Schwarz formula and the Schwarz-Witten formula i…
Paper proves a generalized Torres formula for twisted Reidemeister torsion.
Derives an integral formula for G2-structures.
Derives integral formulae on weighted manifolds.
By studying modular invariance properties of some characteristic forms, we prove some new anomaly cancellation formulas which generalize the Han-Zhang and Han-Liu-Zhang anomaly cancellation formulas
Computes tube formulas for valuations in complex space forms.
Generalizations of the classical affine Lelieuvre formula to surfaces in projective three-dimensional space and to hypersurfaces in multi- dimensional projective space are given. A discrete version of the projective Lelieuvre formula is presented too.
We prove a quasi-Poisson bracket formula for the space of representations of the fundamental groupoid of a surface with boundary, which generalizes Goldman's Poisson bracket formula. We also deduce a similar formula for quasi-Poisson cross-sections.
New methods derive a generalized Frenkel trace formula for Lie groups.
The article generalizes Clairaut's formula for geodesics on submanifolds.
In this paper, we prove a generalization of Reilly's formula in \cite{Reilly}. We apply such general Reilly's formula to give alternative proofs of the Alexandrov's Theorem and the Heintze-Karcher inequality in the hemisphere and in the hyperbolic space. Moreover, we use the general Reilly's formula to prove a new Hein…
We give a formula of the colored Alexander invariant in terms of the homological representation of the braid groups which we call truncated Lawrence's representation. This formula generalizes the famous Burau representation formula of the Alexander polynomial.
Researchers prove formulas for flag area measures, extending previous work.
We give an immersion formula, the Sym-Bobenko formula, for minimal surfaces in the 3-dimensional Heisenberg space. Such a formula can be used to give a generalized Weierstrass type representation and construct explicit examples of minimal surfaces.
The paper derives inequalities and formulas for generalized Ricci flow.
The famous Whitney formula relates the winding number of the smooth generic curve in the real plane to the number of its self-intersection points counted with appropriate signs. We extend this formula to smooth immersions of R^n to R^{2n}. Then use this result together with the general technique of Laplace integrals to…
We give a direct proof of a cancellation formula raised in [7] on the level of differential forms. We also obtain more cancellation formulas for even dimensional Riemannian manifolds with a complex line bundle involved. Relations among these cancellation formulas are discussed.
We formulate and prove a formula for transgressing characteristic forms in general associated bundles following a method of Chern. As applications, we derive D. Johnson's explicit formula for such general transgression and Chern's first transgression formula for the Euler class.
The paper develops residue currents for cohesive modules and proves a generalized Poincaré-Lelong formula.
New Crofton formulae derived from existing ones.
Formula connects curvature to volume in special geometric spaces.
Wave trace singularity formula for fibre bundles generalizes Poisson summation.
We develop two types of integral formulas for the perimeter of a convex body K in planar geometries. We derive Cauchy-type formulas for perimeter in planar Hilbert geometries. Specializing to H^2 we get a formula that appears to be new. We show that it implies the standard Cauchy-Santalo formula involving a central ang…
New formulas for measuring geometric properties of definable sets.
This work extends Tweedie's formulae to non-Gaussian processes for better diffusion model generation.
Matrix formulas for super Teichmüller spaces generalize previous work and yield super λ-lengths.
Formula for HOMFLY polynomial in link diagrams.
Paper derives matrix formulae and proves skein relations for non-orientable surfaces in quasi-cluster algebras.
An index formula is proposed for contact transformations between contact manifolds equipped with CR structures or with fillings by symplectic manifolds. The formula generalizes the Atiyah-Singer formula and gives a conjectured formula for the index of Fourier integral operators, as well as Epstein's relative index for …
Generalized Gauss-Bonnet formula for conical metrics on compact Riemann surfaces.
Extending Itô's formula to non-smooth functions is important both in theory and applications. One of the fairly general extensions of the formula, known as Meyer-Itô, applies to one dimensional semimartingales and convex functions. There are also satisfactory generalizations of Itô's formula for diffusion processes whe…
Formula extends mean curvature to convex sets.
In this paper, we study monotonicity formulas of eigenvalues and entropies along the rescaled List's extended Ricci flow. We derive some monotonicity formulas of eigenvalues of Laplacian which generalize those of Li in [8] and Cao-Hou-Ling in [3]. Moreover, we also consider monotonicity formulas of -func…
New geometric measure simplifies complex analysis.
New anomaly formulas from E8 bundles.
Paper derives trace formula for magnetic Laplacian at zero energy.
In this note, we give a generalization of the inversion formulas of Pestov-Uhlmann for the geodesic ray transform of functions and vector fields on simple 2-dimensional manifolds of constant curvature. The inversion formulas given here hold for 2-dimensional simple manifolds whose curvatures close to a constant.
Generalized Cauchy's surface area formula to arbitrary submanifolds in R^n.
In this short article, we extend the cosine formula for the Möbius energy to generalized O'Hara energies. The newly derived formula gives us a condition for which the right circle minimizes the energy under the length-constraint. Furthermore, it shows us how far the energy is from the Möbius invariant property.
We prove a localization formula for group-valued equivariant de Rham cohomology of a compact G-manifold. This formula is a non-trivial generalization of the localization formula of Berline-Vergne and Atiyah-Bott for the usual equivariant de Rham cohomology. As an application, we obtain a version of the Duistermaat-Heck…
New formulas derived for Jones polynomial of rational links.