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 on multiple linking numbers, extending Gauss diagram formulas.
Formula for Milnor triple linking number in link diagrams with multiple crossings.
The paper proves integral formulas for manifolds with multiple orthogonal distributions.
The paper develops a new formula for financial pricing under multiple interest rates and collateralization.
Three counterexamples show higher eigenvalue multiplicities than conjectured.
We provide explicit formulas for integrating multiplicative forms on local Lie groupoids in terms of infinitesimal data. Combined with our previous work [8], which constructs the local Lie groupoid of a Lie algebroid, these formulas produce concrete integrations of several geometric stuctures defined infinitesimally. I…
New formula and properties of inverted Habiro series derived from GM series.
Formulas for spectra of higher spin operators on sphere subbundles.
This paper derives an explicit formula for Branson's Q-curvature in even-dimensional conformal geometry. The ingredients in the formula come from the Poincare metric in one higher dimension; hence the formula is called holographic. When specialized to the conformally flat case, the holographic formula expresses Q-curva…
The paper simplifies calculus for semimartingales using multiplicative compensation.
The paper studies complex genera and related geometric applications, deriving formulas for multiple zeta values.
The paper calculates asymptotic Betti numbers and homology multiplicities for graph configuration spaces.
We prove a multiplicity formula for Riemann-Roch numbers of reductions of Hamiltonian actions of loop groups. This includes as a special case the factorization formula for the quantum dimension of the moduli space of flat connections over a Riemann surface.
We give a short and simple proof of Cauchy's surface area formula, which states that the average area of a projection of a convex body is equal to its surface area up to a multiplicative constant in the dimension.
The complex analytic methods have found a wide range of applications in the study of multiplicity-free representations. This article discusses, in particular, its applications to the question of restricting highest weight modules with respect to reductive symmetric pairs. We present a number of multiplicity-free branch…
We prove a formula for the multiplicities of the index of an equivariant transversally elliptic operator on a -manifold. The formula is a sum of integrals over blowups of the strata of the group action and also involves eta invariants of associated elliptic operators. Among the applications, we obtain an index formu…
New method handles complex systems with discontinuous, heavy-tailed noise.
New formula calculates volumes of ideal hyperbolic drums.
We apply the Guillemin-Lerman-Sternberg theorem to reprove a formula of Heckman for the Duistermaat-Heckman measure associated to the coadjoint action of , a maximal torus of a compact semisimple Lie group , on a regular coadjoint -orbit in the dual space of the Lie algebra of . This formula is, in an appro…
Several formulas for computing coarse indices of twisted Dirac type operators are introduced. One type of such formulas is by composition product in -theory. The other type is by module multiplications in -theory, which also yields an index theoretic interpretation of the duality between Roe algebra and stable Hi…
In this paper we prove a useful formula for the graded commutator of the Hodge codifferential with the left wedge multiplication by a fixed -form acting on the de Rham algebra of a Riemannian manifold. Our formula generalizes a formula stated by Samuel I. Goldberg for the case of 1-forms. As first examples of applic…
We study multiple defaults where the global market information is modelled as progressive enlargement of filtrations. We shall provide a general pricing formula by establishing a relationship between the enlarged filtration and the reference default-free filtration in the random measure framework. On each default scena…
We give a new proof of a slightly weaker form of a theorem of P. Colmez. This theorem gives a formula for the Faltings height of abelian varieties with complex multiplication by a C.M. field whose Galois group over is abelian; it reduces to the formula of Chowla and Selberg in the case of elliptic curves. We sh…
The paper studies how surfaces move by mean curvature flow and what happens at singular points.
We provide a general and tractable framework under which all multiple yield curve modeling approaches based on affine processes, be it short rate, Libor market, or HJM modeling, can be consolidated. We model a numeraire process and multiplicative spreads between Libor rates and simply compounded OIS rates as functions …
We construct certain spectral triples in the sense of A. ~Connes and H. Moscovici (``The local index formula in noncommutative geometry'' {\it Geom. Funct. Anal.}, 5(2):174--243, 1995) that is transversally elliptic but not necessarily elliptic. We prove that these spectral triples satisfie the conditions which ensure …
We give multiplicity results for the problem of prescribing the scalar curvature on Cauchy- Riemann spheres under Beta-flatness condition. To give a lower bound for the number of solutions, we use Bahri methods based on the theory of critical points at infinity and a Poincare-Hopf type formula.
Closed formulas for η-corrections in the once-punctured torus identified.
Jeffrey and Kirwan suggested expressions for intersection pairings on the reduced space of a Hamiltonian G-space in terms of multiple residues. In this paper we prove a residue formula for symplectic volumes of reduced spaces of a quasi-Hamiltonian SU(2)-space. The definition of quasi-Hamiltonian G-spaces was recently …
We present generating functions for extensions of multiplicative invariants of wreath symmetric products of orbifolds presented as the quotient by the locally free action of a compact, connected Lie group in terms of orbifold sector decompositions. Particularly interesting instances of these product formulas occur for …
This paper derives a portfolio decomposition formula when the agent maximizes utility of her wealth at some finite planning horizon. The financial market is complete and consists of multiple risky assets (stocks) plus a risk free asset. The stocks are modelled as exponential Brownian motions with drift and volatility b…
We extend asymptotic formulas for saddle connections on translation surfaces.
We introduce a multiple curve framework that combines tractable dynamics and semi-analytic pricing formulas with positive interest rates and basis spreads. Negatives rates and positive spreads can also be accommodated in this framework. The dynamics of OIS and LIBOR rates are specified following the methodology of the …
In this paper we develop a framework for discretely compounding interest rates which is based on the forward price process approach. This approach has a number of advantages, in particular in the current market environment. Compared to the classical as well as the Lévy Libor market model, it allows in a natural way for…
We prove several results on Almgren's multiple valued functions and their links to integral currents. In particular, we give a simple proof of the fact that a Lipschitz multiple valued map naturally defines an integer rectifiable current; we derive explicit formulae for the boundary, the mass and the first variations a…
A Gauss diagram is a simple, combinatorial way to present a knot. It is known that any Vassiliev invariant may be obtained from a Gauss diagram formula that involves counting (with signs and multiplicities) subdiagrams of certain combinatorial types. These formulas generalize the calculation of a linking number by coun…
The paper proves the existence of a folded annulus with multiple creases.
We study the conditions for a nilpotent Lie group to be foliated into subgroups that have square integrable (relative discrete series) unitary representations, that fit together to form a filtration by normal subgroups. Then we use that filtration to construct a class of "stepwise square integrable" representations on …
Polynomial algorithm for multiplication on one-hole torus skein algebra.
In this expository paper, we explain a formula for the multiplicities of the index of an equivariant transversally elliptic operator on a -manifold. The formula is a sum of integrals over blowups of the strata of the group action and also involves eta invariants of associated elliptic operators. Among the applicatio…
Formula decomposes multiplicative forms on Poisson groupoids into two parts.
In this article, we first establish the main tool - an integral formula for Riemannian manifolds with multiple boundary components (or without boundary). This formula generalizes Reilly's original formula from \cite{Re2} and the recent result from \cite{QX}. It provides a robust tool for sub-static manifolds regardless…
We extend our earlier work in [TZ1], where an analytic approach to the Guillemin-Sternberg conjecture [GS] was developed, to cases where the Spin-complex under consideration is allowed to be further twisted by certain natural exterior power bundles. The main result is a weighted quantization formula in the presence…
We propose and study the following Mirror Principle: certain sequences of multiplicative equivariant characteristic classes on Kontsevich's stable map moduli spaces can be computed in terms of certain hypergeometric type classes. As applications, we compute the equivariant Euler classes of obstruction bundles induced b…
This paper and its sequel prove a generalization of the usual gluing theorem for two index 1 pseudoholomorphic curves u_+ and u_- in the symplectization of a contact 3-manifold. We assume that for each embedded Reeb orbit gamma, the total multiplicity of the negative ends of u_+ at covers of gamma agrees with the total…
We compute the measure with multiplicity of the set of complex planes intersecting a compact domain in a complex space form. The result is given in terms of the so-called hermitian intrinsic volumes. Moreover, we obtain two different versions for the Gauss-Bonnet-Chern formula in complex space forms. One of them gives …
We extend our earlier work in [TZ1], where an analytic approach to the Guillemin-Sternberg conjecture [GS] was developed, to cases where the Spin^c-complex under consideration is allowed to be further twisted by certain exterior power bundles of the cotangent bundle. The main result is a weighted quantization formula i…
We determine the complete conjugate locus along all geodesics parallel or perpendicular to the center (Theorem 2.3). When the center is 1-dimensional we obtain formulas in all cases (Theorem 2.5), and when a certain operator is also diagonalizable these formulas become completely explicit (Corollary 2.7). These yield s…