arXiv research

Prove a generalization of Werner's formula for the volume of illumination bodies on Riemannian manifolds.

New $L_p$-Steiner quermassintegrals defined from Steiner formula.

We study the eta invariants of Dirac operators and the regularized determinants of Dirac Laplacians over hyperbolic manifolds with cusps. We follow Werner M"uller and use relative traces to define these spectral invariants. We show the regularity of eta and zeta functions at s=0. The Selberg trace formula and the detai…

We pursue a geometrical approach to gravitational lensing theory. We present a survey of the background theory of General Relativity, including particular properties of the Schwarzschild and Kerr solutions. Next we outline a proof of the Gauss Bonnet theorem and its applications to surfaces in optical geometry, as deve…

We show that the Craighero-Gattazzo surface, the minimal resolution of an explicit complex quintic surface with four elliptic singularities, is simply-connected. This was conjectured by Dolgachev and Werner, who proved that its fundamental group has a trivial profinite completion. The Craighero-Gattazzo surface is the …

The paper connects Riemann surface length spectra to Brownian loop measures.

The paper provides a combinatorial criterion for realizing tropical pluri-canonical divisors.

Werner Meyer constructed a cocycle in $H^2(Sp(2g, \mathbb{Z}); \mathbb{Z})$ which computes the signature of a closed oriented surface bundle over a surface, with fibre a surface of genus g. By studying properties of this cocycle, he also showed that the signature of such a surface bundle is a multiple of 4. In this pap…

If V and W are varieties of algebras such that any V-algebra A has a reduct U(A) in W, there is a forgetful functor U: V->W that acts by A |-> U(A) on objects, and identically on homomorphisms. This functor U always has a left adjoint F: W->V by general considerations. One calls F(B) the V-algebra freely generated by t…

This paper studies iteration convergence of Kronecker graphical lasso (KGLasso) algorithms for estimating the covariance of an i.i.d. Gaussian random sample under a sparse Kronecker-product covariance model and MSE convergence rates. The KGlasso model, originally called the transposable regularized covariance model by …

Proves a general connected sum formula for families Seiberg-Witten invariants.

Derives an integral formula for G2-structures.

Derives integral formulae on weighted manifolds.

Paper derives trace formula for magnetic Laplacian at zero energy.

The Gauss formula is extended to various Laplacians on submanifolds.

The paper is devoted to the problem of finding explicit combinatorial formulae for the Pontryagin classes. We discuss two formulae, the classical Gabrielov-Gelfand-Losik formula based on investigation of configuration spaces and the local combinatorial formula obtained by the author in 2004. The latter formula is based…

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, …

Note on new cancellation formulas for manifolds.

The main result of the present paper is a coincidence formula for foliated manifolds. To prove this we establish Kuenneth formula, Poincare duality and intersection product in the context of tangential de Rham cohomology and homology of tangential currents. We apply the formula to get a dynamical Lefschetz formula for …

Formula calculates volume of two-bridge knots.

Introduces a universal Bochner formula for scalar curvature.

Formula connects surgeries to Seiberg-Witten invariants.

It has been shown that the Alvarez-Gaum$\mathrm{\acute{e}}$-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…

Proves a formula for a special invariant of 4-manifolds.

Proves a special case of the Gaussian kinematic formula using large sphere limits.

New Crofton formulae derived from existing ones.

Formulae for non-symmetric connections derived from covariant derivatives.

Formula connects curvature to volume in special geometric spaces.

Kenmotsu's formula describes surfaces in Euclidean 3-space by their mean curvature functions and Gauss maps. In Lorentzian 3-space, Akutagawa-Nishikawa's formula and Magid's formula are Kenmotsu-type formulas for spacelike surfaces and for timelike surfaces, respectively. We apply them to a few problems concerning rota…

The paper proves T-duality and Hori formulae for winding loop spaces.

New formulas for measuring geometric properties of definable sets.

Guillemin trace formula adapted for group actions.

Unified entropy formula for real, complex, and quaternionic DLNs.

Proves an Euler-type formula for Möbius strip partitions.

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.

Paper derives matrix formulae and proves skein relations for non-orientable surfaces in quasi-cluster algebras.

New formulas for coassociative submanifolds' volume variation.

New methods derive a generalized Frenkel trace formula for Lie groups.

Alternative closed-form formula for spread call option prices under log-normal models.

The paper derives new Gauss-Bonnet formulas for frontal bundles over surfaces with boundary.

In this paper, we obtain asymptotic formulas with error estimates for the implied volatility associated with a European call pricing function. We show that these formulas imply Lee's moment formulas for the implied volatility and the tail-wing formulas due to Benaim and Friz. In addition, we analyze Pareto-type tails o…

Proves a formula in Heegaard Floer homology using combinatorial methods.

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.

We derive formulas for F measures' standard error and confidence intervals.

Derives Selberg trace formula on Riemann surfaces and generalizes to other spaces.

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…

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.

Wave trace singularity formula for fibre bundles generalizes Poisson summation.