arXiv research

The paper analyzes heat trace asymptotics for de Rham and Dolbeault complexes in both real and complex settings.

Compactifies CR structures for complex hyperbolic manifolds.

Study shows Roller compactification's median graph has limited asymptotic dimension.

We combine aspects of the notions of finite decomposition complexity and asymptotic property C into a notion that we call finite APC-decomposition complexity. Any space with finite decomposition complexity has finite APC-decomposition complexity and any space with asymptotic property C has finite APC-decomposition comp…

We prove a positive mass theorem for complete Kähler manifolds that are asymptotic to the complex hyperbolic space.

Study mapping class groups on CAT(0) cube complexes.

We give a bound, linear in the complexity of the surface, on the asymptotic dimension of the curve complex as well as the capacity dimension of the ending lamination space.

Open problem: fixed-budget best arm identification complexity.

Compactify complex hyperbolic almost Hermitian manifolds.

The paper studies translation lengths on sphere complexes and related cones.

Analytic torsion expansions for symmetric and complex homogeneous spaces.

Study minimal surfaces in complex hyperbolic space, linking entropy and volume.

We consider a planar surface Σof infinite type which has the Thompson group T as asymptotic mapping class group. We construct the asymptotic pants complex C of Σand prove that the group T acts transitively by automorphisms on it. Finally, we establish that the automorphism group of the complex C is an extension of the …

We find the entropy's infinite-size behavior in complex manifold sections.

Paper studies robust MDPs, improving sample complexity and asymptotic performance.

The aim of this paper is to investigate properties preserved and co-preserved by coarsely $n$-to-1 functions, in particular by the quotient maps $X\to X/\sim$ induced by a finite group $G$ acting by isometries on a metric space $X$. The coarse properties we are mainly interested in are related to asymptotic dimension a…

Study non-asymptotic BPI guarantees for online RL.

The braided Thompson group $\mathcal B$ is an asymptotic mapping class group of a sphere punctured along the standard Cantor set, endowed with a rigid structure. Inspired from the case of finite type surfaces we consider a Hatcher-Thurston cell complex whose vertices are asymptotically trivial pants decompositions. We …

Complex $b$-$6j$ symbols relate to hyperbolic tetrahedron volumes and determinants.

Any Kaehler metric on the ball which is strongly asymptotic to complex hyperbolic space and whose scalar curvature is no less than the one of the complex hyperbolic space must be isometrically biholomorphic to it. This result has been known for some time in odd complex dimension and we provide here a proof in even dime…

Researchers found infinitely many non-collapsed steady Ricci solitons on complex line bundles.

Study minimal translation lengths on curve complexes, providing bounds and constructing examples.

Study slopes of direct images in complex manifolds, proving a Mehta-Ramanathan type theorem.

New algorithm achieves near optimal sample complexity for 1-identification problem.

Study on determinants of unitary Brownian motion and their asymptotic laws.

Let $φ\in C^\infty(\Complex^n)$ be a given real valued function. We assume that $\pr\ddbarφ$ is non-degenerate of constant signature $(n_-,n_+)$ on $\Complex^n$. When $q=n_-$, it is well-known that the Bergman kernel for $(0,q)$ forms with respect to the $k$-th weight $e^{-2kφ}$, $k>0$, admits a full asymptotic expansi…

Asymptotic dimension of planes and graphs is at most three.

Proves uniqueness of embedding complex manifold into infinite-dimensional space.

We study the asymptotic behavior of the asymptotic translation lengths on the curve complexes of pseudo-Anosov monodromies in a fibered cone of a fibered hyperbolic 3-manifold $M$ with $b_1(M) \geq 2$. For a sequence $(Σ_n, ψ_n)$ of fibers and monodromies in the fibered cone, we show that the asymptotic translation len…

We observe inequalities involving the Herzlich volume of a 4-dimensional asymptotically complex hyperbolic Einstein manifold and its Euler characteristic provided the metrics is either Kaehler or selfdual. In the selfdual case we have to assume furthermore that the Kronheimer-Mrowka invariant is non vanishing.

We introduce canonical measures on a locally finite simplicial complex $K$ and study their asymptotic behavior under infinitely many barycentric subdivisions. We also compute the face polynomial of the asymptotic link and dual block of a simplex in the $d^{th}$ barycentric subdivision $Sd^d(K)$ of $K$, $d\gg0$. It is a…

The study examines Bergman kernels on complex manifolds with boundary and their asymptotic expansions.

DETC algorithm achieves asymptotic optimality in multi-armed bandit problems.

Let $M$ be a hyperbolic fibered 3-manifold with $b_1(M) \geq 2$ and let $S$ be a fiber with pseudo-Anosov monodromy $ψ$. We show that there exists a sequence $(R_n, ψ_n)$ of fibers and monodromies contained in the fibered cone of $(S,ψ)$ such that the asymptotic translation length of $ψ_n$ on the curve complex $\mathca…

E$^4$ algorithm optimizes batched linear bandits with minimal regret and batches.

We calculate the asymptotic behavior of hyperbolic volume and Chern-Simons invariant.

We introduce the notion of regular finite decomposition complexity of a metric family. This generalizes Gromov's finite asymptotic dimension and is motivated by the concept of finite decomposition complexity (FDC) due to Guentner, Tessera and Yu. Regular finite decomposition complexity implies FDC and has all the perma…

By recognizing them as fundamental groups of developable complexes of groups we prove that mapping class groups of compact orientable surfaces have finite asymptotic dimension.

Uniqueness proven for a specific type of complex manifold's solitons.

We prove extension theorems for several geometric properties such as asymptotic property C (APC), finite decomposition complexity (FDC), strict finite decomposition complexity (sFDC) which are weakenings of Gromov's finite asymptotic dimension (FAD). The context of all theorems is a finitely generated group $G$ with a …

We prove an existence theorem for Asymptotically Conical Ricci Flat Kahler metrics in $\mathbb{C}^2$ with cone singularities along a smooth complex curve. These metrics are expected to arise as blow up limits of non collapsed sequences of Kahler Einstein metrics with cone singularities.

Estimates holomorphic sections on Bohr-Sommerfeld Lagrangian submanifolds.

Study complex lines in symplectic geometry, generalizing previous results.

For a finite function class we describe the large sample limit of the sequential Rademacher complexity in terms of the viscosity solution of a $G$-heat equation. In the language of Peng's sublinear expectation theory, the same quantity equals to the expected value of the largest order statistics of a multidimensional $…

Paper develops online statistical inference methods for stochastic optimization using Kiefer-Wolfowitz algorithms.

The paper studies the asymptotic behavior of HCMA equations on ALE Kahler manifolds.

Solves complex equation for specific geometric solitons.

Starting from a real analytic conformal Cartan connection on a real analytic surface $S$, we construct a complex surface $T$ containing a family of pairs of projective lines. Using the structure on $S$ we also construct a complex $3$-space $Z$, such that $Z$ is a twistor space of a self-dual conformal $4$-fold and $T$ …