arXiv research

Survey of open problems in finite-dimensional integrable systems.

Survey of recent results on homogeneous finite-dimensional spaces.

Develops a finite construction for self-duality and related moduli spaces over Riemann surfaces.

New result on finite gerbes simplifies classification of certain bundles.

Paper finds conditions for finite-dimensional vector spaces of cross-sections.

We prove that there is no faithful finite-dimensional representation by skew-hermitian matrices of a ``basic algebra of observables'' B on a noncompact symplectic manifold M. Consequently there exists no finite-dimensional quantization of any Lie subalgebra of the Poisson algebra C^\infty(M) containing B.

Finite-dimensional spaces of biharmonic functions on manifolds are explored.

We approximate the Sobolev discrepancy for finite dimensional kernels from samples.

The paper studies multi-curve interest rate models and their consistency and finite-dimensional realizations.

Paper develops a finite dimensional approximation scheme for Riemannian manifolds.

Finite spaces can be or not coproducts of subspaces.

Solves classical problem with Kähler-Einstein metrics in complex projective spaces.

Abstract: Geometrically reformulates estimation theory for finite-dimensional C*-algebras.

We show that a continuous local semiflow of $C^k$-maps on a finite-dimensional $C^k$-manifold M can be embedded into a local $C^k$-flow on M under some weak (necessary) assumptions. This result is applied to an open problem in [fil/tei:01]. We prove that finite-dimensional realizations for interest rate models are high…

We solve a linear equation on affine manifolds, finding finite-dimensional solutions.

We propose a method for pricing American options whose pay-off depends on the moving average of the underlying asset price. The method uses a finite dimensional approximation of the infinite-dimensional dynamics of the moving average process based on a truncated Laguerre series expansion. The resulting problem is a fin…

We prove a version of the countable union theorem for asymptotic dimension and we apply it to groups acting on asymptotically finite dimensional metric spaces. As a consequence we obtain the following finite dimensionality theorems. A) An amalgamated product of asymptotically finite dimensional groups has finite asympt…

A homological selection theorem for C-spaces, as well as, a finite-dimensional homological selection theorem is established. We apply the finite-dimensional homological selection theorem to obtain fixed-point theorems for usco homologically UV^n set-valued maps.

In this paper, we refine the notion of Z-boundaries of groups introduced by Bestvina and further developed by Dranishnikov. We then show that the standard assumption of finite-dimensionality can be omitted as the result follows from the other assumptions.

Infinite-dimensional polynomial diffusions preserve tractability of finite-dimensional counterparts.

In this paper we prove that the holonomy group of a simply connected locally projectively flat Finsler manifold of constant curvature is a finite dimensional Lie group if and only if it is flat or it is Riemannian.

We show that groups satisfying Kazhdan's property (T) have no unbounded actions on finite dimensional CAT(0) cube complexes, and deduce that there is a locally CAT(-1) Riemannian manifold which is not homotopy equivalent to any finite dimensional, locally CAT(0) cube complex.

Using the categorical description of supergeometry we give an explicit construction of the diffeomorphism supergroup of a compact finite-dimensional supermanifold. The construction provides the diffeomorphism supergroup with the structure of a Frechet supermanifold. In addition, we derive results about the structure of…

This manuscript studies statistical properties of linear classifiers obtained through minimization of an unregularized convex risk over a finite sample. Although the results are explicitly finite-dimensional, inputs may be passed through feature maps; in this way, in addition to treating the consistency of logistic reg…

The paper explores mapping class groups and their quantum field theory representations.

The Kuperberg invariant is shown to be gauge invariant for certain framed 3-manifolds.

The study examines polynomial growth functions on gradient shrinking Ricci solitons.

The study connects Kato bounds to finite-dimensional RCD spaces.

Unified formula for higher traces of linear maps on finite-dimensional normed spaces.

We introduce a class of regularisable infinite dimensional principal fibre bundles which includes fibre bundles arising in gauge field theories like Yang-Mills and string theory and which generalise finite dimensional Riemannian principal fibre bundles induced by an isometric action. We show that the orbits of regulari…

The paper solves integrable systems of PDEs, including famous equations.

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

Study finds conditions for finite-dimensional Lie group structure in basic automorphism groups of certain Cartan foliations.

Classifies vector field algebras in complex space.

We determine the set of Busemann points of an arbitrary finite-dimensional normed space. These are the points of the horofunction boundary that are the limits of "almost-geodesics". We prove that all points in the horofunction boundary are Busemann points if and only if the set of extreme sets of the dual unit ball is …

Compact embedding for forward rate curves simplifies approximations.

It is known that the only finite-dimensional diffeological vector space that admits a diffeologically smooth scalar product is the standard space of appropriate dimension. In this note we consider a way to circumnavigate this issue, by introducing a notion of pseudo-metric, which, said informally, is the least-degenera…

Proves Lipschitz regularity of harmonic maps from Alexandrov spaces.

Study geodesics on finite-dimensional manifolds.

Categorifies Jones polynomial using Lie theory.

We show that the Kuratowski imbedding of a Riemannian manifold in L^\infty, exploited in Gromov's proof of the systolic inequality for essential manifolds, admits an approximation by a (1+C)-bi-Lipschitz (onto its image), finite-dimensional imbedding for every C>0. Our key tool is the first variation formula thought of…

We prove that a monomorphic functor $F:Comp\to Comp$ with finite supports is epimorphic, continuous, and its maximal $\emptyset$-modification $F^\circ$ preserves intersections. This implies that a monomorphic functor $F:Comp\to Comp$ of finite degree $deg F\le n$ preserves (finite-dimensional) compact ANR's if the spac…

We prove properties of the Schweitzer complex and its cohomologies.

The paper proves stability in compact finite dimensional Alexandrov spaces using equivariant Gromov--Hausdorff convergence.

Refines Kronheimer-Mrowka's invariant for 4-manifolds with specific boundary conditions.

Outer space for RAAGs is a contractible finite-dimensional space for automorphisms.

Proof shows local convexity implies global convexity in special geometric spaces.

New method constructs Floer homologies without hard analysis.