arXiv research

Classifies jets of surfaces in 4-space based on their projections.

Study on volumes of random inscribed polytopes in projective geometries.

In the quantum Teichmuller theory, based on Penner coordinates, the mapping class groups of punctured surfaces are represented projectively. The case of a genus three surface with one puncture is worked out explicitly. The projective factor is calculated. It is given by the exponential of the Liouville central charge.

The article considers the problem of existence and uniqueness of centrally symmetrical convex body for which the projection curvature radius function coincides with a given flag function. A necessary and sufficient condition is found that ensures a positive answer. An algorithm for construction the body in question is …

Finite order elements with infinite centralizers in 3-manifold groups imply specific structure.

We consider a projection from the center of the unit sphere to a tangent space of it, the central projection, and study two area minimizing problems of the image of a closed subset in the sphere. One of the problems is the uniqueness of the tangent plane that minimizes the area for an arbitrary fixed subset. The other …

We present a local classification of smooth projective surfaces in 3-space via projective transformations in accordance with singularity types of central projections up to codimension 4. We also discuss relations between our classification of Monge forms and bifurcations of parabolic curves and flecnodal curves.

Research uses machine learning to find central nodes and cliques in YouTube social networks.

We determine the lower central and derived series of the n-string braid groups B_n(RP^2) of the real projective plane. We are motivated in part by the study of Fadell-Neuwirth short exact sequences, but the problem is interesting in its own right. For n=1,2, B_n(RP^2) is finite and its lower central and derived series …

Quantization of universal Teichmüller space provides projective representations of the Ptolemy-Thompson group, which is isomorphic to the Thompson group $T$. This yields certain central extensions of $T$ by $\mathbb{Z}$, called dilogarithmic central extensions. We compute a presentation of the dilogarithmic central ext…

Python package for projecting onto quadratic hypersurfaces.

The study proves residual finiteness for certain lattice extensions and negatively curved projective varieties.

The paper proves residual finiteness of certain lattices and constructs surfaces with specific fundamental groups.

We show a correspondence between the set of all G-invariant projectively flat connections on a homogeneous apace $M=G/K$, and the one of all {G}^~-invariant flat connections on a homogeneous space {M}^~={G}^~/K, where {G}^~ is a central extension of G.

Compute central extension of mapping class group from stated skein algebra

Given a (smooth) complex analytic family of compact complex manifolds, we prove that the central fibre must be Moishezon if the other fibres are Moishezon. Using a "strongly Gauduchon metric" on the central fibre whose existence was proved in our previous work on limits of projective manifolds, we show that the irreduc…

Projective loops generate rational loop groups without needing nilpotent loops.

Kähler-Einstein metrics on toric submanifolds cannot be induced by projective immersions.

Many modern datasets can be represented as graphs and hence spectral decompositions such as graph principal component analysis (PCA) can be useful. Distinct from previous graph decomposition approaches based on subspace projection of a single topological feature, e.g., the Fiedler vector of centered graph adjacency mat…

We present the theory of tensors with Young tableau symmetry as an efficient computational tool in dealing with the polynomial first integrals of a natural system in classical mechanics. We relate a special kind of such first integrals, already studied by Lundmark, to Beltrami's theorem about projectively flat Riemanni…

For a convex body $K\subset\R^n$ and $i\in\{1,...,n-1\}$, the function assigning to any $i$-dimensional subspace $L$ of $\R^n$, the $i$-dimensional volume of the orthogonal projection of $K$ to $L$, is called the $i$-th projection function of $K$. Let $K, K_0\subset \R^n$ be smooth convex bodies of class $C^2_+$, and l…

Study on when the lower central series stops for various groups, including braid groups.

We create a minimal triangulation of 5D real projective space.

Paper improves performance guarantees for Rademacher projections.

An $L_\infty$-algebra is built on symplectic manifold homology.

Characterizes W-congruences to study their stable umbilical points.

Projective preferential Bayesian optimization learns user preferences in high dimensions.

We define several homology theories for central hyperplane arrangements, categorifying well-known polynomial invariants including the characteristic polynomial, Poincare polynomial, and Tutte polynomial. We consider basic algebraic properties of such chain complexes, including long-exact sequences associated to deletio…

Call {\em i-hedrite} any 4-valent n-vertex plane graph, whose faces are 2-, 3- and 4-gons only and $p_2+p_3=i$. The edges of an i-hedrite, as of any Eulerian plane graph, are partitioned by its {\em central circuits}, i.e. those, which are obtained by starting with an edge and continuing at each vertex by the edge oppo…

Geometrically transforms nonconservative dynamics to linearize Kepler and Manev systems.

We examine the relationships between the differential invariants of objects and of their images under a surjective map. We analyze both the case when the underlying transformation group is projectable and hence induces an action on the image, and the case when only a proper subgroup of the entire group acts projectably…

When can a map between manifolds be deformed away from itself? We describe a (normal bordism) obstruction which is often computable and in general much stronger than the classical primary obstruction in cohomology. In particular, it answers our question completely in a large dimension range. As an illustration we give …

We present a novel algorithm for deciding whether a given planar curve is an image of a given spatial curve, obtained by a central or a parallel projection with unknown parameters. The motivation comes from the problem of establishing a correspondence between an object and an image, taken by a camera with unknown posit…

Second part of a series on higher coverings of racks and quandles.

A new method predicts compounds for orphan proteins.

We consider forecasting a single time series when there is a large number of predictors and a possible nonlinear effect. The dimensionality was first reduced via a high-dimensional (approximate) factor model implemented by the principal component analysis. Using the extracted factors, we develop a novel forecasting met…

FORE evaluates occupancy ratios without requiring Bellman completeness.

Given a real vector space V of finite dimension, together with a particular homogeneous field of bivectors that we call a "field of projective forces", we define a law of dynamics such that the position of the particle is a "ray" i.e. a half-line drawn from the origin of V. The impulsion is a bivector whose support is …

A canonical branched covering over each sufficiently good simplicial complex is constructed. Its structure depends on the combinatorial type of the complex. In this way, each closed orientable 3-manifold arises as a branched covering over the 3-sphere from some triangulation of S^3. This result is related to a theorem …

The paper proves a Donaldson-Uhlenbeck-Yau theorem for normal varieties and semistable bundles.

The aim of this talk is to explain how symmetry breaking in a quantum field theory problem leads to a study of projective bundles, Dixmier-Douady classes, and associated gerbes. A gerbe manifests itself in different equivalent ways. Besides the cohomological description as a DD class, it can be defined in terms of a fa…

This work improves understanding of projection robust optimal transport distances.

AGOP from KRR recovers central subspace in fewer samples than needed for prediction.

Study on positivity of CM line bundles on moduli space of klt good minimal models with κ=1.

Optimizes differentially private kernel learning with random projection.

Study nondegenerate fibrations of Euclidean spaces and their relation to sphere fibrations.

The paper explores triangulations of spheres and projective spaces, focusing on Hopf triangulations and equilibrium structures.

ProDAG uses variational inference to learn DAGs with uncertainty quantification.