arXiv research

New rigidity result for convex co-compact actions in products of spaces.

Study on stability of non-diagonal Einstein metrics on specific homogeneous spaces.

Diagonal metrics solve Hermitian-Einstein equations for decomposed Higgs bundles.

Maximal open subset found for product of CAT(-1) spaces.

It is shown that if one uses the notion of infinity nilpotent elements due to Moerdijk and Reyes, instead of the usual definition of nilpotents to define reduced $C^\infty$-schemes, the resulting de Rham spaces are given as quotients by actions of germs of diagonals, instead of the formal neighbourhoods of the diagonal…

We prove that every slim double Lie groupoid with proper core action is completely determined by a factorization of a certain canonically defined "diagonal" Lie groupoid.

We propose a method of constructing completely integrable systems based on reduction of bihamiltonian structures. More precisely, we give an easily checkable necessary and sufficient conditions for the micro-kroneckerity of the reduction (performed with respect to a special type action of a Lie group) of micro-Jordan b…

We consider quotients of spheres by linear actions of real tori. To each quotient we associate a matroid built out of a diagonalization of the torus action. We find the integral homology groups of the resulting quotient spaces in terms of the Tutte polynomial of the matroid. We also find the homotopy type and homology …

We explore transformation groups of manifolds of the form $M\times S^n$, where $M$ is an asymmetric manifold, i.e. a manifold which does not admit any non-trivial action of a finite group. In particular, we prove that for $n=2$ there exists an infinite family of distinct non-diagonal effective circle actions on such pr…

Noise in linear networks minimizes sharpness and leads to shrinkage-thresholding.

We show the non-positivity of the Einstein-Hilbert action for conformal flat Riemannian metrics. The action vanishes only when the metric is constant flat. This recovers an earlier result of Fathizadeh-Khalkhali in the setting of spectral triples on noncommutative four-torus. Furthermore, computations of the gradient f…

We study some dynamical properties of the canonical Aut(F_n)-action on the space R_n(G) of redundant representations of the free group F_n in G, where G is the group of rational points of a simple algebraic group over a local field. We show that this action is always minimal and ergodic, confirming a conjecture of A. L…

Cohomogeneity-one actions on symmetric spaces of mixed type

For simple and simply-connected complex algebraic group G, we conjecture the existence of a functor eta_G from the category of 2-bordisms to the category of holomorphic symplectic varieties with Hamiltonian action, such that gluing of boundaries corresponds to the holomorphic symplectic quotient with respect to the dia…

Study of a $G_2$ cone quotient with $U(1)$ action.

The paper studies groups with specific actions on hyperbolic spaces and finds that subgroups are either amenable or contain a free group.

Study on Einstein metrics on complex projective spaces with specific group actions.

Researchers establish a connection between knot homology and Lie algebra actions.

We extend the techniques of [CH] to build an inductive procedure for studying actions in the boundary of the Culler-Vogtmann Outer Space, the main novelty being an adaptation of he classical Rauzy-Veech induction for studying actions of surface type. As an application, we prove that a tree in the boundary of Outer spac…

Let G be the Heisenberg group of real lower triangular 3x3 matrices with unit diagonal. A locally free smooth action of G on a manifold M^4 is given by linearly independent vector fields X_1, X_2, X_3 such that X_3 = [X_1,X_2] and [X_1,X_3] = [X_2, X_3] = 0. The C^1 topology for vector fields induces a topology in the …

The paper proves no exotic actions of diffeomorphism groups on 1-manifolds.

Let $J$ be a semisimple Lie group with all simple factors of real rank at least two. Let $Γ<J$ be a lattice. We prove a very general local rigidity result about actions of $J$ or $Γ$. This shows that almost all so-called "standard actions" are locally rigid. As a special case, we see that any action of $Γ$ by toral aut…

Let (M,g) be a Riemannian manifold with an isometric action of the Lie group G. Let g_G be a left invariant metric on G. Consider the diagonal G action on the product $M \times G$ with the metric g+g_G. In this paper we calculate the formula for the metric h on the quotient space $(M \times G) / G$; the map from g to h…

We study the family of holomorphic maps from the polydisk to the disk which restrict to the identity on the diagonal. In particular, we analyze the asymptotics of the orbit of such a map under the conjugation action of a unipotent subgroup of $\text{PSL}_2(\mathbb{R})$. We discuss an application our results to the stud…

Researchers classify curvature homogeneous metrics on 4D manifolds.

PSI-LinUCB improves scalability for large recommender systems.

This paper solves matrix blind joint block diagonalization with noise.

Diagonalizes metrics of 3D Lorentzian manifolds.

Study projective derivative cocycles for circle diffeomorphisms.

The paper constructs new structures for manifolds using connections and combinations.

We construct an action of the braid group B_N on the twisted quantized enveloping algebra U'_q(o_N) where the elements of B_N act as automorphisms. In the classical limit q -> 1 we recover the action of B_N on the polynomial functions on the space of upper triangular matrices with ones on the diagonal. The action prese…

Parallelizes DEC on curved meshes using group actions.

Study Ricci vector fields on 2D space with diagonal metrics.

Develops a novel stochastic algorithm for diagonal estimation of large matrices.

Octagon map accelerates diagonal changes algorithm.

Study finds symmetries in a special 3D space with a diagonal metric.

New diagonal knots found with non-torus structure.

Proves existence of equivariant maps avoiding diagonal in n-space.

Chevalley theorems extended to isotropic functions on matrix spaces.

We use mathematical induction to prove that the horizontal composition in the class of coherently diagonal complexes is indeed a binary operation. That is to say, the embedding of two coherently diagonal complexes in an alternating planar diagram produces a coherently diagonal complex.

Most known four-dimensional cohomogeneity-one Einstein metrics are diagonal in the basis defined by the left-invariant one-forms, though some essentially non-diagonal ones are known. We consider the problem of explicitly seeking non-diagonal Einstein metrics, and we find solutions which in some cases exhaust the possib…

The crossing matrix of a braid on $N$ strands is the $N\times N$ integer matrix with zero diagonal whose $i,j$ entry is the algebraic number (positive minus negative) of crossings by strand $i$ over strand $j$ . When restricted to the subgroup of pure braids, this defines a homomorphism onto the additive subgroup of $N…

New method improves Pham's algorithm for joint diagonalization.

Equal diagonal energies proven on Liouville surfaces.

By the work of Li, a compact co-Kähler manifold $M$ is a mapping torus $K_\varphi$, where $K$ is a Kähler manifold and $\varphi$ is a Hermitian isometry. We show here that there is always a finite cyclic cover $\bar M$ of the form $\bar M \cong K \times S^1$, where $\cong$ is equivariant diffeomorphism with respect to …

Diagonal linear networks converge to lasso regularization path during training.

We show that a basis of a semisimple Lie algebra of compact type, for which any diagonal left-invariant metric has a diagonal Ricci tensor, is characterized by the Lie algebraic condition of being "nice". Namely, the bracket of any two basis elements is a multiple of another basis element. This extends the work of Laur…

New diagonal move simplifies knots and links efficiently.