arXiv research

Proves a formula for Kontsevich-Witten tau-function using Schur Q-polynomials.

Paper proves BGW tau-function can be represented as Q-polynomials.

Qazaqzeh and Chbili showed that for any quasi-alternating link, the degree of $Q$-polynomial is less than its determinant. We give a refinement of their evaluation.

We classify rooted trees which have strictly unimodal q-polynomials (plucking polynomial). We also give criteria for a trapezoidal shape of a plucking polynomial. We generalize results of Pak and Panova on strict unimodality of q-binomial coefficients. We discuss which polynomials can be realized as plucking polynomial…

New formulas for knot polynomial evaluations from covering spaces.

This is an extended abstract of the talk given at the Oberwolfach Workshop "Algebraic Structures in Low-Dimensional Topology", 25 May -- 31 May 2014. My goal was to describe progress in distributive homology from the previous Oberwolfach Workshop June 3 - June 9, 2012, in particular my work on Yang-Baxter homology; how…

Paper extends Schur's theorem to spherical curves via monotonicity.

Paper proves a new volume comparison theorem for Riemannian manifolds.

The paper defines new types of positivity and proves properties of Schur forms for vector bundles.

In this paper, we study a general almost Schur Lemma on pseudo-Hermitian (2n+1)-manifolds $(M,J,θ)$ for $n\geq2$. When the equality of almost Schur inequality holds, we derive the contact form $θ$ is pseudo-Einstein and the pseudo-Hermitian scalar curvature is constant.

In the paper, we give a Schur-Toponogov theorem in Riemannian geometry, which not only generalizes Schur's and Toponogov's theorem but also indicates their relation. Inspired by its proof, we also supply a new proof of Toponogov's theorem (in the large) in Alexandrov geometry.

New CR almost Schur Lemma estimates curvature on compact manifolds.

Let $G$ be a signed graph. Let $\hat{G}$ be the graph obtained from $G$ by replacing each edge $e$ by a chain or a sheaf. We first establish a relation between the $Q$-polynomial of $\hat{G}$[6] and the $W$-polynomial of $G$ [9]. Two special dual cases are derived from the relation, one of which has been studied in [8]…

We show that the Schur multiplier of $Sp(2g,\mathbb Z/D\mathbb Z)$ is $\mathbb Z/2\mathbb Z$, when $D$ is divisible by 4.

Quantifies Schur's theorem for curves in CAT(k) spaces.

New unoriented versions of Schur and Bogomolov multipliers for finite groups.

Let X=G/P be cominuscule rational homogeneous variety. (Equivalently, X admits the structure of a compact Hermitian symmetric space.) We say a Schubert class [S] is Schur rigid if the only irreducible subvarieties Y of X with homology class [Y] = r [S], for an integer r, are Schubert varieties. Robles and The identifie…

Efficiently computes embeddings for large graphs using coarsening.

Schur theorem proven for weakly Landsberg Finsler metrics.

New basis and Schur-Weyl duality for loop Hecke algebra defined.

New method connects neural networks to diagrammatic algebra.

The paper proves new curvature estimates in quaternionic contact geometry.

Study framizations of algebras using Schur--Weyl duality and tied braids.

In this paper, we prove almost Schur Lemma on closed smooth metric measure spaces, which implies the results of X. Cheng and De Lellis-Topping whenever the weighted function f is constant.

Given any unoriented link diagram, a group of new knot invariants are constructed. Each of them satisfies a generalized 4 term skein relation. The coefficients of each invariant is from a commutative ring. Homomorphisms and representations of such a ring defines new link invariants. In this sense, they produce the well…

Let L be a link in a thickened annulus. We show that its sutured annular Khovanov homology carries an action of the exterior current algebra of the Lie algebra sl_2. When L is an m-framed n-cable of a knot K in the three-sphere, its sutured annular Khovanov homology carries a commuting action of the symmetric group S_n…

Researchers prove a stability result for a 3-sphere inequality, extending previous work.

A new method for efficient portfolio optimization using graph structures.

The Schur's theorem of antiholomorphic type is proved for arbitrary almost Hermitian manifolds, namely: If a connected almost Hermitian manifold of dimension greater or equal to 6 is of pointwise constant antiholomorphic sectional curvature, then this curvature is a global constant.

The paper studies connectivity of Schur-Horn map images in real Grassmannians.

We define a map from second quandle homology to the Schur multiplier and examine its properties. Furthermore, we express the second homology of Alexander quandles in terms of exterior algebras. Additionally, we present a self-contained proof of its structure and provide some computational examples.

Defines odd Khovanov homology via categorification of q-Schur algebra.

New gauge invariants from framed 3-manifolds match Hopf algebra indicators.

Constructs new topological theories in 2D not fitting standard axioms.

In this short note we establish an integral geometric inequality in a smooth metric measure space of the nonnegative Bakry-Émery Ricci curvature. This result can be regarded as a mild generalization of the almost Schur theorem due to De Lellis and Topping (Calc. Var., DOI: 10.1007/s00526-011-0413-z).

Method for conditional sampling with pre-trained normalizing flows.

New algorithm learns ReLU networks efficiently using Schur polynomials.

Schur's lemma states that every Einstein manifold of dimension $n\geq 3$ has constant scalar curvature. Here $(M,g)$ is defined to be Einstein if its traceless Ricci tensor $$\Rico:=\Ric-\frac{R}{n}g$$ is identically zero. In this short note we ask to what extent the scalar curvature is constant if the traceless Ricci …

The paper finds new inequalities for convex polygons.

In our previous paper in \cite{C}, we generalized the almost-Schur lemma of De Lellis and Topping for closed manifolds with nonnegative Rcci curvature to any closed manifolds. In this paper, we generalize the above results to symmetric $(2,0)$-tensors and give the applications including $r$th mean curvatures of closed …

This paper introduces Schur-constant equilibrium distribution models of dimension n for arithmetic non-negative random variables. Such a model is defined through the (several orders) equilibrium distributions of a univariate survival function. First, the bivariate case is considered and analyzed in depth, stressing the…

Spatial statisticians and quantitative investors use the same mathematical object: a Schur complement, damped by one parameter.

The paper proves positivity of characteristic forms for certain vector bundles.

Preprint proves quantum coideal Schur-Weyl duality and generalizes Jones-Wenzl projectors.

Fix a finite group $G$ and a conjugacy invariant subset $C\subseteq G$. Let $Σ$ be an oriented surface, possibly with punctures. We consider the question of when two homomorphisms $π_1(Σ) \to G$ taking punctures into $C$ are equivalent up to an orientation preserving diffeomorphism of $Σ$. We provide an answer to this …

The paper optimizes policies constrained to Schur stabilizing controllers using a Newton-type algorithm.

We describe in this note a new invariant of rooted trees. We argue that the invariant is interesting on it own, and that it has connections to knot theory and homological algebra. However, the real reason that we propose this invariant to readers is that we deal here with an elementary, interesting, new mathematics, an…

Paper improves performance guarantees for Rademacher projections.