arXiv research

Optimizes quantum channel mapping between Hilbert spaces.

We give a 3-page description of the Gassner invariant / representation of braids / pure braids, along with a description and a proof of its unitarity property.

New method preserves unitarity for Schrödinger equation learning, reducing errors and improving time generalization.

Study non-semisimple TQFT for Burau representation density and unitarity.

New method shows unitarity in quantization for toric manifolds.

We prove the existence of a new class of constant mean curvature cylinders with an arbitrary number of umbilics by unitarizing the monodromy of Hill's equation.

This is the first in a series of papers devoted to an analogue of the metaplectic representation, namely, the minimal unitary representation of an indefinite orthogonal group; this representation corresponds to the minimal nilpotent coadjoint orbit in the philosophy of Kirillov-Kostant. We begin by applying methods fro…

We describe the unitary globalization of cohomologically induced modules $A_{\fq}(λ)$. The purpose of the paper is to give a geometric realization of the unitarizable modules. Our results do not constitute a proof of unitarity.

Paper connects algebraic and analytic methods for braid group representations.

A natural one-parameter family of Kähler quantizations of the cotangent bundle $T^*K$ of a compact Lie group $K$, taking into account the half-form correction, was studied in \cite{FMMN}. In the present paper, it is shown that the associated Blattner-Kostant-Sternberg (BKS) pairing map is unitary and coincides with the…

We provide a geometric construction of the unitary structure which is projectively preserved by the Hitchin connection. We analyze the asymptotic behavior of it and we establish that it is uniformly in the level equivalent to the Hermitian structure induced by the L2 inner product on smooth sections.

We decompose the de Rham Laplacian on Sasaki-Einstein manifolds as a sum over mostly positive definite terms. An immediate consequence are lower bounds on its spectrum. These bounds constitute a supergravity equivalent of the unitarity bounds in dual superconformal field theories. The proof uses a generalization of Kah…

We present a theorem on the unitarizability of loop group valued monodromy representations and apply this to show the existence of new families of constant mean curvature surfaces homeomorphic to a thrice-punctured sphere in the simply-connected 3-dimensional space forms $\R^3$, $\bbS^3 $ and $\bbH^3$. Additionally, we…

We use some Lie group theory and Budney's unitarization of the Lawrence-Krammer representation, to prove that for generic parameters of definite form the image of the representation (also on certain types of subgroups) is dense in the unitary group. This implies that, except possibly for closures of full-twist braids, …

We extend the coherent state transform (CST) of Hall to the context of the moduli spaces of semistable holomorphic vector bundles with fixed determinant over elliptic curves. We show that by applying the CST to appropriate distributions, we obtain the space of level k, rank n and genus one non-abelian theta functions w…

We describe two simple obstructions to the existence of Ricci-flat Kahler cone metrics on isolated Gorenstein singularities or, equivalently, to the existence of Sasaki-Einstein metrics on the links of these singularities. In particular, this also leads to new obstructions for Kahler-Einstein metrics on Fano orbifolds.…

We establish various results on the large level limit of projective quantum representations of surface mapping class groups obtained by quantizing moduli spaces of flat SU(n)-bundle. Working with the metaplectic correction, we proved that these projective representations lift to asymptotic representations. We show that…

Factorization of the differential expansion coefficients for HOMFLY-PT polynomials of double braids, discovered in arXiv:1606.06015 in the case of rectangular representations $R$, is extended to the first non-rectangular representations $R=[2,1]$ and $R=[3,1]$. This increases chances that such factorization will take p…

RP-GFRFT unifies fractional order and rotation control for graph signals.

Hybrid QML model improves recovery rate prediction accuracy.

This work discovers algebraic structures from data using a differentiable measure.

An differential field $(F;\partial_1,...,\partial_m)$ of characteristic zero, a subgroup $H$ of affine group $GL(n,C)\propto C^n$ with respect to its identical representation in $F^n$ and the following two fields of differential rational functions in $x=(x_1,x_2,...,x_n)$-column vector, $$C< x, \partial >^H=\{f^{\part…

The $L^2$-$\partial\overline\partial$-Lemma is extended to complete Kähler manifolds with a gap in the spectrum.

Sharp Hölder regularity found for complex Frobenius theorem coordinates.

In a recent paper~\cite{DDL10} we studied basic properties of partial immersions and partially free maps, a generalization of free maps introduced first by Gromov in~\cite{Gro70}. In this short note we show how to build partially free maps out of partial immersions and use this fact to prove that the partially free map…

Two-dimensional Riemannian manifolds uniquely determined by boundary data.

Study cohomologies of complex manifolds with symplectic forms and their stability.

Let $M$ be a surface sum of 3-manifolds $M_1$ and $M_2$ along a bounded connected surface $F$ and $\partial_i$ be the component of $\partial M_i$ containing $F$. If $M_i$ has a high distance Heegaard splitting, then any minimal Heegaard splitting of $M$ is the amalgamation of those of $M^1, M^2$ and $M^*$, where $M^i=M…

We present a simple, flexible, and general framework titled Partial Registration Network (PRNet), for partial-to-partial point cloud registration. Inspired by recently-proposed learning-based methods for registration, we use deep networks to tackle non-convexity of the alignment and partial correspondence problems. Whi…

The paper studies maps from pseudo-Hermitian to Kähler manifolds, proving harmonic map properties.

The paper proves Hodge decompositions and partial bar partial lemmas for G2 and Calabi-Yau manifolds.

The paper studies holomorphic Poisson manifolds and their deformations under specific cohomology conditions.

The paper characterizes when the $\partial \overline{\partial}$-lemma holds for twistor spaces.

Let $M$ be a compact hypersurface with boundary $\partial M=\partial D_1 \cup \partial D_2$, $\partial D_1 \subset Π_1$, $\partial D_2 \subset Π_2$, $Π_1$ and $Π_2$ two parallel hyperplanes in $\mathbb{R}^{n+1}$ ($n \geq 2$). Suppose that $M$ is contained in the slab determined by these hyperplanes and that the mean cu…

The paper studies deformations of Calabi-Yau manifolds using Gauduchon metrics.

Paper tackles distribution matching by partially matching distributions, achieving robust results.

We give a simple proof of a result on the $\partial\bar{\partial}$-lemma property under a blow-up transformation by Deligne--Griffiths--Morgan--Sullivan's criterion. Here, we use an explicit blow-up formula for Dolbeault cohomology given in our previous work, which can be induced by a morphism expressed on the level of…

Differential structure on partial isometries over Grassmannian constructed.

Ribbon cobordism forms a partial order in 3-manifolds.

On a compact complex manifold $X$, we prove a Frölicher-type inequality for Bott-Chern cohomology and we show that the equality holds if and only if $X$ satisfies the $\partial\overline{\partial}$-Lemma.

Abstract study of HKT manifolds, proving Hodge theory and formality properties.

On a compact $\partial\bar\partial$-manifold $X$, one has the Hodge decomposition: the de Rham cohomology groups split into subspaces of pure-type classes as $H_{dR}^k (X)=\oplus_{p+q=k}H^{p,\,q}(X)$, where the $H^{p,\,q}(X)$ are canonically isomorphic to the Dolbeault cohomology groups $H_{\bar\partial}^{p,\,q}(X)$. F…

Study on $4$-dimensional almost-Hermitian manifolds, proving $\overline\partial$-harmonic forms invariant under certain metrics.

We consider partial matchings, which are finite graphs consisting of edges and vertices of degree zero or one. We consider transformations between two states of partial matchings. We introduce a method of presenting a transformation between partial matchings. We introduce the notion of the lattice presentation of a par…

It is shown that any smooth strictly convex global solution of $\det(\frac{\partial^{2}u}{\partial ξ_{i}\partial ξ_{j}}) = \exp \left\{-\sum_{i=1}^n d_i \frac{\partial u}{\partial ξ_{i}} - d_0\right\},$ where $d_0$, $d_1$,...,$d_n$ are constants, must be a quadratic polynomial. This extends a well-known theorem of Jö…

New theorems on Hodge numbers and Kähler structures derived from complex differential forms.

3-manifold curvature comparison with rotationally symmetric bodies.

Study shows partial hyperbolicity leads to Anosov dynamics in 3-manifolds.