arXiv research

Study of conformal limits in Nakajima quiver varieties.

Study of conformal limits for special opers in Lie groups.

We show that the conformal Penrose limit is an ordinary plane wave limit in a higher dimensional framework which resolves the spacetime singularity. The higher dimensional framework is provided by Ricci-flat manifolds which are of the form M_D = M_d x B, where M_d is an Einstein spacetime that has a negative cosmologic…

This research connects Higgs bundles to projective structures via conformal limits.

The paper studies Lagrangian structures in Higgs bundle moduli spaces and their conformal limits.

We consider a geometrically finite discrete group of conformal transformations of the sphere. Further we consider distributions which are supported on the limit set and are invariant with conformal weight. We estimate their regularity in terms of the conformal weight, the Hausdorff dimension of the limit set, and the m…

In this note we prove that a generic Riemannian manifold of dimension $\geq 3$ does not admit any nontrivial local conformal diffeomorphisms. This is a conformal analog of a result of Sunada concerning local isometries, and makes precise the principle that generic manifolds in high dimensions do not have conformal symm…

Research proves the semi-classical limit of Liouville conformal field theory, describing deterministic geometry from random fluctuations.

Study on Kähler-Ricci flow and conformal submersion singularity formation.

Paper generalizes Higgs bundle limits to parabolic setting.

Paper derives sub-Riemannian versions of Kastler-Kalau-Walze and Dabrowski-Sitarz-Zalecki theorems for twisted BCV spaces.

Foundation models improve time series prediction reliability, especially with limited data.

The paper examines the blow-up of Ricci curvatures in conformal metrics.

This paper proves compactness of conformal Chern-minimal surfaces in Hermitian surfaces.

The paper examines compactness of scalar curvature sequences on conformal manifolds.

This paper describes the connection between scattering matrices on conformally compact asymptotically Einstein manifolds and conformally invariant objects on their boundaries at infinity. The conformally invariant powers of the Laplacian arise as residues of the scattering matrix and Branson's Q-curvature in even dimen…

Derives conformal parameters of curves using inscribed circular polygons.

In this paper we investigate the Hausdorff dimension of limit sets of Anosov representations. In this context we revisit and extend the framework of hyperconvex representations and establish a convergence property for them, analogue to a differentiability property. As an application of this convergence, we prove that t…

Proposes PFWCP for multi-agent tasks with privacy and validity guarantees.

EPICSCORE improves conformal scores by explicitly accounting for epistemic uncertainty.

We consider bosonic supersymmetric backgrounds of ten-dimensional conformal supergravity. Up to local conformal isometry, we classify the maximally supersymmetric backgrounds, determine their conformal symmetry superalgebras and show how they arise as near-horizon geometries of certain half-BPS backgrounds or as a plan…

The paper proves stability of critical points for conformally invariant Lagrangians.

We show that any grafting ray in Teichmüller space is (strongly) asymptotic to some Teichmüller geodesic ray. As an intermediate step we introduce surfaces that arise as limits of these degenerating Riemann surfaces. Given a grafting ray, the proof involves a Teichmüller ray with a conformally equivalent limit, and bui…

Anosov groups' measures on limit sets are uniquely determined by their dimension.

We review the relation between homotopy algebras of conformal field theory and geometric structures arising in sigma models. In particular we formulate conformal invariance conditions, which in the quasi-classical limit are Einstein equations with extra fields, as generalized Maurer-Cartan equations.

Study of Lorentzian manifolds with specific transformations.

We extend the concept of renormalized volume for geometrically finite hyperbolic $3$-manifolds, and show that is continuous for geometrically convergent sequences of hyperbolic structures over an acylindrical 3-manifold $M$ with geometrically finite limit. This allows us to show that the renormalized volume attains its…

Improved conformalized quantile regression for adaptive prediction intervals.

We study sequences of conformal deformations of a smooth closed Riemannian manifold of dimension $n$, assuming uniform volume bounds and $L^{n/2}$ bounds on their scalar curvatures. Singularities may appear in the limit. Nevertheless, we show that under such bounds the underlying metric spaces are pre-compact in the Gr…

We consider harmonic diffeomorphisms to a fixed hyperbolic target $Y$, from a family of domain Riemann surfaces degenerating along a Teichmüller ray. We use the work of Minsky to show that there is a limiting harmonic map from the conformal limit of the Teichmüller ray, to a crowned hyperbolic surface. The target surfa…

In this paper, we investigate the behavior of the normalized Ricci flow on asymptotically hyperbolic manifolds. We show that the normalized Ricci flow exists globally and converges to an Einstein metric when starting from a non-degenerate and sufficiently Ricci pinched metric. More importantly we use maximum principles…

Using the reformulation in divergence form of the Euler-Lagrange equation for the Willmore functional as it was developed in "Analysis of the Willmore Functional" by T. Riviere (Invent. Math. 174), we study the limit of a local Palais-Smale sequence of weak Willmore immersions with locally square-integrable second fund…

This article studies the smoothness of conformal mappings between two Riemannian manifolds whose metric tensors have limited regularity. We show that any bi-Lipschitz conformal mapping or $1$-quasiregular mapping between two manifolds with $C^r$ metric tensors ($r > 1$) is a $C^{r+1}$ conformal (local) diffeomorphism. …

The paper classifies and proves properties of ALE manifolds and orbifolds.

New method converts p-values to e-values for more efficient CP and aggregation.

New approach for adaptive conformal inference using Blackwell's theory.

In the paper arXiv:1411.4887 [math.AP] it is shown that the set of Riemannian metrics which do not admit global limiting Carleman weights is open and dense, by studying the conformally invariant Weyl and Cotton tensors. In the paper arXiv:1011.2507 [math.DG] it is shown that the set of Riemannian metrics which do not a…

New method improves conditional coverage of conformal prediction.

A $W^{1,p}$-metric on an $n$-dimensional closed Riemannian manifold naturally induces a distance function, provided $p$ is sufficiently close to $n$. If a sequence of metrics $g_k$ converges in $W^{1,p}$ to a limit metric $g$, then the corresponding distance functions $d_{g_k}$ subconverge to a limit distance function …

New methods improve anomaly detection with reduced false positives.

The paper analyzes how conformal prediction works with contaminated reference data.

In this paper, we focus on the geometry of compact conformally flat manifolds $(M^n,g)$ with positive scalar curvature. Schoen-Yau proved that its universal cover $(\widetilde{M^n},\tilde{g})$ is conformally embedded in $\mathbb{S}^n$ such that $M^n$ is a Kleinian manifold. Moreover, the limit set of the Kleinian group…

Anosov representations are linked to specific spacetimes.

A new conformal prediction framework for graph-valued outputs using Z-Gromov-Wasserstein distances.

Develops an efficient approximation for full conformal prediction regions.

Proposes a method to improve class-conditional conformal prediction for many classes.

Kaehler-Einstein metrics on orbifolds derived from Einstein sequences.

Exact distribution of split conformal prediction coverage found.