arXiv research

Study shows observability from a measurable set for Gevrey functions.

Researchers extend asymptotic analysis to Bergman projections with Gevrey weights.

New bounds found for nodal sets on special manifolds.

Sharp threshold found for metric uniqueness in Riemannian Calderón-type problems.

Our aim is to prove that two formal power series of importance to quantum topology are Gevrey. These series are the Kashaev invariant of a knot (reformulated by Huynh and the second author) and the Gromov norm of the LMO of an integral homology 3-sphere. It follows that the power series associated to a simple Lie algeb…

We give upper bounds for the Bergman kernels associated to tensor powers of a smooth positive line bundle in terms of the rate of growth of the Taylor coefficients of the Kähler potential. As applications, we obtain improved off-diagonal rate of decay for the classes of analytic, quasi-analytic, and more generally Gevr…

We study the asymptotic properties of the Bergman kernels associated to tensor powers of a positive line bundle on a compact Kähler manifold. We show that if the Kähler potential is in Gevrey class $G^a$ for some $a>1$, then the Bergman kernel accepts a complete asymptotic expansion in a neighborhood of the diagonal of…

We study the problem of coupling Einstein's equations to a relativistic and physically well-motivated version of the Navier-Stokes equations. Under a natural evolution condition for the vorticity, we prove existence and uniqueness in a suitable Gevrey class if the fluid is incompressible, where this condition is given …

Using a simple and well-motivated modification of the stress-energy tensor for a viscous fluid proposed by Lichnerowicz, we prove that Einstein's equations coupled to a relativistic version of the Navier-Stokes equations are well-posed in a suitable Gevrey class if the fluid is incompressible and irrotational. These la…

We are interested in global properties of systems of left-invariant differential operators on compact Lie groups: regularity properties, properties on the closedness of the range and finite dimensionality of their cohomology spaces, when acting on various function spaces e.g. smooth, analytic and Gevrey. Extending the …

Analytic networks with bounded coefficients can't outperform polynomial approximations.

Heat kernel resurgent structure from Picard-Lefschetz theory

The free energy of a closed 3-manifold is a 2-parameter formal power series which encodes the perturbative Chern-Simons invariant (also known as the LMO invariant) of a closed 3-manifold with gauge group U(N) for arbitrary $N$. We prove that the free energy of an arbitrary closed 3-manifold is uniformly Gevrey-1. As a …

Let $N$ be a smooth $(n+l)$-dimensional Riemannian manifold. We show that if $V$ is an area-stationary union of three or more $C^{1,μ}$ $n$-dimensional submanifolds-with-boundary $M_k \subset N$ with a common boundary $Γ$, then $Γ$ is smooth and each $M_k$ is smooth up to $Γ$ (real-analytic in the case $N$ is real-anal…

The main goal of the paper is to address the issue of the existence of Kempf's distortion function and the Tian-Yau-Zelditch (TYZ) asymptotic expansion for the Kepler manifold - an important example of non compact manfold. Motivated by the recent results for compact manifolds we construct Kempf's distortion function an…

Classifies manifolds with dense conjugacy classes in their mapping class groups.

This paper tackles worst-class error rate in classification tasks.

New method learns multi-class from single-class data with confidences.

Paper constructs a cohomology class related to McDuff's secondary class, proving it transgresses to the Euler class of foliated sphere bundles.

One of the earliest conjectures in computational learning theory-the Sample Compression conjecture-asserts that concept classes (equivalently set systems) admit compression schemes of size linear in their VC dimension. To-date this statement is known to be true for maximum classes---those that possess maximum cardinali…

The paper proves inequalities for orbifold second Chern classes in Fujiki's class.

Study on characteristic classes for foliation deformations.

The hyperelliptic mapping class group has been studied in various contexts within topology and algebraic geometry. What makes this study tractable is that there is a surjective map from the hyperelliptic mapping class group to a mapping class group of a punctured sphere. The more general family of superelliptic mapping…

CILF learns adaptive embeddings for class-incremental learning with novel class detection and model update.

In this paper we give explicit formulas of differential characteristic classes of principal $G$-bundles with connections and prove their expected properties. In particular, we obtain explicit formulas for differential Chern classes, differential Pontryagin classes and differential Euler class. Furthermore, we show that…

A new method identifies class-specific covariates in multi-class prediction tasks.

Study of conjugacy classes in infinite-type surfaces' mapping class groups.

The paper classifies dense conjugacy classes in mapping class groups of locally finite graphs.

We give a complete description of conjugacy classes of finite subgroups of the mapping class group of the sphere with r marked points. As a corollary we obtain a description of conjugacy classes of maximal finite subgroups of the hyperelliptic mapping class group. In particular, we prove that for a fixed genus g there …

We present a simple generative framework for learning to predict previously unseen classes, based on estimating class-attribute-gated class-conditional distributions. We model each class-conditional distribution as an exponential family distribution and the parameters of the distribution of each seen/unseen class are d…

SWRLDA improves LDA for multi-class classification with edge classes.

For a local Lie group M we define odd order cohomology classes. The first class is an obstruction to globalizability of the local Lie group. The third class coincides with Godbillon-Vey class in a particular case. These classes are secondary as they emerge when curvature vanishes.

This paper proposes a novel generic one-class feature learning method based on intra-class splitting. In one-class classification, feature learning is challenging, because only samples of one class are available during training. Hence, state-of-the-art methods require reference multi-class datasets to pretrain feature …

This research sets limits on how complex multi-class learning problems can be.

Infinitely many unique ways to generate a surface's mapping class group.

Characteristic classes of oriented vector bundles can be identified with cohomology classes of the disjoint union of classifying spaces BSO_n of special orthogonal groups SO_n with n=0,1,... A characteristic class is stable if it extends to a cohomology class of a homotopy colimit BSO of classifying spaces BSO_n. Simil…

Study rigid classes on hyperkahler manifolds, showing general ones are rigid.

Defines kappa classes on KSBA spaces, generalizing classes on curves.

By analyzing how the Borel regulator classes vanish on various groups related to $\mathrm{GL}(n,\mathrm{Z})$, we define three series of secondary characteristic classes for subgroups of automorphism groups of free groups. The first case is the $\mathrm{IA}$-automorphism groups and we show that our classes coincide with…

DRAGON improves learning for rare classes in unbalanced datasets using class descriptions.

Gen1S learns novel classes with 1-shot data using residual space and generative models.

We study types of mapping classes which arise as a product of a given mapping class and powers of certain pure mapping classes. We derive an explicit constant depending only on a surface such that almost all above pure mapping classes give rise to pseudo-Anosov type whenever their powers are larger than the constant. F…

New classes defined for manifold pseudogroups, linking to cohomology and bundle structures.

Paper tackles many-class few-shot learning with class hierarchy, improving accuracy.

Solutions to Strominger system found for square of Kähler class.

Continuous epimorphisms between certain mapping class groups are induced by homeomorphisms.

We construct closed symplectic manifolds for which spherical classes generate arbitrarily large subspaces in 2-homology, such that the first Chern class and cohomology class of the symplectic form both vanish on all spherical classes. We construct both Kaehler and non-Kaehler examples, and show independence of the cond…

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