arXiv research

The abstract discusses how sub-Riemannian manifolds can have branching geodesics.

Paper finds surface groups can deform in reductive symmetric spaces.

We consider the action of Anosov subgroups of a semi-simple Lie group on the associated flag manifolds. A systematic approach to construct cocompact domains of discontinuity for this action was given by Kapovich, Leeb and Porti in arXiv:1306.3837. For $Δ$-Anosov representations, we prove that every cocompact domain of …

The paper studies proper discontinuity of actions on Weyl chamber flow spaces.

The paper classifies fiber structures of discontinuity domains for Anosov representations.

Every lattice H in a connected semi-simple Lie group G acts properly discontinuously by isometries on the contractible manifold G/K (K a maximal compact subgroup of G). We prove that if H acts on a contractible manifold W and if either 1) the action is properly discontinuous, or 2) W is equipped with a complete Riemann…

Study nearly geodesic immersions in symmetric spaces, leading to explicit fibrations.

Margulis space-times with parabolic holonomy elements are stable under sufficiently small deformations.

Study consumption-investment problem in markets with rank-based returns.

The Tits alternative applies to groups acting on specific CAT(0) spaces.

New findings on stability and Q-conditions for free group actions in hyperbolic spaces.

We study the topology and geometry of compact complex manifolds associated to Anosov representations of surface groups and other hyperbolic groups in a complex semisimple Lie group $G$. These manifolds are obtained as quotients of the domains of discontinuity in generalized flag varieties $G/P$ constructed by Kapovich-…

This survey is based on a series of lectures that we gave at MSRI in Spring 2015 and on a series of papers, mostly written jointly with Joan Porti. Our goal here is to: 1. Describe a class of discrete subgroups $Γ<G$ of higher rank semisimple Lie groups, which exhibit some "rank 1 behavior". 2. Give different character…

Proves nonemptyness of domains for specific group actions.

Study of SU(2,1) character varieties on one-holed torus.

The paper defines infinite Schottky groups and their applications to infinite type surfaces.

We consider the deformation of a discontinuous group acting on the Euclidean space by affine transformations. A distinguished feature here is that even a `small' deformation of a discrete subgroup may destroy proper discontinuity of its action. In order to understand the local structure of the deformation space of disc…

Cut-DeepONet handles discontinuities and sharp transitions in neural operators.

Study proves existence of equilibrium in incomplete economies with discontinuous volatility.

New domains of discontinuity found for Anosov representations.

As early as 1972, Penrose - in a purely formal way - introduced a "discontinuous coordinate transformation", which relates a continuous representation of the metric of impulsive pp-waves to a discontinuous one. On the basis of the invertibility concept for generalized functions developed recently by the first author, w…

Recovering a large matrix from limited measurements is a challenging task arising in many real applications, such as image inpainting, compressive sensing and medical imaging, and this kind of problems are mostly formulated as low-rank matrix approximation problems. Due to the rank operator being non-convex and discont…

Study the discontinuity of functions not embeddable in Euclidean space.

Paper tackles low-rank matrix recovery with column $\ell_{2,0}$-norm regularization.

Study new symmetries in non-symmetric spaces and discontinuous groups.

For the action of the outer automorphism group of the rank two free group on the corresponding variety of PSL(2,C) characters, two domains of discontinuity have been known to exist that are strictly larger than the set of Schottky characters. One is introduced by Bowditch in 1998 (followed by Tan, Wong and Zhang in 200…

We study the Weyl chamber length boundary both of the Hitchin and of the maximal character varieties and determine therein an open set of discontinuity for the action of the mapping class group. This result is obtained as consequence of a canonical decomposition of a geodesic current on a surface of finite type arising…

A new method for unsupervised disentanglement using axis-aligned cliffs.

New method estimates active subspaces for jump-discontinuous functions.

This article gives an up-to-date account of the theory of discrete group actions on non-Riemannian homogeneous spaces. As an introduction of the motifs of this article, we begin by reviewing the current knowledge of possible global forms of pseudo-Riemannian manifolds with constant curvatures, and discuss what kind of …

The first known example of a complete Riemannian manifold whose isoperimetric profile is discontinuous is given.

Paper analyzes error in stochastic approximation for discontinuous functions.

Bayesian emulator tackles models with discontinuities efficiently.

We characterise completely when limit sets, as parametrised by Cannon-Thurston maps, move discontinuously for a sequence of algebraically convergent quasi-Fuchsian groups.

We show that there is a complete connected 2-dimensional Riemannian manifold with discontinuous isoperimetric profile, answering a question of Nardulli and Pansu.

Volunteer labor can temporarily yield lower benefits to charities than its costs. In such instances, organizations may wish to defer volunteer donations to a later date. Exploiting a discontinuity in blood donations' eligibility criteria, we show that deferring donors reduces their future volunteerism. In our setting, …

We develop a general term structure framework taking stochastic discontinuities explicitly into account. Stochastic discontinuities are a key feature in interest rate markets, as for example the jumps of the term structures in correspondence to monetary policy meetings of the ECB show. We provide a general analysis of …

Study proves rigid spectral properties of planets with metric discontinuities.

We study the properly discontinuous and isometric actions on the unit sphere of infinite dimensional Hilbert spaces and we get some new examples of Hilbert manifold with costant positive sectional curvature. We prove some necessary conditions for a group to act isometrically and properly discontinuously and in the case…

In this paper, we present a method for the accurate estimation of the derivative (aka.~sensitivity) of expectations of functions involving an indicator function by combining a stochastic algorithmic differentiation and a regression. The method is an improvement of the approach presented in [Risk Magazine April 2018]. T…

This work models overnight rates with jumps and discontinuities, extending classical short-rate models.

Geometric methods for surface group representations in higher rank SL(2m+1,R).

Quasi-experimental research designs, such as regression discontinuity and interrupted time series, allow for causal inference in the absence of a randomized controlled trial, at the cost of additional assumptions. In this paper, we provide a framework for discontinuity-based designs using Bayesian model comparison and …

The study explores deformations of discrete subgroups in non-compact homogeneous spaces.

Paper analyzes SGHMC for non-convex optimization with discontinuous gradients.

This paper tackles discontinuous neural networks for better approximation of piecewise continuous functions.

In the present paper, we prove that no infinite group acts isometrically, effectively, and properly discontinuously on a certain class of Lorentzian manifolds that are not necessarily homogeneous.

Framework uses deep learning and statistical models to solve PDEs with discontinuous coefficients.