Related papers: Period Integrals and Tautological Systems
By topological arguments, we prove new results on the existence, non-existence, localization and multiplicity of nontrivial solutions of a class of perturbed nonlinear integral equations. These type of integral equations arise, for example,…
It was recently conjectured that every component of a discrete-time rational dynamical system is a solution to an algebraic difference equation that is linear in its highest-shift term (a quasi-linear equation). We prove that the conjecture…
Topological photonics has emerged as a novel paradigm for the design of electromagnetic systems from microwaves to nanophotonics. Studies to date have largely focused on the demonstration of fundamental concepts, such as non-reciprocity and…
Periods are numbers represented as integrals of rational functions over algebraic domains. A survey of their elementary properties is provided. Examples of periods includes Feynman Integrals from Quantum Physics and Multiple Zeta Values…
Partial symmetries are described by generalized group structures known as symmetric inverse semigroups. We use the algebras arising from these structures to realize supersymmetry in (0+1) dimensions and to build many-body quantum systems on…
We explicitly construct a dynamically incoherent partially hyperbolic endomorphisms of $\mathbb{T}^2$ in the homotopy class of any linear expanding map with integer eigenvalues. These examples exhibit branching of centre curves along…
A novel class of graphs, here named quasiperiodic, are constructed via application of the Horizontal Visibility algorithm to the time series generated along the quasiperiodic route to chaos. We show how the hierarchy of mode-locked regions…
The notion of higher-order topological phases can have interesting generalizations to systems with subsystem symmetries that exhibit fractonic dynamics for charged excitations. In this work, we systematically study the higher-order…
Aperiodic tilings are non-periodic tilings defined by local rules. They are widely used to model quasicrystals, and a central question is to understand which of the non-periodic tilings are actually aperiodic. Among tilings, those by rhombi…
Non-Hermitian systems give rise to distinct topological phenomena, yet their manifestations at temporal interfaces characterized by abrupt changes in system parameters remain largely unex plored. Upon an abrupt alteration of the Hamiltonian…
We compute the periods associated with a special class of hyperplane arrangements. In particular, we exhibit a combinatorial condition on the intersection lattice of a hyperplane arrangement that ensures that its associated periods are…
Developing robust representations of chemical structures that enable models to learn topological inductive biases is challenging. In this manuscript, we present a representation of atomistic systems. We begin by proving that our…
Given an arrangement of subtori of arbitrary codimension in a torus, we compute the cohomology groups of the complement. Then, using the Leray spectral sequence, we describe the multiplicative structure on the graded cohomology. We also…
This survey article concerns inducing schemes in the context of interval maps. We explain how the study of these induced systems allows for the fine description of, not only, the thermodynamic formalism for certain multimodal maps, but also…
Systems with time delay play an important role in modeling of many physical and biological processes. In this paper we describe generic properties of systems with time delay, which are related to the appearance and stability of periodic…
The chapter contains a detailed presentation of the surface integral theory for modelling light diffraction by surface-relief diffraction gratings having a one-dimensional periodicity. Several different approaches are presented, leading…
Understanding how temporal order degrades in quantum systems remains a central issue in nonequilibrium physics. Here we study the melting of discrete time crystals in a periodically driven holographic system, where a distinct (discrete)…
Under relatively mild and natural conditions, we establish an integral period relations for the (real or imaginary) quadratic base change of an elliptic cusp form. This answers a conjecture of Hida regarding the {\it congruence number}…
This article presents an overview of the theory of integrable systems with symmetries, focusing on toric systems, semitoric systems, and their classifications via decorated polygons. We discuss certain one-parameter families of integrable…
Contact geometry allows to describe some thermodynamic and dissipative systems. In this paper we introduce a new geometric structure in order to describe time-dependent contact systems: cocontact manifolds. Within this setting we develop…