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Congruences between modular forms
We survey the connections between modular forms and representations of Galois groups that are predicted by the Langlands programme. We focus in...
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Controlling the BMO Semi-Norm of the Unit Normal
Earlier we have estimated a certain brand of singular integral operators in terms of the geometry of the underlying “surface” in terms of the BMO...
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Reducible M-curves for Le-networks in the totally-nonnegative Grassmannian and KP-II multiline solitons
We associate real and regular algebraic–geometric data to each multi-line soliton solution of Kadomtsev–Petviashvili II (KP) equation. These...
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An Algebraic Geometric Foundation for a Classification of Second-Order Superintegrable Systems in Arbitrary Dimension
Second-order (maximally) superintegrable systems in dimensions two and three are essentially classified. With increasing dimension, however, the...
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Learning port-Hamiltonian Systems—Algorithms
AbstractIn this article we study the possibilities of recovering the structure of port-Hamiltonian systems starting from “unlabelled” ordinary...
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An introduction to the algebraic geometry of the Putman–Wieland conjecture
We give algebraic and geometric perspectives on our prior results toward the Putman–Wieland conjecture. This leads to interesting new constructions...
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Contact foliations and generalised Weinstein conjectures
We consider contact foliations: objects which generalise to higher dimensions the flow of the Reeb vector field on contact manifolds. We list several...
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A Non-archimedean Variant of Littlewood–Paley Theory for Curves
We prove a variant of a square function estimate for the extension operator associated to the moment curve in non-archimedean local fields. The...
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A note on Flenner’s extension theorem
We show that any p -form on the smooth locus of a normal complex space extends to a resolution of singularities, possibly with logarithmic poles, as...
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Model Verification & Validation
With the development of computer technology, various simulation models have been applied to take the place of physical experiments to save the time...
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Kac-Rice formula for transverse intersections
We prove a generalized Kac-Rice formula that, in a well defined regular setting, computes the expected cardinality of the preimage of a submanifold...
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Lightlike manifolds and Cartan geometries
Lightlike Cartan geometries are introduced as Cartan geometries modelled on the future lightlike cone in Lorentz-Minkowski spacetime. Then, we...
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Random Processes on Non-Archimedean Spaces
The Lévy stochastic processes on p-adic numbers have been constructed by different methods. We present the construction by Albeverio and Karwowski...
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Unboundedness of Tate–Shafarevich groups in fixed cyclic extensions
In this paper we prove two unboundedness results about the Tate–Shafarevich groups of abelian varieties in a fixed nontrivial cyclic extension L / K of...
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Basic Properties of Drinfeld Modules
A Drinfeld module over a field K, our principal object of study in this book, is a field K equipped with an action of the ring of polynomials...
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Optimal Synthesis in a Time-Optimal Problem for the Double Integrator System with a Linear State Constraint
We consider a time-optimal problem for the classical “double integrator” system under an arbitrary linear state constraint. Using the maximum...
