On nonlinear instability of Prandtl's boundary layers: the case of
Rayleigh's stable shear flows
June 5, 2017
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Mathematics
Physics
Mathematical Physics
Mathematical Physics
Analysis of PDEs
In 1904, Prandtl introduced his famous boundary layer in order to describe
the behavior of solutions of Navier Stokes equations near a boundary as the
viscosity goes to 0. His Ansatz has later been justified for analytic data by
R.E. Cafl...
Mapping properties of the Hilbert and Fubini--Study maps in K\"ahler
geometry
May 31, 2017
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Mathematics
Differential Geometry
Differential Geometry
Suppose that we have a compact K\"ahler manifold X with a very ample line
bundle L. We prove that any positive definite hermitian form on the
space H0(X,L) of holomorphic sections can be written as an
L2-inner...
Birkhoff's Theorem for Quasi-Metric Gravity
May 31, 2017
Physics
General Relativity and Quantum Cosmology
Working within the quasi-metric framework (QMF), it is examined if the
gravitational field exterior to an isolated, spherically symmetric body is
necessarily metrically static, or equivalently, whether or not Birkhoff's
theorem holds for qu...
Counterfactual Multi-Agent Policy Gradients
May 24, 2017
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Computer Science
Artificial Intelligence
Multiagent Systems
Artificial Intelligence
Multiagent Systems
Cooperative multi-agent systems can be naturally used to model many real
world problems, such as network packet routing and the coordination of
autonomous vehicles. There is a great need for new reinforcement learning
methods that can effic...
Real models for the framed little n-disks operads
May 23, 2017
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Mathematics
Quantum Algebra
Algebraic Topology
Quantum Algebra
Algebraic Topology
We study the action of the orthogonal group on the little n-disks operads.
As an application we provide small models (over the reals) for the framed
little n-disks operads. It follows in particular that the framed little
n-disks opera...
Corrigendum to "Model Theory of Fields with Virtually Free Group
Actions"
May 18, 2017
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Mathematics
Logic
There is an irreparable error in the proof of Theorem 3.26 in our "Model
Theory of Fields with Virtually Free Group Actions" paper and we withdraw the
claim of having proved that theorem. In fact, that theorem is false in a very
strong sens...
Subalgebras of the rank two semisimple Lie algebras
May 9, 2017
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Mathematics
Rings and Algebras
In this expository article, we describe the classification of the subalgebras
of the rank 2 semisimple Lie algebras. Their semisimple subalgebras are
well-known, and in a recent series of papers, we completed the classification
of the subal...
Discretisation of regularity structures
May 8, 2017
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Mathematics
Probability
Analysis of PDEs
We introduce a general framework allowing to apply the theory of regularity
structures to discretisations of stochastic PDEs. The approach pursued in this
article is that we do not focus on any one specific discretisation procedure.
Instead...
Existence of Infinite Product Measures
May 3, 2017
Mathematics
Functional Analysis
A construction of product measures is given for an arbitrary sequence of
measure spaces via outer measure techniques without imposing any condition on
the underlying measure spaces. This approach concludes finally the problem of
the existen...
Modulo quantifiers over functional vocabularies extending addition
April 30, 2017
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Computer Science
Logic in Computer Science
Logic in Computer Science
We show that first order logic (FO) and first order logic extended with
modulo counting quantifiers (FOMOD) over purely functional vocabularies which
extend addition, satisfy the Crane beach property (CBP) if the logic satisfies
a normal fo...