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
|
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...
The First Syzygy of Hibi Rings Associated with Planar distributive
lattices
April 26, 2017
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Mathematics
Commutative Algebra
Let L be a finite distributive lattice and S=K[xα:α∈L] be a polynomial ring over a field K and $I=\langle x_\alpha
x_\beta - x_{\alpha\vee \beta} x_{\alpha\wedge\beta} : \alpha \nsim
\beta,\alpha,\b...
Vaidya Spacetime in the Diagonal Coordinates
April 23, 2017
| |
Physics
General Relativity and Quantum Cosmology
We have analyzed the transformation from initial coordinates (v,r) of the
Vaidya metric with light coordinate v to the most physical diagonal
coordinates (t,r). An exact solution has been obtained for the corresponding
metric tensor i...
The lost proof of Fermat's last theorem
April 20, 2017
Mathematics
General Mathematics
This work contains two papers: the first published in 2022 and entitled "On
the nature of some Euler's double equations equivalent to Fermat's last
theorem" provides a marvellous proof through the so-called discordant forms of
appropriate E...
To compute orientations of Morse flow trees in Legendrian contact
homology
April 17, 2017
Mathematics
Symplectic Geometry
Let Λ be a closed, connected Legendrian submanifold of the 1-jet
space of a smooth n-dimensional manifold. Associated to Λ there is a
Legendrian invariant called Legendrian contact homology, which is defined by
counting ri...
Algorithmic releases on the spanning trees of suitable graphs
April 17, 2017
| |
Mathematics
Combinatorics
In this paper algebraic and combinatorial properties and a computation of the
number of the spanning trees are developed for certain graphs. To this purpose,
an original method, independent of the spectrum of the Laplacian matrix
associated...