ARI, GARI, Zig and Zag: An introduction to Ecalle's theory of multiple
zeta values
July 6, 2015
|
Mathematics
Number Theory
Number Theory
This text has two goals. The first is to give an introduction to Ecalle's
work on mould theory, multiple zeta values and double shuffle theory and relate
this work explicitly to the classical theory of multiple zeta values and double
shuffl...
Autonomic Cloud Computing: Research Perspective
July 6, 2015
Computer Science
Distributed, Parallel, and Cluster Computing
As the cloud infrastructure grows, it becomes more challenging to manage
resources in such a massive, diverse, and distributed setting, despite the fact
that cloud computing provides computational capabilities on-demand. Due to
resource var...
Proof of Union-Closed Sets Conjecture
July 5, 2015
|
Mathematics
Combinatorics
We prove Union-Closed sets conjecture....
Elliptic multiple zeta values, Grothendieck-Teichm\"uller and mould
theory
June 30, 2015
Mathematics
Number Theory
In this article we define an elliptic double shuffle Lie algebra dsell
that generalizes the well-known double shuffle Lie algebra ds to the elliptic
situation. The double shuffle, or dimorphic, relations satisfied by elements of
the ...
Lie Transformation Groups -- An Introduction to Symmetry Group Analysis
of Differential Equations
June 23, 2015
|
Mathematics
Differential Geometry
Differential Geometry
These are lecture notes of a course on symmetry group analysis of
differential equations, based mainly on P. J. Olver's book 'Applications of Lie
Groups to Differential Equations'. The course starts out with an introduction
to the theory of...
Recovering p-adic valuations from pro-p Galois groups
June 19, 2015
|
Mathematics
Number Theory
Let K be a field with GK(2)≃GQ(2), where GF(2)
denotes the maximal pro-2 quotient of the absolute Galois group of a field F.
We prove that then K admits a (non-trivial) valuation v which is
2-henselian and h...
An introduction to Galton-Watson trees and their local limits
June 18, 2015
|
Mathematics
Probability
The aim of this lecture is to give an overview of old and new resultson
Bienaym\'e-Galton-Watson (BGW) trees. After introducing the framework of
discretetrees, we first give alternative proofs of classical results on
theextinction probabili...
Open questions about Ramsey-type statements in reverse mathematics
June 15, 2015
|
Mathematics
Logic
Logic
Ramsey's theorem states that for any coloring of the n-element subsets of N
with finitely many colors, there is an infinite set H such that all n-element
subsets of H have the same color. The strength of consequences of Ramsey's
theorem has...
Bounded morphisms
June 12, 2015
|
Mathematics
Logic
Commutative Algebra
Logic
Commutative Algebra
A bounded automorphism of a field or a group with trivial approximate centre
is definable. In an expansion of a field by a Pfaffian family F of additive
endomorphisms such that algebraic closure in the expansion coincides with
relative fiel...
Superiorization and Perturbation Resilience of Algorithms: A
Continuously Updated Bibliography
June 12, 2015
Mathematics
Optimization and Control
This document presents a (mostly) chronologically-ordered bibliography of
scientific publications on the superiorization methodology and perturbation
resilience of algorithms which is compiled and continuously updated by us at:
http://math....