We introduce a groupoid {\mathbf{\Pi MG}}}, called the fundamental modular
groupoid, which is a variant of Penner's mapping class groupoid. We study how
it relates to the surface mapping class groups and Thompson's group T. We a...
Fundamental groups and group presentations with bounded relator lengths
July 23, 2018
Mathematics
Metric Geometry
Algebraic Topology
Group Theory
We study the geometry of compact geodesic spaces with trivial first Betti
number admitting large finite groups of isometries. We show that if a finite
group G acts by isometries on a compact geodesic space X whose first Betti
number van...
A model for framed configuration spaces of points
July 22, 2018
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Mathematics
Algebraic Topology
Quantum Algebra
Algebraic Topology
Quantum Algebra
We study configuration spaces of framed points on oriented closed smooth
manifolds. Such configuration spaces admit natural actions of the framed little
discs operads, that play an important role in the study of embedding spaces of
manifold...
Looking to the Blue Sky with Colored Patterns
July 20, 2018
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Physics
Physics Education
This work presents a simple alternative technique to observe the polarization
of the skylight on Earth. Using a birefringent material and a polarizer to look
at the polarized light from the blue sky, it is possible to see a colored
pattern ...
On the cardinality of unique range sets with weight one
July 19, 2018
|
Mathematics
Complex Variables
Two meromorphic functions f and g are said to share the set S⊂C∪{∞} with weight l∈N∪{0}∪{∞},
if Ef(S,l)=Eg(S,l) where $$E_{f}(S,l)=\bigcup\limits_{a \in S}\{(z,t)
\in \math...
First-Passage Duality
July 19, 2018
|
Physics
Statistical Mechanics
We show that the distribution of times for a diffusing particle to first hit
an absorber is \emph{independent} of the direction of an external flow field,
when we condition on the event that the particle reaches the target for flow
away fro...
On the L-polynomials of curves over finite fields
July 19, 2018
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Mathematics
Algebraic Geometry
Number Theory
We discuss, in a non-archimedean setting, the distribution of the
coefficients of L-polynomials of curves of genus g over Fq. This
allows us to prove, among other things, that the Q-vector space
spanned by such char...
Convergence of martingale solutions to the hybrid slow-fast system
July 18, 2018
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Mathematics
Dynamical Systems
Analysis of PDEs
This paper is devoted to studying the weak convergence for a slow-fast system
with jumps modulated by Markovian switching regimes with the martingale method.
However, due to the coexistence of fast component and Markovian switching
regimes,...
Topological and nonlinearity-induced thermalization in a PT-symmetric
split-Langevin bath
July 17, 2018
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Physics
Statistical Mechanics
Pattern Formation and Solitons
Statistical Mechanics
Pattern Formation and Solitons
Open classical systems with balanced, separated gain and loss, called
PT-symmetric systems, have been extensively studied over the past decade. Here,
we investigate the properties of a uniform, harmonic chain with spatially
separated viscou...
Near-Optimal Bootstrapping of Hitting Sets for Algebraic Models
July 17, 2018
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Computer Science
Computational Complexity
Computational Complexity
The Polynomial Identity Lemma (also called
the "Schwartz--Zippel lemma") states ...