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Characterization of positive links and the $s$invariant for links Abe, Tetsuya; Tagami, Keiji Published: 20161129
We characterize positive links in terms of strong quasipositivity,
homogeneity and the value of Rasmussen and BeliakovaWehrli's
$s$invariant.
We also study almost positive links,
in particular, determine the $s$invariants of
almost positive links.
This result suggests that all almost positive links might
be strongly quasipositive.
On the other hand, it implies that
almost positive links are never homogeneous links.


Weyl images of Kantor pairs Allison, Bruce; Faulkner, John; Smirnov, Oleg Published: 20170420
Kantor pairs arise naturally in the study of
$5$graded Lie algebras. In this article, we introduce
and study Kantor pairs with short Peirce gradings and relate
them to Lie algebras
graded by the root system of type
$\mathrm{BC}_2$.
This relationship
allows us to define so called Weyl images
of short Peirce graded Kantor pairs. We use Weyl images to construct
new examples of Kantor pairs, including a class of infinite
dimensional
central simple Kantor pairs over a field of characteristic $\ne
2$ or $3$, as well as a family of forms of a split
Kantor pair of type
$\mathrm{E}_6$.


Anisotropic HardyLorentz spaces with variable exponents Almeida, Víctor; Betancor, Jorge J.; RodríguezMesa, Lourdes Published: 20170519
In this paper we introduce HardyLorentz spaces with variable
exponents associated to dilations in ${\mathbb R}^n$. We establish
maximal characterizations and atomic decompositions for our variable
exponent anisotropic HardyLorentz spaces.


Dynamics and regularization of the Kepler problem on surfaces of constant curvature Andrade, Jaime; Dávila, Nestor; PérezChavela, Ernesto; Vidal, Claudio Published: 20160617
We classify and analyze the orbits of the Kepler problem on surfaces
of constant curvature (both positive and negative, $\mathbb S^2$ and
$\mathbb H^2$, respectively) as function of the angular momentum and
the energy. Hill's region are characterized and the problem of
timecollision is studied. We also regularize the problem in
Cartesian and intrinsic coordinates, depending on the constant
angular momentum and we describe the orbits of the regularized
vector field. The phase portrait both for $\mathbb S^2$ and $\mathbb H^2$
are pointed out.


CM periods, CM Regulators and Hypergeometric Functions, I Asakura, Masanori; Otsubo, Noriyuki Author's Draft
We prove the GrossDeligne conjecture on CM periods for motives
associated with $H^2$ of certain surfaces fibered over the projective
line. Then we prove for the same motives a formula which expresses
the $K_1$regulators in terms of hypergeometric functions ${}_3F_2$,
and obtain a new example of nontrivial regulators.


On Dirichlet spaces with a class of superharmonic weights Bao, Guanlong; Göğüş, Nihat Gökhan; Pouliasis, Stamatis Published: 20170519
In this paper, we investigate Dirichlet spaces $\mathcal{D}_\mu$ with
superharmonic weights induced by positive Borel measures $\mu$
on
the open unit disk. We establish the AlexanderTaylorUllman
inequality for $\mathcal{D}_\mu$ spaces and we characterize the cases where
equality occurs.
We define a class of weighted Hardy spaces $H_{\mu}^{2}$ via
the balayage of the measure $\mu$.
We show that $\mathcal{D}_\mu$
is equal to $H_{\mu}^{2}$ if and only if $\mu$ is a
Carleson measure for $\mathcal{D}_\mu$. As an application, we obtain the
reproducing kernel of $\mathcal{D}_\mu$ when $\mu$ is an infinite
sum of point mass measures. We consider the boundary
behavior and innerouter factorization of functions in $\mathcal{D}_\mu$.
We also characterize the boundedness and
compactness of composition operators on $\mathcal{D}_\mu$.


Partial Hasse invariants, partial degrees, and the canonical subgroup Bijakowski, Stephane Published: 20170512
If the Hasse invariant of a $p$divisible group is small enough,
then one can construct a canonical subgroup inside its $p$torsion.
We prove that, assuming the existence of a subgroup of adequate
height in the $p$torsion with high degree, the expected properties
of the canonical subgroup can be easily proved, especially the
relation between its degree and the Hasse invariant. When one
considers a $p$divisible group with an action of the ring of
integers of a (possibly ramified) finite extension of $\mathbb{Q}_p$,
then much more can be said. We define partial Hasse invariants
(they are natural in the unramified case, and generalize a construction
of Reduzzi and Xiao in the general case), as well as partial
degrees. After studying these functions, we compute the partial
degrees of the canonical subgroup.


Weights of the mod $p$ kernel of the theta operators Böcherer, Siegfried; Kikuta, Toshiyuki; Takemori, Sho Author's Draft
Let $\Theta ^{[j]}$ be an analogue of the Ramanujan theta operator
for Siegel modular forms.
For a given prime $p$, we give the weights of elements of mod
$p$ kernel of $\Theta ^{[j]}$,
where the mod $p$ kernel of $\Theta ^{[j]}$ is the set of all
Siegel modular forms $F$ such that $\Theta ^{[j]}(F)$ is congruent
to zero modulo $p$.
In order to construct examples of the mod $p$ kernel of $\Theta
^{[j]}$ from any Siegel modular form,
we introduce new operators $A^{(j)}(M)$ and show the modularity
of $FA^{(j)}(M)$ when $F$ is a Siegel modular form.
Finally, we give some examples of the mod $p$ kernel of $\Theta
^{[j]}$ and the filtrations of some of them.


Comparison Properties of the Cuntz semigroup and applications to C*algebras Bosa, Joan; Petzka, Henning Published: 20170525
We study comparison properties in the category $\mathrm{Cu}$ aiming to
lift results to the C*algebraic setting. We introduce a new
comparison property and relate it to both the CFP and $\omega$comparison.
We show differences of all properties by providing examples,
which suggest that the corona factorization for C*algebras might
allow for both finite and infinite projections. In addition,
we show that R{\o}rdam's simple, nuclear C*algebra with a finite
and an infinite projection does not have the CFP.


Classification of regular parametrized onerelation operads Bremner, Murray; Dotsenko, Vladimir Author's Draft
JeanLouis Loday introduced a class of symmetric operads generated
by one bilinear operation subject to one
relation making each leftnormed product of three elements equal
to a linear combination
of rightnormed products:
\[
(a_1a_2)a_3=\sum_{\sigma\in S_3}x_\sigma\, a_{\sigma(1)}(a_{\sigma(2)}a_{\sigma(3)})\
;
\]
such an operad is called a parametrized onerelation operad.
For a particular choice of parameters $\{x_\sigma\}$,
this operad is said to be regular if each of its components is
the regular representation of the symmetric group; equivalently, the corresponding free algebra on a vector space $V$ is, as a
graded vector space, isomorphic to the tensor
algebra of $V$. We classify, over an algebraically closed field
of characteristic zero, all regular parametrized onerelation
operads.
In fact, we prove that each such operad is isomorphic to one
of the following five operads: the leftnilpotent operad
defined by the relation $((a_1a_2)a_3)=0$, the associative operad,
the Leibniz operad, the dual Leibniz (Zinbiel) operad, and the
Poisson operad.
Our computational methods combine linear algebra over polynomial
rings, representation theory of the symmetric group, and
Gröbner bases for determinantal ideals and their radicals.


Stability for the BrunnMinkowski and Riesz rearrangement inequalities, with applications to Gaussian concentration and finite range nonlocal isoperimetry Carlen, Eric; Maggi, Francesco Published: 20161108
We provide a simple, general argument to obtain improvements
of concentrationtype inequalities starting from improvements
of their corresponding isoperimetrictype inequalities. We apply
this argument to obtain robust improvements of the BrunnMinkowski
inequality (for Minkowski sums between generic sets and convex
sets) and of the Gaussian concentration inequality. The former
inequality is then used to obtain a robust improvement of the
Riesz rearrangement inequality under certain natural conditions.
These conditions are compatible with the applications to a finiterange
nonlocal isoperimetric problem arising in statistical mechanics.


A Beurling Theorem for Generalized Hardy Spaces on a Multiply Connected Domain Chen, Yanni; Hadwin, Don; Liu, Zhe; Nordgren, Eric Author's Draft
The object of this paper is to prove a version of the BeurlingHelsonLowdenslager
invariant subspace theorem for operators on certain Banach spaces
of functions on a multiply connected domain in $\mathbb{C}$. The norms
for these spaces are either the usual Lebesgue and Hardy space
norms or certain continuous gauge norms.
In the Hardy space case the expected corollaries include the
characterization of the cyclic vectors as the outer functions
in this context, a demonstration that the set of analytic multiplication
operators is maximal abelian and reflexive, and a determination
of the closed operators that commute with all analytic multiplication
operators.


Wedge operations and torus symmetries II Choi, Suyoung; Park, Hanchul Published: 20161129
A fundamental idea in toric topology is that classes of manifolds
with wellbehaved torus actions (simply, toric spaces) are classified
by pairs of simplicial complexes and (nonsingular) characteristic
maps. The authors in their previous paper provided a new way
to find all characteristic maps on a simplicial complex $K(J)$
obtainable by a sequence of wedgings from $K$. The main idea
was that characteristic maps on $K$ theoretically determine all
possible characteristic maps on a wedge of $K$.


Fixed point theorems for maps with local and pointwise contraction properties Ciesielski, Krzysztof Chris; Jasinski, Jakub Author's Draft
The paper constitutes a comprehensive study of ten classes of
selfmaps on metric spaces $\langle X,d\rangle$ with the local
and pointwise (a.k.a. local radial) contraction properties.
Each of those classes appeared previously in the literature in
the context of fixed point theorems.


Transfer of Representations and Orbital Integrals for Inner Forms of $GL_n$ Cohen, Jonathan Author's Draft
We characterize the Local Langlands Correspondence (LLC) for
inner forms of $\operatorname{GL}_n$ via the JacquetLanglands Correspondence
(JLC) and compatibility with the Langlands Classification. We
show that LLC satisfies a natural compatibility with parabolic
induction and characterize LLC for inner forms as a unique family
of bijections $\Pi(\operatorname{GL}_r(D)) \to \Phi(\operatorname{GL}_r(D))$ for each $r$,
(for a fixed $D$) satisfying certain properties. We construct
a surjective map of Bernstein centers $\mathfrak{Z}(\operatorname{GL}_n(F))\to
\mathfrak{Z}(\operatorname{GL}_r(D))$
and show this produces pairs of matching distributions in the
sense of Haines. Finally, we construct explicit Iwahoribiinvariant
matching functions for unit elements in the parahoric Hecke
algebras
of $\operatorname{GL}_r(D)$, and thereby produce many explicit pairs of matching
functions.


Transport inequalities for logconcave measures, quantitative forms and applications CorderoErausquin, Dario Published: 20170327
We review some simple techniques based on monotone mass transport
that allow us to obtain transporttype inequalities for any
logconcave
probability measure, and for more general measures as well. We
discuss quantitative forms of these inequalities, with application
to the BrascampLieb variance inequality.


Amenability and covariant injectivity of locally compact quantum groups II Crann, Jason Published: 20170125
Building on our previous work, we study the nonrelative homology
of quantum group convolution algebras. Our main result establishes
the equivalence of amenability of a locally compact quantum group
$\mathbb{G}$ and 1injectivity of
$L^{\infty}(\widehat{\mathbb{G}})$
as an operator
$L^1(\widehat{\mathbb{G}})$module.
In particular, a locally compact group $G$ is amenable if and
only if its group von Neumann algebra
$VN(G)$
is 1injective as
an operator module over the Fourier algebra $A(G)$. As an application,
we provide a decomposability result for completely bounded
$L^1(\widehat{\mathbb{G}})$module
maps on
$L^{\infty}(\widehat{\mathbb{G}})$,
and give a simplified proof that amenable discrete
quantum groups have coamenable compact duals which avoids the
use of modular theory and the PowersStørmer inequality, suggesting
that our homological techniques may yield a new approach to the
open problem of duality between amenability and coamenability.


The BishopPhelpsBollobás property for compact operators Dantas, Sheldon; García, Domingo; Maestre, Manuel; Martín, Miguel Published: 20170525
We study the BishopPhelpsBollobás property (BPBp for short)
for compact operators. We present some abstract techniques which
allows to carry the BPBp for compact operators from sequence
spaces to function spaces. As main applications, we prove the
following results. Let $X$, $Y$ be Banach spaces. If $(c_0,Y)$
has the BPBp for compact operators, then so do $(C_0(L),Y)$ for
every locally compact Hausdorff topological space $L$ and $(X,Y)$
whenever $X^*$ is isometrically isomorphic to $\ell_1$.
If $X^*$ has the RadonNikodým property and $(\ell_1(X),Y)$
has the BPBp for compact operators, then so does $(L_1(\mu,X),Y)$
for every positive measure $\mu$; as a consequence, $(L_1(\mu,X),Y)$
has the the BPBp for compact operators when $X$ and $Y$ are finitedimensional
or $Y$ is a Hilbert space and $X=c_0$ or $X=L_p(\nu)$ for any
positive measure $\nu$ and $1\lt p\lt \infty$.
For $1\leq p \lt \infty$, if $(X,\ell_p(Y))$ has the BPBp for compact
operators, then so does $(X,L_p(\mu,Y))$ for every positive measure
$\mu$ such that $L_1(\mu)$ is infinitedimensional. If $(X,Y)$
has the BPBp for compact operators, then so do $(X,L_\infty(\mu,Y))$
for every $\sigma$finite positive measure $\mu$ and $(X,C(K,Y))$
for every compact Hausdorff topological space $K$.


The classical $N$body problem in the context of curved space Diacu, Florin Published: 20170515
We provide the differential equations that generalize the Newtonian
$N$body problem of celestial mechanics to spaces of constant
Gaussian curvature, $\kappa$, for all $\kappa\in\mathbb R$. In
previous studies, the equations of motion made sense only for
$\kappa\ne 0$. The system derived here does more than just include
the Euclidean case in the limit $\kappa\to 0$: it recovers the
classical equations for $\kappa=0$. This new expression of the
laws of motion allows the study of the $N$body problem in the
context of constant curvature spaces and thus offers a natural
generalization of the Newtonian equations that includes the classical
case. We end the paper with remarks about the bifurcations of
the first integrals.


Normality versus paracompactness in locally compact spaces Dow, Alan; Tall, Franklin D. Published: 20170525
This note provides a correct proof of the result claimed by the
second author that locally compact normal spaces are collectionwise
Hausdorff in certain models obtained by forcing with a coherent
Souslin tree. A novel feature of the proof is the use of saturation
of the nonstationary ideal on $\omega_1$, as well as of a strong
form of Chang's Conjecture. Together with other improvements,
this enables the consistent characterization of locally compact
hereditarily paracompact spaces as those locally compact, hereditarily
normal spaces that do not include a copy of $\omega_1$.


Multiplication formulas and canonical bases for quantum affine gln Du, Jie; Zhao, Zhonghua Author's Draft
We will give a representationtheoretic proof for the multiplication
formula
in the RingelHall algebra
$\mathfrak{H}_\Delta(n)$ of a cyclic quiver $\Delta(n)$. As a first
application, we see immediately the existence of Hall polynomials
for cyclic quivers, a fact established
by J. Y. Guo and C. M. Ringel,
and derive a recursive formula
to compute them.
We will further use the formula and the construction of a certain
monomial base for $\mathfrak{H}_\Delta(n)$ given
by Deng, Du, and Xiao
together with the double RingelHall algebra realisation of
the quantum loop algebra $\mathbf{U}_v(\widehat{\mathfrak{g}\mathfrak{l}}_n)$
given by
Deng, Du, and Fu
to develop some algorithms and to compute the canonical basis
for $\mathbf{U}_v^+(\widehat{\mathfrak{g}\mathfrak{l}}_n)$. As examples,
we will show explicitly the part of the canonical basis
associated with modules of Lowey length at most $2$ for the quantum
group $\mathbf{U}_v(\widehat{\mathfrak{g}\mathfrak{l}}_2)$.


Geometric classification of graph C*algebras over finite graphs Eilers, Søren; Restorff, Gunnar; Ruiz, Efren; Sørensen, Adam P. W. Author's Draft
We address the classification problem for graph $C^*$algebras of
finite graphs (finitely many edges and vertices), containing
the class of CuntzKrieger algebras as a
prominent special case. Contrasting earlier work, we do not assume
that the graphs satisfy the standard condition (K), so that the
graph
$C^*$algebras may come with uncountably many ideals.


The minimal free resolution of fat almost complete intersections in $\mathbb{P}^1\times \mathbb{P}^1$ Favacchio, Giuseppe; Guardo, Elena Published: 20161223
A current research theme is to compare symbolic powers of an
ideal
$I$ with the regular powers of $I$. In this paper, we focus on
the
case that $I=I_X$ is an ideal defining an almost complete
intersection (ACI) set of points $X$ in
$\mathbb{P}^1 \times \mathbb{P}^1$.
In particular,
we describe a minimal free bigraded resolution of a non
arithmetically CohenMacaulay (also non homogeneous) set $\mathcal
Z$ of fat
points whose support is an ACI, generalizing
a result of S. Cooper et al.
for homogeneous sets of triple points. We call
$\mathcal Z$ a fat ACI. We also show that its symbolic and ordinary
powers are equal, i.e,
$I_{\mathcal Z}^{(m)}=I_{\mathcal Z}^{m}$ for any $m\geq 1.$


Splitting, Bounding, and Almost Disjointness can be quite Different Fischer, Vera; Mejia, Diego Alejandro Published: 20160719
We prove the consistency of
$$
\operatorname{add}(\mathcal{N})\lt
\operatorname{cov}(\mathcal{N})
\lt \mathfrak{p}=\mathfrak{s}
=\mathfrak{g}\lt \operatorname{add}(\mathcal{M})
= \operatorname{cof}(\mathcal{M}) \lt \mathfrak{a}
=\mathfrak{r}=\operatorname{non}(\mathcal{N})=\mathfrak{c}
$$
with $\mathrm{ZFC}$, where each of these cardinal
invariants assume arbitrary
uncountable regular values.


Weingarten type surfaces in $\mathbb{H}^2\times\mathbb{R}$ and $\mathbb{S}^2\times\mathbb{R}$ Folha, Abigail; Penafiel, Carlos Published: 20170316
In this article, we study complete surfaces $\Sigma$, isometrically
immersed in the product space $\mathbb{H}^2\times\mathbb{R}$ or
$\mathbb{S}^2\times\mathbb{R}$
having positive extrinsic curvature $K_e$. Let $K_i$ denote the
intrinsic curvature of $\Sigma$. Assume that the equation $aK_i+bK_e=c$
holds for some real constants $a\neq0$, $b\gt 0$ and $c$. The main
result of this article state that when such a surface is a topological
sphere it is rotational.


On asymptotically orthonormal sequences Fricain, Emmanuel; Rupam, Rishika Published: 20170331
An asymptotically orthonormal sequence is a sequence which is
"nearly" orthonormal in the sense that it satisfies the Parseval
equality up to two constants close to one. In this paper, we
explore such sequences formed by normalized reproducing kernels
for model spaces and de BrangesRovnyak spaces.


Dirichlet's theorem in function fields Ganguly, Arijit; Ghosh, Anish Published: 20160729
We study metric Diophantine approximation for function fields
specifically the problem of improving Dirichlet's theorem in
Diophantine
approximation.


A Class of Abstract Linear Representations for Convolution Function Algebras over Homogeneous Spaces of Compact Groups Ghaani Farashahi, Arash Published: 20170221
This paper introduces a class of abstract linear representations
on
Banach convolution function algebras over
homogeneous spaces of compact groups. Let $G$ be a compact group
and $H$ be a closed subgroup of $G$.
Let $\mu$ be the normalized $G$invariant measure over the compact
homogeneous space $G/H$ associated to the
Weil's formula and $1\le p\lt \infty$.
We then present a structured class of abstract linear representations
of the
Banach convolution function algebras $L^p(G/H,\mu)$.


Inequalities for the surface area of projections of convex bodies Giannopoulos, Apostolos; Koldobsky, Alexander; Valettas, Petros Published: 20170327
We provide general inequalities that compare the surface area
$S(K)$ of a convex body $K$ in ${\mathbb R}^n$
to the minimal, average or maximal surface area of its hyperplane
or lower dimensional projections. We discuss the
same questions for all the quermassintegrals of $K$. We examine
separately the dependence of the constants
on the dimension in the case where $K$ is in some of the classical
positions or $K$ is a projection body.
Our results are in the spirit of the hyperplane problem, with
sections replaced by projections and volume by
surface area.


$L^q$ norms of Fekete and related polynomials Günther, Christian; Schmidt, KaiUwe Published: 20160628
A Littlewood polynomial is a polynomial in $\mathbb{C}[z]$ having all
of its coefficients in $\{1,1\}$. There are various old unsolved
problems, mostly due to Littlewood and Erdős, that ask for
Littlewood polynomials that provide a good approximation to a
function that is constant on the complex unit circle, and in
particular have small $L^q$ norm on the complex unit circle.
We consider the Fekete polynomials
\[
f_p(z)=\sum_{j=1}^{p1}(j\,\,p)\,z^j,
\]
where $p$ is an odd prime and $(\,\cdot\,\,p)$ is the Legendre
symbol (so that $z^{1}f_p(z)$ is a Littlewood polynomial). We
give explicit and recursive formulas for the limit of the ratio
of $L^q$ and $L^2$ norm of $f_p$ when $q$ is an even positive
integer and $p\to\infty$. To our knowledge, these are the first
results that give these limiting values for specific sequences
of nontrivial Littlewood polynomials and infinitely many $q$.
Similar results are given for polynomials obtained by cyclically
permuting the coefficients of Fekete polynomials and for Littlewood
polynomials whose coefficients are obtained from additive characters
of finite fields. These results vastly generalise earlier results
on the $L^4$ norm of these polynomials.


Periodic solutions of an indefinite singular equation arising from the Kepler problem on the sphere Hakl, Robert; Zamora, Manuel Published: 20170221
We study a secondorder ordinary differential
equation coming from the Kepler problem on $\mathbb{S}^2$. The
forcing term under consideration is a piecewise constant with
singular nonlinearity which changes sign. We establish necessary
and
sufficient conditions to the existence and multiplicity of
$T$periodic solutions.


On computable field embeddings and difference closed fields HarrisonTrainor, Matthew; Melnikov, Alexander; Miller, Russell Published: 20170525
We investigate when a computable automorphism of a computable
field can be effectively extended to a computable automorphism
of its (computable) algebraic closure. We then apply our results
and techniques to study effective embeddings of computable difference
fields into computable difference closed fields.


Free product C*algebras associated to graphs, free differentials, and laws of loops Hartglass, Michael Published: 20160920
We study a canonical C$^*$algebra, $\mathcal{S}(\Gamma, \mu)$, that
arises from a weighted graph $(\Gamma, \mu)$, specific cases
of which were previously studied in the context of planar algebras.
We discuss necessary and sufficient conditions of the weighting
which ensure simplicity and uniqueness of trace of $\mathcal{S}(\Gamma,
\mu)$, and study the structure of its positive cone. We then
study the $*$algebra, $\mathcal{A}$, generated by the generators of
$\mathcal{S}(\Gamma, \mu)$, and use a free differential calculus and
techniques of Charlesworth and Shlyakhtenko, as well as Mai,
Speicher, and Weber to show that certain ``loop" elements have
no atoms in their spectral measure. After modifying techniques
of Shlyakhtenko and Skoufranis to show that self adjoint elements
$x \in M_{n}(\mathcal{A})$ have algebraic Cauchy transform, we explore
some applications to eigenvalues of polynomials in Wishart matrices
and to diagrammatic elements in von Neumann algebras initially
considered by Guionnet, Jones, and Shlyakhtenko.


Absolute continuity of Wasserstein barycenters over Alexandrov spaces Jiang, Yin Published: 20161206
In this paper, we prove that, on a compact, $n$dimensional Alexandrov
space with curvature $\geqslant 1$, the Wasserstein barycenter of
Borel probability measures $\mu_1,...,\mu_m$ is absolutely continuous
with respect to the $n$dimensional Hausdorff measure if one
of them is.


The $ER(2)$cohomology of $B\mathbb{Z}/(2^q)$ and $\mathbb{C} \mathbb{P}^n$ Kitchloo, Nitu; Lorman, Vitaly; Wilson, W. Stephen Author's Draft
The $ER(2)$cohomology of $B\mathbb{Z}/(2^q)$ and $\mathbb{C}\mathbb{P}^n$ are computed
along with
the AtiyahHirzebruch spectral sequence for
$ER(2)^*(\mathbb{C}\mathbb{P}^\infty)$.
This, along with other papers in this series, gives
us the $ER(2)$cohomology of all EilenbergMacLane spaces.


Regulators of an infinite family of the simplest quartic function fields Lee, Jungyun; Lee, Yoonjin Published: 20161206
We explicitly find regulators of an infinite family $\{L_m\}$
of the simplest quartic function fields
with a parameter $m$ in a polynomial ring $\mathbb{F}_q [t]$, where
$\mathbb{F}_q$
is the finite field of order $q$
with odd characteristic. In fact, this infinite family of the
simplest quartic function fields are
subfields of maximal real subfields of cyclotomic function fields,
where they have the same conductors.
We obtain a lower bound on the class numbers of the family $\{L_m\}$
and some result on the divisibility
of the divisor class numbers of cyclotomic function fields which
contain $\{L_m\}$ as their subfields.
Furthermore, we find an explicit criterion for the characterization
of splitting types of all the primes
of the rational function field $\mathbb{F}_q (t)$ in $\{L_m\}$.


On the asymptotic growth of BlochKatoShafarevichTate groups of modular forms over cyclotomic extensions Lei, Antonio; Loeffler, David; Zerbes, Sarah Livia Published: 20161206
We study the asymptotic behaviour of the BlochKatoShafarevichTate
group of a modular form $f$ over the cyclotomic $\mathbb{Z}_p$extension
of $\mathbb{Q}$ under the assumption that $f$ is nonordinary at $p$.
In particular, we give upper bounds of these groups in terms
of Iwasawa invariants of Selmer groups defined using $p$adic
Hodge Theory. These bounds have the same form as the formulae
of Kobayashi, Kurihara and Sprung for supersingular elliptic
curves.


Spherical fundamental lemma for metaplectic groups Luo, Caihua Author's Draft
In this paper, we prove the spherical fundamental lemma for
metaplectic group $Mp_{2n}$ based on the formalism of endoscopy
theory by J.Adams, D.Renard and WenWei Li.


Toric geometry of $SL_2(\mathbb{C})$ free group character varieties from outer space Manon, Christopher Published: 20170302
Culler and Vogtmann defined a simplicial space $O(g)$ called
outer space to study the outer automorphism group
of the free group $F_g$. Using representation theoretic methods,
we give an embedding of $O(g)$ into the analytification of $\mathcal{X}(F_g,
SL_2(\mathbb{C})),$ the $SL_2(\mathbb{C})$ character variety
of $F_g,$ reproving a result of Morgan and Shalen. Then we show
that every point $v$ contained in a maximal cell of $O(g)$ defines
a flat degeneration of $\mathcal{X}(F_g, SL_2(\mathbb{C}))$ to
a toric variety $X(P_{\Gamma})$. We relate $\mathcal{X}(F_g,
SL_2(\mathbb{C}))$ and $X(v)$ topologically by showing that there
is a surjective, continuous, proper map $\Xi_v: \mathcal{X}(F_g,
SL_2(\mathbb{C})) \to X(v)$. We then show that this map is a
symplectomorphism on a dense, open subset of $\mathcal{X}(F_g,
SL_2(\mathbb{C}))$ with respect to natural symplectic structures
on $\mathcal{X}(F_g, SL_2(\mathbb{C}))$ and $X(v)$. In this
way, we construct an integrable Hamiltonian system in $\mathcal{X}(F_g,
SL_2(\mathbb{C}))$ for each point in a maximal cell of $O(g)$,
and we show that each $v$ defines a topological decomposition
of $\mathcal{X}(F_g, SL_2(\mathbb{C}))$ derived from the decomposition
of $X(P_{\Gamma})$ by its torus orbits. Finally, we show that
the valuations coming from the closure of a maximal cell in $O(g)$
all arise as divisorial valuations built from an associated projective
compactification of $\mathcal{X}(F_g, SL_2(\mathbb{C})).$


Gamma factors, root numbers, and distinction Matringe, Nadir; Offen, Omer Author's Draft
We study a relation between distinction and special values of
local invariants for representations of the general linear group
over a quadratic extension of $p$adic fields.
We show that the local RankinSelberg root number of any pair
of distinguished representation is trivial and as a corollary
we obtain an analogue for the global root number of any pair
of distinguished cuspidal representations. We further study the
extent to which the gamma factor at $1/2$ is trivial for distinguished
representations as well as the converse problem.


On the digits of sumsets Mauduit, Christian; Rivat, Joël; Sárközy, András Published: 20160510
Let $\mathcal A$, $\mathcal B$ be large subsets of $\{1,\ldots,N\}$.
We study the number of pairs $(a,b)\in\mathcal A\times\mathcal B$ such that
the sum of binary digits of $a+b$ is fixed.


Mori's program for $\overline{M}_{0,7}$ with symmetric divisors Moon, HanBom Published: 20160418
We complete Mori's program with symmetric divisors for the moduli
space of stable sevenpointed rational curves. We describe all
birational models in terms of explicit blowups and blowdowns.
We also give a moduli theoretic description of the first flip,
which has not appeared in the literature.


Closed convex hulls of unitary orbits in certain simple real rank zero C$^*$algebras Ng, P. W.; Skoufranis, P. Published: 20170216
In this paper, we characterize the closures of convex hulls of
unitary orbits of selfadjoint operators in unital, separable,
simple C$^*$algebras with nontrivial tracial simplex, real
rank zero, stable rank one, and strict comparison of projections
with respect to tracial states. In addition, an upper bound
for the number of unitary conjugates in a convex combination
needed to approximate a selfadjoint are obtained.


Extremal sequences for the Bellman function of the dyadic maximal operator and applications to the Hardy operator Nikolidakis, Eleftherios Nikolaos Published: 20160727
We prove that the extremal sequences for the
Bellman function of the dyadic maximal operator behave approximately
as eigenfunctions of this operator for a specific eigenvalue.
We use this result to prove the analogous one with respect to
the Hardy operator.


Almost disjointness preservers Oikhberg, Timur; Tradacete, Pedro Published: 20160927
We study the stability of disjointness preservers on Banach lattices.
In many cases, we prove that an "almost disjointness preserving"
operator is well approximable by a disjointness preserving one.
However, this approximation is not always possible, as our
examples show.


Tannakian categories with semigroup actions Ovchinnikov, Alexey; Wibmer, Michael Published: 20160916
Ostrowski's theorem implies that $\log(x),\log(x+1),\dots$ are
algebraically independent over $\mathbb{C}(x)$. More generally, for
a linear differential or difference equation, it is an important
problem to find all algebraic dependencies among a nonzero solution
$y$ and particular transformations of $y$, such as derivatives
of $y$ with respect to parameters, shifts of the arguments, rescaling,
etc. In the present paper, we develop a theory of Tannakian categories
with semigroup actions, which will be used to attack such questions
in full generality, as each linear differential equation gives
rise to a Tannakian category.
Deligne studied actions of braid groups on categories and obtained
a finite collection of axioms that characterizes such actions
to apply it to various geometric constructions. In this paper,
we find a finite set of axioms that characterizes actions of
semigroups that are finite free products of semigroups of the
form $\mathbb{N}^n\times
\mathbb{Z}/{n_1}\mathbb{Z}\times\cdots\times\mathbb{Z}/{n_r}\mathbb{Z}$
on Tannakian categories. This is the class of semigroups that
appear in many applications.


The weak ideal property and topological dimension zero Pasnicu, Cornel; Phillips, N. Christopher Author's Draft
Following up on previous work,
we prove a number of results for C*algebras
with the weak ideal property
or topological dimension zero,
and some results for C*algebras with related properties.
Some of the more important results include:
$\bullet$
The weak ideal property
implies topological dimension zero.


Eulertype relative equilibria in spaces of constant curvature and their stability PérezChavela, Ernesto; SánchezCerritos, Juan Manuel Published: 20170525
We consider three point positive masses moving on $S^2$ and $H^2$.
An Eulerianrelative equilibrium, is a relative equilibrium where
the three masses are on the same geodesic, in this paper we analyze
the spectral stability of these kind of orbits where the mass
at the middle is arbitrary and the masses at the ends are equal
and located at the same distance from the central mass. For the
case of $S^2$, we found a positive measure set in the set of
parameters where the relative equilibria are spectrally stable,
and we give a complete classification of the spectral stability
of these solutions, in the sense that, except on an algebraic
curve in the space of parameters, we can determine if the corresponding
relative equilibria is spectrally stable or unstable.
On $H^2$, in the elliptic case, we prove that generically all
Eulerianrelative equilibria are unstable; in the particular
degenerate case when the two equal masses are negligible we get
that the corresponding solutions are spectrally stable. For the
hyperbolic case we consider the system where the mass in the
middle is negligible, in this case the Eulerianrelative equilibria
are unstable.


Erratum: Translation Groupoids and Orbifold Cohomology Pronk, Dorette; Scull, Laura Published: 20170426
We correct an error in the proof of a
lemma in
"Translation Groupoids and Orbifold Cohomology",
Canadian J. Math Vol 62 (3), pp 614645 (2010).
This error was pointed out to the authors
by Li Du of the GeorgAugustUniversität at Gottingen, who
also suggested the outline for the corrected proof.


Global and non global solutions for some fractional heat equations with pure power nonlinearity Saanouni, Tarek Published: 20160621
The initial value problem for a semilinear fractional heat equation
is investigated. In the focusing case, global wellposedness
and exponential decay are obtained. In the focusing sign, global
and non global existence of solutions are discussed via the potential
well method.


Order and spectrum preserving maps on positive operators Semrl, Peter Published: 20161206
We describe the general form of surjective maps on the cone of
all positive operators which preserve order and spectrum. The
result is optimal as shown by
counterexamples. As an easy consequence we characterize surjective
order and spectrum preserving maps on the set of all selfadjoint
operators.


The seven dimensional perfect Delaunay polytopes and Delaunay simplices Sikirić, Mathieu Dutour Published: 20160621
For a lattice $L$ of $\mathbb{RR}^n$, a sphere $S(c,r)$ of center $c$
and radius $r$
is called empty if for any $v\in L$ we have $\Vert v 
c\Vert \geq r$.
Then the set $S(c,r)\cap L$ is the vertex set of a {\em Delaunay
polytope}
$P=\operatorname{conv}(S(c,r)\cap L)$.
A Delaunay polytope is called {\em perfect} if any affine transformation
$\phi$ such that $\phi(P)$ is a Delaunay polytope is necessarily
an isometry
of the space composed with an homothety.


Quasianalytic Ilyashenko algebras Speissegger, Patrick Published: 20170427
I construct a quasianalytic field $\mathcal{F}$ of germs at $+\infty$
of real functions with logarithmic generalized power series as
asymptotic expansions, such that $\mathcal{F}$ is closed under differentiation
and $\log$composition; in particular, $\mathcal{F}$ is a Hardy field.
Moreover, the field $\mathcal{F} \circ (\log)$ of germs at $0^+$ contains
all transition maps of hyperbolic saddles of planar real analytic
vector fields.


On Residues of Intertwining Operators in Cases with Prehomogeneous Nilradical Varma, Sandeep Published: 20161209
Let $\operatorname{P} = \operatorname{M} \operatorname{N}$ be a Levi decomposition of a maximal parabolic
subgroup of a connected
reductive group $\operatorname{G}$ over a $p$adic field $F$. Assume that there
exists $w_0 \in \operatorname{G}(F)$ that normalizes $\operatorname{M}$ and conjugates $\operatorname{P}$
to an opposite parabolic subgroup.
When $\operatorname{N}$ has a Zariski dense $\operatorname{Int} \operatorname{M}$orbit,
F. Shahidi and X. Yu describe a certain distribution $D$ on
$\operatorname{M}(F)$
such that,
for irreducible unitary supercuspidal representations $\pi$ of
$\operatorname{M}(F)$ with
$\pi \cong \pi \circ \operatorname{Int} w_0$,
$\operatorname{Ind}_{\operatorname{P}(F)}^{\operatorname{G}(F)} \pi$ is
irreducible
if and only if $D(f) \neq 0$ for some pseudocoefficient $f$ of
$\pi$. Since
this irreducibility is conjecturally related to $\pi$ arising
via
transfer from certain twisted endoscopic groups of $\operatorname{M}$, it is
of interest
to realize $D$ as endoscopic transfer from a simpler distribution
on a twisted
endoscopic group $\operatorname{H}$ of $\operatorname{M}$. This has been done in many situations
where $\operatorname{N}$ is abelian. Here, we handle the `standard examples'
in cases
where $\operatorname{N}$ is nonabelian but admits a Zariski dense
$\operatorname{Int} \operatorname{M}$orbit.


The algebraic de Rham cohomology of representation varieties Xia, Eugene Z. Author's Draft
The $\operatorname{SL}(2,\mathbb C)$representation varieties of punctured surfaces
form natural families parameterized by monodromies at the punctures.
In this paper, we compute the loci where these varieties are
singular for the cases of oneholed and twoholed tori and the
fourholed sphere. We then compute the de Rham cohomologies
of these varieties of the oneholed torus and the fourholed
sphere when the varieties are smooth via the Grothendieck theorem.
Furthermore, we produce the explicit GaussManin connection
on the natural family of the smooth $\operatorname{SL}(2,\mathbb C)$representation
varieties of the oneholed torus.


Anisotropic Sobolev Capacity with Fractional Order Xiao, Jie; Ye, Deping Published: 20160316
In this paper, we introduce the anisotropic
Sobolev capacity with fractional order and develop some basic
properties for this new object. Applications to the theory of
anisotropic fractional Sobolev spaces are provided. In particular,
we give geometric characterizations for a nonnegative Radon
measure $\mu$ that naturally induces an embedding of the anisotropic
fractional Sobolev class $\dot{\Lambda}_{\alpha,K}^{1,1}$ into
the $\mu$basedLebesguespace $L^{n/\beta}_\mu$ with $0\lt \beta\le
n$. Also, we investigate the anisotropic fractional $\alpha$perimeter.
Such a geometric quantity can be used to approximate the anisotropic
Sobolev capacity with fractional order. Estimation on the constant
in the related Minkowski inequality, which is asymptotically
optimal as $\alpha\rightarrow 0^+$, will be provided.


On Moeglin's parametrization of Arthur packets for padic quasisplit $Sp(N)$ and $SO(N)$ Xu, Bin Published: 20161110
We give a survey on Moeglin's construction of representations
in the Arthur packets for $p$adic quasisplit symplectic and
orthogonal groups. The emphasis is on comparing Moeglin's
parametrization of elements in the Arthur packets with that of
Arthur.


On a class of fully nonlinear elliptic equations containing gradient terms on compact Hermitian manifolds Yuan, Rirong Author's Draft
In this paper we study a class of second order fully nonlinear
elliptic equations
containing gradient terms on compact Hermitian manifolds and
obtain a priori estimates under
proper assumptions close to optimal.
The analysis developed here should
be useful to deal with other Hessian equations containing gradient
terms in other contexts.

