1. CJM Online first
 Lee, Jungyun; Lee, Yoonjin

Regulators of an infinite family of the simplest quartic function fields
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 $\{L_m\}$.
Keywords:regulator, function field, quartic extension, class number Categories:11R29, 11R58 

2. CJM Online first
 Lei, Antonio; Loeffler, David; Zerbes, Sarah Livia

On the asymptotic growth of BlochKatoShafarevichTate groups of modular forms over cyclotomic extensions
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.
Keywords:cyclotomic extension, ShafarevichTate group, BlochKato Selmer group, modular form, nonordinary prime, padic Hodge theory Categories:11R18, 11F11, 11R23, 11F85 

3. CJM Online first
 Pan, ShuYen

$L$Functoriality for Local Theta Correspondence of Supercuspidal Representations with Unipotent Reduction
The preservation principle of local theta correspondences of reductive dual pairs over
a $p$adic field predicts the existence of a sequence of irreducible supercuspidal
representations of classical groups.
Adams/HarrisKudlaSweet
have a conjecture
about the Langlands parameters for the sequence of supercuspidal representations.
In this paper we prove modified versions of their conjectures for the case of
supercuspidal representations with unipotent reduction.
Keywords:local theta correspondence, supercuspidal representation, preservation principle, Langlands functoriality Categories:22E50, 11F27, 20C33 

4. CJM Online first
 Lee, Hun Hee; Youn, Sanggyun

New deformations of convolution algebras and Fourier algebras on locally compact groups
In this paper we introduce a new way of deforming convolution
algebras and Fourier algebras on locally compact groups. We demonstrate
that this new deformation allows us to reveal some information
of the underlying groups by examining Banach algebra properties
of deformed algebras. More precisely, we focus on representability
as an operator algebra of deformed convolution algebras on compact
connected Lie groups with connection to the real dimension of
the underlying group. Similarly, we investigate complete representability
as an operator algebra of deformed Fourier algebras on some finitely
generated discrete groups with connection to the growth rate
of the group.
Keywords:Fourier algebra, convolution algebra, operator algebra, Beurling algebra Categories:43A20, 43A30, 47L30, 47L25 

5. CJM Online first
 Hartglass, Michael

Free product C*algebras associated to graphs, free differentials, and laws of loops
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.
Keywords:free probability, C*algebra Category:46L09 

6. CJM Online first
 Ovchinnikov, Alexey; Wibmer, Michael

Tannakian categories with semigroup actions
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.
Keywords:semigroup actions on categories, Tannakian categories, difference algebraic groups, differential and difference equations with parameters Categories:18D10, 12H10, 20G05, 33C05, 33C80, 34K06 

7. CJM Online first
 Chen, Xianghong; Seeger, Andreas

Convolution powers of Salem measures with applications
We study the regularity of convolution powers for measures supported
on
Salem sets, and prove related results on Fourier restriction
and Fourier multipliers. In particular we show
that for $\alpha$ of the form
${d}/{n}$, $n=2,3,\dots$ there exist $\alpha$Salem measures
for which the $L^2$ Fourier restriction theorem holds in the
range $p\le \frac{2d}{2d\alpha}$.
The results rely on ideas of KÃ¶rner.
We extend some of his constructions to obtain upper regular $\alpha$Salem
measures, with sharp regularity results for $n$fold convolutions
for all $n\in \mathbb{N}$.
Keywords:convolution powers, Fourier restriction, Salem sets, Salem measures, random sparse sets, Fourier multipliers of BochnerRiesz type Categories:42A85, 42B99, 42B15, 42A61 

8. CJM 2016 (vol 68 pp. 1382)
 Zydor, Michał

La Variante infinitÃ©simale de la formule des traces de JacquetRallis pour les groupes unitaires
We establish an infinitesimal version of the
JacquetRallis trace formula for unitary groups.
Our formula is obtained by integrating a
truncated kernel Ã la Arthur.
It has a geometric side which is a
sum of distributions $J_{\mathfrak{o}}$ indexed by classes of
elements
of the Lie algebra of $U(n+1)$ stable by $U(n)$conjugation
as well as the "spectral side"
consisting of the Fourier transforms
of the aforementioned distributions.
We prove that the distributions $J_{\mathfrak{o}}$
are invariant and depend only on the choice of
the Haar measure on $U(n)(\mathbb{A})$.
For regular semisimple classes $\mathfrak{o}$, $J_{\mathfrak{o}}$
is
a relative orbital integral of JacquetRallis.
For classes $\mathfrak{o}$ called relatively regular semisimple,
we express $J_{\mathfrak{o}}$
in terms of relative orbital integrals regularised by means of
zÃªta functions.
Keywords:formule des traces relative Categories:11F70, 11F72 

9. CJM Online first
10. CJM Online first
 Fischer, Vera; Mejia, Diego Alejandro

Splitting, Bounding, and Almost Disjointness can be quite Different
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.
Keywords:cardinal characteristics of the continuum, splitting, bounding number, maximal almostdisjoint families, template forcing iterations, isomorphismofnames Categories:03E17, 03E35, 03E40 

11. CJM 2016 (vol 68 pp. 1285)
 Ehrig, Michael; Stroppel, Catharina

2row Springer Fibres and Khovanov Diagram Algebras for Type D
We study in detail two row Springer fibres of even orthogonal
type from an algebraic as well as topological point of view.
We show that the irreducible components and their pairwise intersections
are iterated $\mathbb{P}^1$bundles. Using results of Kumar and Procesi
we compute the cohomology ring with its action of the Weyl group.
The main tool is a type $\operatorname D$ diagram calculus labelling the
irreducible components in a convenient way which relates to a
diagrammatical algebra describing the category of perverse sheaves
on isotropic Grassmannians based on work of Braden. The diagram
calculus generalizes Khovanov's arc algebra to the type
$\operatorname
D$ setting and should be seen as setting the framework for generalizing
wellknown connections of these algebras in type $\operatorname A$ to other
types.
Keywords:Springer fibers, Khovanov homology, Weyl group type D Category:1711 

12. CJM 2016 (vol 68 pp. 1120)
 Stange, Katherine E.

Integral Points on Elliptic Curves and Explicit Valuations of Division Polynomials
Assuming Lang's conjectured lower bound on the heights of nontorsion
points on an elliptic curve, we show that there exists an absolute
constant $C$ such that for any elliptic curve $E/\mathbb{Q}$ and nontorsion
point $P \in E(\mathbb{Q})$, there is at most one integral multiple
$[n]P$ such that $n \gt C$. The proof is a modification of a proof
of Ingram giving an unconditional but not uniform bound. The
new ingredient is a collection of explicit formulae for the
sequence $v(\Psi_n)$ of valuations of the division polynomials.
For $P$ of nonsingular reduction, such sequences are already
well described in most cases, but for $P$ of singular reduction,
we are led to define a new class of sequences called \emph{elliptic
troublemaker sequences}, which measure the failure of the NÃ©ron
local height to be quadratic. As a corollary in the spirit of
a conjecture of Lang and Hall, we obtain a uniform upper bound
on $\widehat{h}(P)/h(E)$ for integer points having two large
integral multiples.
Keywords:elliptic divisibility sequence, Lang's conjecture, height functions Categories:11G05, 11G07, 11D25, 11B37, 11B39, 11Y55, 11G50, 11H52 

13. CJM Online first
 Grinberg, Darij

Dual immaculate creation operators and a dendriform algebra structure on the quasisymmetric functions
The dual immaculate functions are a basis of the ring $\operatorname*{QSym}$
of quasisymmetric functions, and form one of the most natural
analogues of the
Schur functions. The dual immaculate function corresponding to
a composition
is a weighted generating function for immaculate tableaux in
the same way as a
Schur function is for semistandard Young tableaux; an "
immaculate tableau" is defined similarly to be
a semistandard
Young tableau, but the shape is a composition rather than a partition,
and
only the first column is required to strictly increase (whereas
the other
columns can be arbitrary; but each row has to weakly increase).
Dual
immaculate functions have been introduced by Berg, Bergeron,
Saliola, Serrano
and Zabrocki in arXiv:1208.5191, and have since been found to
possess numerous
nontrivial properties.
In this note, we prove a conjecture of Mike Zabrocki which provides
an
alternative construction for the dual immaculate functions in
terms of certain
"vertex operators". The proof uses a dendriform structure on
the ring
$\operatorname*{QSym}$; we discuss the relation of this structure
to known
dendriform structures on the combinatorial Hopf algebras
$\operatorname*{FQSym}$ and $\operatorname*{WQSym}$.
Keywords:combinatorial Hopf algebras, quasisymmetric functions, dendriform algebras, immaculate functions, Young tableaux Category:05E05 

14. CJM 2016 (vol 68 pp. 999)
 Izumi, Masaki; Morrison, Scott; Penneys, David

Quotients of $A_2 * T_2$
We study unitary quotients of the free product unitary pivotal
category $A_2*T_2$.
We show that such quotients are parametrized by an integer $n\geq
1$ and an $2n$th root of unity $\omega$.
We show that for $n=1,2,3$, there is exactly one quotient and
$\omega=1$.
For $4\leq n\leq 10$, we show that there are no such quotients.
Our methods also apply to quotients of $T_2*T_2$, where we have
a similar result.
The essence of our method is a consistency check on jellyfish
relations.
While we only treat the specific cases of $A_2 * T_2$ and $T_2
* T_2$, we anticipate that our technique can be extended to a
general method for proving nonexistence of planar algebras with
a specified principal graph.
During the preparation of this manuscript, we learnt of Liu's
independent result on composites of $A_3$ and $A_4$ subfactor
planar algebras
(arxiv:1308.5691).
In 1994, BischHaagerup showed that the principal graph of a
composite of $A_3$ and $A_4$ must fit into a certain family,
and Liu has classified all such subfactor planar algebras.
We explain the connection between the quotient categories and
the corresponding composite subfactor planar algebras.
As a corollary of Liu's result, there are no such quotient categories
for $n\geq 4$.
This is an abridged version of
arxiv:1308.5723.
Keywords:pivotal category, free product, quotient, subfactor, intermediate subfactor Category:46L37 

15. CJM Online first
 Kaftal, Victor; Ng, Ping Wong; Zhang, Shuang

Strict comparison of positive elements in multiplier algebras
Main result: If a C*algebra $\mathcal{A}$ is simple, $\sigma$unital,
has finitely many extremal traces, and has strict comparison
of positive elements by traces, then its multiplier algebra
$\operatorname{\mathcal{M}}(\mathcal{A})$
also has strict comparison of positive elements by traces. The
same results holds if ``finitely many extremal traces" is replaced
by ``quasicontinuous scale".
A key ingredient in the proof is that every positive element
in the multiplier algebra of an arbitrary $\sigma$unital C*algebra
can be approximated by a bidiagonal series.
An application of strict comparison: If $\mathcal{A}$ is a simple separable
stable C*algebra with real rank zero, stable rank one, and
strict comparison of positive elements by traces, then whether
a positive element is a positive linear combination of projections
is determined by the trace values of its range projection.
Keywords:strict comparison, bidiagonal form, positive combinations Categories:46L05, 46L35, 46L45, 47C15 

16. CJM Online first
 Günther, Christian; Schmidt, KaiUwe

$L^q$ norms of Fekete and related polynomials
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 ErdÅs, 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.
Keywords:character polynomial, Fekete polynomial, $L^q$ norm, Littlewood polynomial Categories:11B83, 42A05, 30C10 

17. CJM 2016 (vol 68 pp. 1201)
 Banks, Jessica; Rathbun, Matt

Monodromy Action on Unknotting Tunnels in Fiber Surfaces
In \cite{RatTOFL}, the second author showed that a tunnel of a tunnel
number one, fibered link in $S^3$ can be isotoped to lie as a properly
embedded arc in the fiber surface of the link. In this paper, we
observe that this is true for fibered links in any 3manifold, we
analyze how the arc behaves under the monodromy action, and we show
that the tunnel arc is nearly clean, with the possible exception of
twisting around the boundary of the fiber.
Keywords:fibered, monodromy, tunnel, clean Category:57M25 

18. CJM Online first
 Brandes, Julia; Parsell, Scott T.

Simultaneous additive equations: Repeated and differing degrees
We obtain bounds for the number of variables required to establish
Hasse principles, both for existence of solutions and for asymptotic
formulÃ¦, for systems of additive equations containing forms
of differing degree but also multiple forms of like degree.
Apart from the very general estimates of Schmidt and BrowningHeathBrown,
which give weak results when specialized to the diagonal situation,
this is the first result on such "hybrid" systems. We also obtain
specialised results for systems of quadratic and cubic forms,
where we are able to take advantage of some of the stronger methods
available in that setting. In particular, we achieve essentially
square root cancellation for systems consisting of one cubic
and $r$ quadratic equations.
Keywords:equations in many variables, counting solutions of Diophantine equations, applications of the HardyLittlewood method Categories:11D72, 11D45, 11P55 

19. CJM Online first
20. CJM 2016 (vol 68 pp. 961)
21. CJM Online first
 Andrade, Jaime; Dávila, Nestor; PérezChavela, Ernesto; Vidal, Claudio

Dynamics and regularization of the Kepler problem on surfaces of constant curvature
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.
Keywords:Kepler problem on surfaces of constant curvature, Hill's region, singularities, regularization, qualitative analysis of ODE Categories:70F16, 70G60 

22. CJM Online first
 Kamgarpour, Masoud

On the notion of conductor in the local geometric Langlands correspondence
Under the local Langlands correspondence, the conductor of an
irreducible representation of $\operatorname{Gl}_n(F)$ is greater than the
Swan conductor of the corresponding Galois representation. In
this paper, we establish the geometric analogue of this statement
by showing that the conductor of a categorical representation
of the loop group is greater than the irregularity of the corresponding
meromorphic connection.
Keywords:local geometric Langlands, connections, cyclic vectors, opers, conductors, SegalSugawara operators, ChervovMolev operators, critical level, smooth representations, affine KacMoody algebra, categorical representations Categories:17B67, 17B69, 22E50, 20G25 

23. CJM Online first
 Marquis, Timothée; Neeb, KarlHermann

Isomorphisms of twisted Hilbert loop algebras
The closest infinite dimensional relatives of compact Lie algebras are HilbertLie algebras, i.e. real Hilbert spaces with a Lie
algebra
structure for which the scalar product is invariant.
Locally affine Lie algebras (LALAs)
correspond to double extensions of (twisted) loop algebras
over simple HilbertLie algebras $\mathfrak{k}$, also called
affinisations of $\mathfrak{k}$.
They possess a root space decomposition
whose corresponding root system is a locally affine root system
of one of the $7$ families $A_J^{(1)}$, $B_J^{(1)}$, $C_J^{(1)}$,
$D_J^{(1)}$, $B_J^{(2)}$, $C_J^{(2)}$ and $BC_J^{(2)}$ for some
infinite set $J$. To each of these types corresponds a ``minimal"
affinisation of some simple HilbertLie algebra $\mathfrak{k}$,
which we call standard.
In this paper, we give for each affinisation $\mathfrak{g}$ of
a simple HilbertLie algebra $\mathfrak{k}$ an explicit isomorphism
from $\mathfrak{g}$ to one of the standard affinisations of $\mathfrak{k}$. The existence of such an isomorphism could also be derived from
the classification
of locally affine root systems, but
for representation theoretic purposes it is crucial to obtain
it explicitly
as a deformation between two twists which is compatible
with the root decompositions.
We illustrate this by applying our isomorphism theorem to the
study of positive energy highest weight representations of $\mathfrak{g}$.
In subsequent work, the present paper will be used to obtain
a complete classification
of the positive energy highest weight representations of affinisations
of $\mathfrak{k}$.
Keywords:locally affine Lie algebra, HilbertLie algebra, positive energy representation Categories:17B65, 17B70, 17B22, 17B10 

24. CJM Online first
 Hartz, Michael

On the isomorphism problem for multiplier algebras of NevanlinnaPick spaces
We continue the investigation of the isomorphism problem for
multiplier algebras of reproducing kernel
Hilbert spaces with the complete NevanlinnaPick property.
In contrast to previous work in this area,
we do not study these spaces by identifying them with restrictions
of a universal space, namely the DruryArveson space.
Instead, we work directly with the Hilbert spaces and their
reproducing kernels. In particular,
we show that two multiplier algebras of NevanlinnaPick spaces
on the same set are equal if and only if the Hilbert
spaces are equal. Most of the article is devoted to the study
of a special class of
complete NevanlinnaPick spaces on homogeneous varieties. We
provide a complete
answer to the question of when two multiplier algebras of spaces
of this type
are algebraically or isometrically isomorphic. This generalizes
results of Davidson, Ramsey, Shalit,
and the author.
Keywords:nonselfadjoint operator algebras, reproducing kernel Hilbert spaces, multiplier algebra, NevanlinnaPick kernels, isomorphism problem Categories:47L30, 46E22, 47A13 

25. CJM 2016 (vol 68 pp. 1227)
 Brasca, Riccardo

Eigenvarieties for Cuspforms over PEL Type Shimura Varieties with Dense Ordinary locus
Let $p \gt 2$ be a prime and let $X$ be a compactified PEL Shimura
variety of type (A) or (C) such that $p$ is an unramified prime
for the PEL datum and such that the ordinary locus is dense in
the reduction of $X$. Using the geometric approach of Andreatta,
Iovita, Pilloni, and Stevens we define the notion of families
of overconvergent locally analytic $p$adic modular forms of
Iwahoric level for $X$. We show that the system of eigenvalues
of any finite slope cuspidal eigenform of Iwahoric level can
be deformed to a family of systems of eigenvalues living over
an open subset of the weight space. To prove these results, we
actually construct eigenvarieties of the expected dimension that
parameterize finite slope systems of eigenvalues appearing in
the space of families of cuspidal forms.
Keywords:$p$adic modular forms, eigenvarieties, PELtype Shimura varieties Categories:11F55, 11F33 
