1. CJM Online first
 Fité, Francesc; González, Josep; Lario, Joan Carles

Frobenius distribution for quotients of Fermat curves of prime exponent
Let $\mathcal{C}$ denote the Fermat curve over $\mathbb{Q}$ of prime
exponent $\ell$. The Jacobian $\operatorname{Jac}(\mathcal{C})$
of~$\mathcal{C}$ splits over $\mathbb{Q}$ as the product of Jacobians
$\operatorname{Jac}(\mathcal{C}_k)$, $1\leq k\leq \ell2$, where
$\mathcal{C}_k$ are curves obtained as quotients of $\mathcal{C}$ by
certain subgroups of automorphisms of $\mathcal{C}$. It is well known
that $\operatorname{Jac}(\mathcal{C}_k)$ is the power of an absolutely
simple abelian variety $B_k$ with complex multiplication. We call
degenerate those pairs $(\ell,k)$ for which $B_k$ has degenerate CM
type. For a nondegenerate pair $(\ell,k)$, we compute the SatoTate
group of $\operatorname{Jac}(\mathcal{C}_k)$, prove the generalized
SatoTate Conjecture for it, and give an explicit method to compute
the moments and measures of the involved distributions. Regardless of
$(\ell,k)$ being degenerate or not, we also obtain Frobenius
equidistribution results for primes of certain residue degrees in the
$\ell$th cyclotomic field. Key to our results is a detailed study of
the rank of certain generalized Demjanenko matrices.
Keywords:SatoTate group, Fermat curve, Frobenius distribution Categories:11D41, 11M50, 11G10, 14G10 

2. 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 

3. CJM Online first
 Garibaldi, Skip; Nakano, Daniel K.

Bilinear and quadratic forms on rational modules of split reductive groups
The representation theory of semisimple algebraic groups over
the complex numbers (equivalently, semisimple complex Lie algebras
or Lie groups, or real compact Lie groups) and the question of
whether a
given complex representation is symplectic or orthogonal has
been solved since at least the 1950s. Similar results for Weyl
modules of split reductive groups over fields of characteristic
different from 2 hold by
using similar proofs. This paper considers analogues of these
results for simple, induced and tilting modules of split reductive
groups over fields of prime characteristic as well as a complete
answer for Weyl modules over fields of characteristic 2.
Keywords:orthogonal representations, symmetric tensors, alternating forms, characteristic 2, split reductive groups Categories:20G05, 11E39, 11E88, 15A63, 20G15 

4. CJM Online first
 da Silva, Genival; Kerr, Matt; Pearlstein, Gregory

Arithmetic of degenerating principal variations of Hodge structure: examples arising from mirror symmetry and middle convolution
We collect evidence in support of a conjecture of Griffiths,
Green
and Kerr
on the arithmetic of extension classes of
limiting
mixed Hodge structures arising from semistable degenerations
over
a number field. After briefly summarizing how a result of Iritani
implies this conjecture for a collection of hypergeometric
CalabiYau threefold examples studied by Doran and Morgan,
the authors investigate a sequence of (nonhypergeometric) examples
in dimensions $1\leq d\leq6$ arising from Katz's theory of the
middle
convolution.
A crucial role is played by the MumfordTate
group (which is $G_{2}$) of the family of 6folds, and the theory
of boundary components of MumfordTate domains.
Keywords:variation of Hodge structure, limiting mixed Hodge structure, CalabiYau variety, middle convolution, MumfordTate group Categories:14D07, 14M17, 17B45, 20G99, 32M10, 32G20 

5. CJM Online first
 Bacher, Roland; Reutenauer, Christophe

Number of right ideals and a $q$analogue of indecomposable permutations
We prove that the number of right ideals of codimension $n$ in
the algebra of noncommutative Laurent polynomials in two variables over the finite field $\mathbb F_q$ is equal to
$(q1)^{n+1} q^{\frac{(n+1)(n2)}{2}}\sum_\theta q^{inv(\theta)}$,
where the
sum is over all indecomposable permutations in $S_{n+1}$ and
where $inv(\theta)$
stands for the number of inversions of $\theta$.
Keywords:permutation, indecomposable permutation, subgroups of free groups Categories:05A15, 05A19 

6. 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 

7. CJM Online first
 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 

8. CJM Online first
9. CJM Online first
 Xiao, Jie; Ye, Deping

Anisotropic Sobolev Capacity with Fractional Order
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.
Keywords:sharpness, isoperimetric inequality, Minkowski inequality, fractional Sobolev capacity, fractional perimeter Categories:52A38, 53A15, 53A30 

10. CJM Online first
 De Bernardi, Carlo Alberto; Veselý, Libor

Tilings of normed spaces
By a tiling of a topological linear space $X$ we mean a
covering of $X$ by at least two closed convex sets,
called tiles, whose nonempty interiors are
pairwise disjoint.
Study of tilings of infinitedimensional spaces initiated in
the
1980's with pioneer papers by V. Klee.
We prove some general properties of tilings of locally convex
spaces,
and then apply these results to study existence of tilings of
normed and Banach spaces by tiles possessing
certain smoothness or rotundity properties. For a Banach space
$X$,
our main results are the following.
1. $X$ admits no tiling by FrÃ©chet smooth bounded tiles.
2. If $X$ is locally uniformly rotund (LUR), it does not admit
any tiling by balls.
3. On the other hand, some $\ell_1(\Gamma)$ spaces, $\Gamma$
uncountable, do admit
a tiling by pairwise disjoint LUR bounded tiles.
Keywords:tiling of normed space, FrÃ©chet smooth body, locally uniformly rotund body, $\ell_1(\Gamma)$space Categories:46B20, 52A99, 46A45 

11. CJM Online first
 Moon, HanBom

Mori's program for $\overline{M}_{0,7}$ with symmetric divisors
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.
Keywords:moduli of curves, minimal model program, Mori dream space Categories:14H10, 14E30 

12. CJM Online first
 Garbagnati, Alice

On K3 surface quotients of K3 or Abelian surfaces
The aim of this paper is to prove that a K3 surface is the minimal
model of the quotient of an Abelian surface by a group $G$ (respectively
of a K3 surface by an Abelian group $G$) if and only if a certain
lattice is primitively embedded in its NÃ©ronSeveri group.
This allows one to describe the coarse moduli space of the K3
surfaces which are (rationally) $G$covered by Abelian or K3
surfaces (in the latter case $G$ is an Abelian group).
If either $G$ has order 2 or $G$ is cyclic and acts on an Abelian
surface, this result was already known, so we extend it to the
other cases.
Moreover, we prove that a K3 surface $X_G$ is the minimal model
of the quotient of an Abelian surface by a group $G$ if and only
if a certain configuration of rational curves is present on $X_G$.
Again this result was known only in some special cases, in particular
if $G$ has order 2 or 3.
Keywords:K3 surfaces, Kummer surfaces, Kummer type lattice, quotient surfaces Categories:14J28, 14J50, 14J10 

13. CJM Online first
 Klep, Igor; Špenko, Špela

Free function theory through matrix invariants
This paper concerns free function theory. Free maps are free
analogs of analytic functions in several complex variables,
and are defined in terms of freely noncommuting variables.
A function of $g$ noncommuting variables is a function on $g$tuples
of square matrices of all sizes that respects direct sums and
simultaneous conjugation.
Examples of such maps include noncommutative polynomials, noncommutative
rational functions and convergent noncommutative power series.
In sharp contrast to the existing literature in free analysis, this article
investigates free maps \emph{with involution} 
free analogs of real analytic functions.
To
get a grip on these,
techniques and tools from invariant theory are developed and
applied to free analysis. Here is a sample of the results obtained.
A characterization of polynomial free maps via properties of
their finitedimensional slices is presented and then used to
establish power series expansions for analytic free maps about
scalar and nonscalar points; the latter are series of generalized
polynomials for which an invarianttheoretic characterization
is given.
Furthermore,
an inverse and implicit function theorem for free maps with
involution is obtained.
Finally, with a selection of carefully chosen examples
it is shown that
free maps with involution
do not exhibit strong rigidity properties
enjoyed by their involutionfree
counterparts.
Keywords:free algebra, free analysis, invariant theory, polynomial identities, trace identities, concomitants, analytic maps, inverse function theorem, generalized polynomials Categories:16R30, 32A05, 46L52, 15A24, 47A56, 15A24, 46G20 

14. CJM 2015 (vol 68 pp. 179)
 Takeda, Shuichiro

Metaplectic Tensor Products for Automorphic Representation of $\widetilde{GL}(r)$
Let $M=\operatorname{GL}_{r_1}\times\cdots\times\operatorname{GL}_{r_k}\subseteq\operatorname{GL}_r$ be a Levi
subgroup of $\operatorname{GL}_r$, where $r=r_1+\cdots+r_k$, and $\widetilde{M}$ its metaplectic preimage
in the $n$fold metaplectic cover $\widetilde{\operatorname{GL}}_r$ of $\operatorname{GL}_r$. For automorphic
representations $\pi_1,\dots,\pi_k$ of $\widetilde{\operatorname{GL}}_{r_1}(\mathbb{A}),\dots,\widetilde{\operatorname{GL}}_{r_k}(\mathbb{A})$,
we construct (under a certain
technical assumption, which is always satisfied when $n=2$) an
automorphic representation $\pi$
of $\widetilde{M}(\mathbb{A})$ which can be considered as the ``tensor product'' of the
representations $\pi_1,\dots,\pi_k$. This is
the global analogue of the metaplectic tensor product
defined by P. Mezo in the sense that locally at each place $v$,
$\pi_v$ is equivalent to the local metaplectic tensor product of
$\pi_{1,v},\dots,\pi_{k,v}$ defined by Mezo. Then we show that if all
of $\pi_i$ are cuspidal (resp. squareintegrable modulo center), then
the metaplectic tensor product is cuspidal (resp. squareintegrable
modulo center). We also show that (both
locally and globally) the metaplectic tensor product behaves in the
expected way under the action of a Weyl group element, and show the
compatibility with parabolic inductions.
Keywords:automorphic forms, representations of covering groups Category:11F70 

15. CJM Online first
 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 

16. CJM Online first
 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 

17. CJM Online first
 Zheng, Tao

The ChernRicci flow on OeljeklausToma manifolds
We study the ChernRicci flow, an evolution equation of Hermitian
metrics, on a family of OeljeklausToma (OT) manifolds which
are nonKÃ¤hler compact complex manifolds with negative Kodaira
dimension. We prove that, after an initial conformal change,
the flow converges, in the
GromovHausdorff sense, to a torus with a flat Riemannian metric
determined by the OTmanifolds themselves.
Keywords:ChernRicci flow, OeljeklausToma manifold, Calabitype estimate, GromovHausdorff convergence Categories:53C44, 53C55, 32W20, 32J18, 32M17 

18. CJM Online first
 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 

19. CJM 2015 (vol 68 pp. 44)
 Fernández Bretón, David J.

Strongly Summable Ultrafilters, Union Ultrafilters, and the Trivial Sums Property
We answer two questions of Hindman, SteprÄns and Strauss,
namely we prove that every
strongly summable
ultrafilter on an abelian group is sparse and has the trivial
sums property. Moreover we
show that in most
cases the sparseness of the given ultrafilter is a
consequence of its being isomorphic to a union ultrafilter. However,
this does not happen
in all cases:
we also construct (assuming Martin's Axiom for countable partial
orders, i.e.
$\operatorname{cov}(\mathcal{M})=\mathfrak c$), on the
Boolean group, a strongly summable ultrafilter that
is not additively isomorphic to any union ultrafilter.
Keywords:ultrafilter, StoneCech compactification, sparse ultrafilter, strongly summable ultrafilter, union ultrafilter, finite sum, additive isomorphism, trivial sums property, Boolean group, abelian group Categories:03E75, 54D35, 54D80, 05D10, 05A18, 20K99 

20. CJM 2015 (vol 68 pp. 3)
 Boden, Hans Ulysses; Curtis, Cynthia L

The SL$(2, C)$ Casson Invariant for Knots and the $\hat{A}$polynomial
In this paper, we extend the definition of the ${SL(2, {\mathbb C})}$ Casson
invariant
to arbitrary knots $K$ in integral homology 3spheres and relate
it to the $m$degree of the $\widehat{A}$polynomial of $K$. We
prove a product formula for the $\widehat{A}$polynomial of the connected
sum $K_1 \# K_2$ of two knots in $S^3$ and deduce additivity
of ${SL(2, {\mathbb C})}$ Casson knot invariant under connected sum for a large
class of knots in $S^3$. We also present an example of a nontrivial
knot $K$ in $S^3$ with trivial $\widehat{A}$polynomial and trivial
${SL(2, {\mathbb C})}$ Casson knot invariant, showing that neither of these invariants
detect the unknot.
Keywords:Knots, 3manifolds, character variety, Casson invariant, $A$polynomial Categories:57M27, 57M25, 57M05 

21. 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 

22. CJM Online first
 Doran, Charles F.; Harder, Andrew

Toric Degenerations and Laurent polynomials related to Givental's LandauGinzburg models
For an appropriate class of Fano complete intersections in toric
varieties, we prove that there is a concrete relationship between
degenerations to specific toric subvarieties and expressions
for Givental's LandauGinzburg models as Laurent polynomials.
As a result, we show that Fano varieties presented as complete
intersections in partial flag manifolds admit degenerations to
Gorenstein toric weak Fano varieties, and their Givental LandauGinzburg
models can be expressed as corresponding Laurent polynomials.
We also use this to show that all of the Laurent polynomials
obtained by Coates, Kasprzyk and Prince by the so called Przyjalkowski
method correspond to toric degenerations of the corresponding
Fano variety. We discuss applications to geometric transitions
of CalabiYau varieties.
Keywords:Fano varieties, LandauGinzburg models, CalabiYau varieties, toric varieties Categories:14M25, 14J32, 14J33, 14J45 

23. CJM 2015 (vol 68 pp. 109)
 Kopotun, Kirill; Leviatan, Dany; Shevchuk, Igor

Constrained Approximation with Jacobi Weights
In this paper, we prove that, for $\ell=1$ or $2$, the rate of
best $\ell$monotone polynomial approximation in the $L_p$
norm ($1\leq p \leq \infty$) weighted by the Jacobi weight
$w_{\alpha,\beta}(x)
:=(1+x)^\alpha(1x)^\beta$ with $\alpha,\beta\gt 1/p$
if $p\lt \infty$, or $\alpha,\beta\geq
0$ if $p=\infty$,
is bounded by an appropriate $(\ell+1)$st modulus of smoothness
with the same weight, and that this rate cannot be bounded by
the $(\ell+2)$nd modulus. Related results on constrained weighted
spline approximation and applications of our estimates are also
given.
Keywords:constrained approximation, Jacobi weights, weighted moduli of smoothness, exact estimates, exact orders Categories:41A29, 41A10, 41A15, 41A17, 41A25 

24. CJM 2015 (vol 68 pp. 67)
25. CJM 2015 (vol 68 pp. 150)
 Stavrova, Anastasia

Nonstable $K_1$functors of Multiloop Groups
Let $k$ be a field of characteristic 0. Let $G$ be a reductive
group over the ring of Laurent polynomials
$R=k[x_1^{\pm 1},...,x_n^{\pm 1}]$. Assume that $G$ contains
a maximal $R$torus, and
that every semisimple normal subgroup of $G$ contains a twodimensional
split torus $\mathbf{G}_m^2$.
We show that the natural map of nonstable $K_1$functors, also
called Whitehead groups,
$K_1^G(R)\to K_1^G\bigl( k((x_1))...((x_n)) \bigr)$ is injective,
and an isomorphism if $G$ is semisimple.
As an application, we provide a way to compute the difference
between the
full automorphism group of a Lie torus (in the sense of YoshiiNeher)
and the subgroup generated by
exponential automorphisms.
Keywords:loop reductive group, nonstable $K_1$functor, Whitehead group, Laurent polynomials, Lie torus Categories:20G35, 19B99, 17B67 
