1. CJM Online first
 Smith, Jerrod Manford

Relative discrete series representations for two quotients of $p$adic $\mathbf{GL}_n$
We provide an explicit construction of representations in the
discrete spectrum of two $p$adic symmetric spaces. We consider
$\mathbf{GL}_n(F) \times \mathbf{GL}_n(F) \backslash \mathbf{GL}_{2n}(F)$
and $\mathbf{GL}_n(F) \backslash \mathbf{GL}_n(E)$, where $E$
is a quadratic Galois extension of a nonarchimedean local field
$F$ of characteristic zero and odd residual characteristic. The
proof of the main result involves an application of a symmetric
space version of Casselman's Criterion for square integrability
due to Kato and Takano.
Keywords:$p$adic symmetric space, relative discrete series, Casselmanâs Criterion Categories:22E50, 22E35 

2. CJM 2013 (vol 66 pp. 721)
 DurandCartagena, E.; Ihnatsyeva, L.; Korte, R.; Szumańska, M.

On Whitneytype Characterization of Approximate Differentiability on Metric Measure Spaces
We study approximately differentiable functions on metric measure spaces admitting a Cheeger differentiable structure. The main result is a Whitneytype characterization of approximately differentiable functions in this setting.
As an application, we prove a Stepanovtype theorem and consider approximate differentiability of Sobolev, $BV$ and maximal functions.
Keywords:approximate differentiability, metric space, strong measurable differentiable structure, Whitney theorem Categories:26B05, 28A15, 28A75, 46E35 

3. CJM 2012 (vol 65 pp. 757)
 Delanoë, Philippe; Rouvière, François

Positively Curved Riemannian Locally Symmetric Spaces are Positively Squared Distance Curved
The squared distance curvature is a kind of twopoint curvature the
sign of which turned out crucial for the smoothness of optimal
transportation maps on Riemannian manifolds. Positivity properties of
that new curvature have been established recently for all the simply
connected compact rank one symmetric spaces, except the Cayley
plane. Direct proofs were given for the sphere, an indirect one
via the Hopf fibrations) for the complex and quaternionic
projective spaces. Here, we present a direct proof of a property
implying all the preceding ones, valid on every positively curved
Riemannian locally symmetric space.
Keywords:symmetric spaces, rank one, positive curvature, almostpositive $c$curvature Categories:53C35, 53C21, 53C26, 49N60 

4. CJM 2012 (vol 65 pp. 222)
 Sauer, N. W.

Distance Sets of Urysohn Metric Spaces
A metric space $\mathrm{M}=(M;\operatorname{d})$ is {\em homogeneous} if for every
isometry $f$ of a finite subspace of $\mathrm{M}$ to a subspace of
$\mathrm{M}$ there exists an isometry of $\mathrm{M}$ onto
$\mathrm{M}$ extending $f$. The space $\mathrm{M}$ is {\em universal}
if it isometrically embeds every finite metric space $\mathrm{F}$ with
$\operatorname{dist}(\mathrm{F})\subseteq \operatorname{dist}(\mathrm{M})$. (With
$\operatorname{dist}(\mathrm{M})$ being the set of distances between points in
$\mathrm{M}$.)
A metric space $\boldsymbol{U}$ is an {\em Urysohn} metric space if
it is homogeneous, universal, separable and complete. (It is not
difficult to deduce
that an Urysohn metric space $\boldsymbol{U}$ isometrically embeds
every separable metric space $\mathrm{M}$ with
$\operatorname{dist}(\mathrm{M})\subseteq \operatorname{dist}(\boldsymbol{U})$.)
The main results are: (1) A characterization of the sets
$\operatorname{dist}(\boldsymbol{U})$ for Urysohn metric spaces $\boldsymbol{U}$.
(2) If $R$ is the distance set of an Urysohn metric space and
$\mathrm{M}$ and $\mathrm{N}$ are two metric spaces, of any
cardinality with distances in $R$, then they amalgamate disjointly to
a metric space with distances in $R$. (3) The completion of every
homogeneous, universal, separable metric space $\mathrm{M}$ is
homogeneous.
Keywords:partitions of metric spaces, Ramsey theory, metric geometry, Urysohn metric space, oscillation stability Categories:03E02, 22F05, 05C55, 05D10, 22A05, 51F99 

5. CJM 2009 (vol 61 pp. 351)
 Graham, William; Hunziker, Markus

Multiplication of Polynomials on Hermitian Symmetric spaces and LittlewoodRichardson Coefficients
Let $K$ be a complex reductive algebraic group and $V$ a
representation of $K$. Let $S$ denote the ring of polynomials on
$V$. Assume that the action of $K$ on $S$ is multiplicityfree. If
$\lambda$ denotes the isomorphism class of an irreducible
representation of $K$, let $\rho_\lambda\from K \rightarrow
GL(V_{\lambda})$ denote the corresponding irreducible representation
and $S_\lambda$ the $\lambda$isotypic component of $S$. Write
$S_\lambda \cdot S_\mu$ for the subspace of $S$ spanned by products of
$S_\lambda$ and $S_\mu$. If $V_\nu$ occurs as an irreducible
constituent of $V_\lambda\otimes V_\mu$, is it true that
$S_\nu\subseteq S_\lambda\cdot S_\mu$? In this paper, the authors
investigate this question for representations arising in the context
of Hermitian symmetric pairs. It is shown that the answer is yes in
some cases and, using an earlier result of Ruitenburg, that in the
remaining classical cases, the answer is yes provided that a
conjecture of Stanley on the multiplication of Jack polynomials is
true. It is also shown how the conjecture connects multiplication in
the ring $S$ to the usual LittlewoodRichardson rule.
Keywords:Hermitian symmetric spaces, multiplicity free actions, LittlewoodRichardson coefficients, Jack polynomials Categories:14L30, 22E46 

6. CJM 2007 (vol 59 pp. 1135)
 Björn, Anders; Björn, Jana; Shanmugalingam, Nageswari

Sobolev Extensions of HÃ¶lder Continuous and Characteristic Functions on Metric Spaces
We study when characteristic and H\"older continuous functions
are traces of Sobolev functions on doubling metric measure spaces.
We provide analytic and geometric conditions sufficient for extending
characteristic and H\"older continuous functions into globally defined
Sobolev functions.
Keywords:characteristic function, Newtonian function, metric space, resolutivity, HÃ¶lder continuous, Perron solution, $p$harmonic, Sobolev extension, Whitney covering Categories:46E35, 31C45 

7. CJM 2002 (vol 54 pp. 1305)