1. CJM 2016 (vol 68 pp. 784)
 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 

2. 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 

3. CJM 2013 (vol 67 pp. 132)
 Clouâtre, Raphaël

Unitary Equivalence and Similarity to Jordan Models for Weak Contractions of Class $C_0$
We obtain results on the unitary equivalence of weak contractions of
class $C_0$ to their Jordan models under an assumption on their
commutants. In particular, our work addresses the case of arbitrary
finite multiplicity. The main tool is the
theory of boundary representations due to Arveson. We also
generalize and improve previously known results concerning unitary
equivalence and similarity to Jordan models when the minimal function
is a Blaschke product.
Keywords:weak contractions, operators of class $C_0$, Jordan model, unitary equivalence Categories:47A45, 47L55 

4. CJM 2013 (vol 66 pp. 903)
 Sargsyan, Grigor; Trang, Nam

Nontame Mice from Tame Failures of the Unique Branch Hypothesis
In this paper, we show that the failure of the unique branch
hypothesis (UBH) for tame trees
implies that in some homogenous generic extension of $V$ there is a
transitive model $M$ containing $Ord \cup \mathbb{R}$ such that
$M\vDash \mathsf{AD}^+ + \Theta \gt \theta_0$. In particular, this
implies the existence (in $V$) of a nontame mouse. The results of
this paper significantly extend J. R. Steel's earlier results
for tame trees.
Keywords:mouse, inner model theory, descriptive set theory, hod mouse, core model induction, UBH Categories:03E15, 03E45, 03E60 

5. CJM 2013 (vol 65 pp. 1125)
 Vandenbergen, Nicolas

On the Global Structure of Special Cycles on Unitary Shimura Varieties
In this paper, we study the reduced loci of special cycles on local
models of the Shimura variety for $\operatorname{GU}(1,n1)$. Those special cycles are defined by Kudla and Rapoport. We explicitly compute the irreducible components of the reduced locus of a single special cycle, as well as of an arbitrary intersection of special cycles, and their intersection behaviour in terms of BruhatTits
theory. Furthermore, as an application of our results, we prove the connectedness of arbitrary intersections of special cycles, as conjectured by Kudla and Rapoport.
Keywords:Shimura varieties, local models, special cycles Category:14G35 

6. CJM 2013 (vol 66 pp. 387)
 Mashreghi, J.; Shabankhah, M.

Composition of Inner Functions
We study the image of the model subspace $K_\theta$ under the
composition operator $C_\varphi$, where $\varphi$ and $\theta$ are
inner functions, and find the smallest model subspace which contains
the linear manifold $C_\varphi K_\theta$. Then we characterize the
case when $C_\varphi$ maps $K_\theta$ into itself. This case leads to
the study of the inner functions $\varphi$ and $\psi$ such that the
composition $\psi\circ\varphi$ is a divisor of $\psi$ in the family of
inner functions.
Keywords:composition operators, inner functions, Blaschke products, model subspaces Categories:30D55, 30D05, 47B33 

7. CJM 2012 (vol 65 pp. 1020)
 Goulden, I. P.; GuayPaquet, Mathieu; Novak, Jonathan

Monotone Hurwitz Numbers in Genus Zero
Hurwitz numbers count branched covers of the Riemann sphere with specified ramification data, or equivalently, transitive permutation factorizations in the symmetric group with specified cycle types. Monotone Hurwitz numbers count a restricted subset of these branched covers related to the expansion of complete symmetric functions in the JucysMurphy elements, and have arisen in recent work on the the asymptotic expansion of the HarishChandraItzyksonZuber integral. In this paper we begin a detailed study of monotone Hurwitz numbers. We prove two results that are reminiscent of those for classical Hurwitz numbers. The first is the monotone joincut equation, a partial differential equation with initial conditions that characterizes the generating function for monotone Hurwitz numbers in arbitrary genus. The second is our main result, in which we give an explicit formula for monotone Hurwitz numbers in genus zero.
Keywords:Hurwitz numbers, matrix models, enumerative geometry Categories:05A15, 14E20, 15B52 

8. CJM 2009 (vol 61 pp. 1325)
 Nien, Chufeng

Uniqueness of Shalika Models
Let $\BF_q$ be a finite field of $q$ elements, $\CF$ a $p$adic field,
and $D$ a quaternion division algebra over $\CF$. This paper proves
uniqueness of Shalika models for $\GL_{2n}(\BF_q) $ and $\GL_{2n}(D)$,
and reobtains uniqueness of Shalika models for $\GL_{2n}(\CF)$ for
any $n\in \BN$.
Keywords:Shalika models, linear models, uniqueness, multiplicity free Category:22E50 

9. CJM 2009 (vol 61 pp. 222)
10. CJM 2008 (vol 60 pp. 734)
 Baba, Srinath; Granath, H\aa kan

Genus 2 Curves with Quaternionic Multiplication
We explicitly construct the canonical rational models of Shimura
curves, both analytically in terms of modular forms and
algebraically in terms of coefficients of genus 2 curves, in the
cases of quaternion algebras of discriminant 6 and 10. This emulates
the classical construction in the elliptic curve case. We also give
families of genus 2 QM curves, whose Jacobians are the corresponding
abelian surfaces on the Shimura curve, and with coefficients that
are modular forms of weight 12. We apply these results to show
that our $j$functions are supported exactly at those primes where
the genus 2 curve does not admit potentially good reduction, and
construct fields where this potentially good reduction is attained.
Finally, using $j$, we construct the fields of moduli and definition
for some moduli problems associated to the AtkinLehner group
actions.
Keywords:Shimura curve, canonical model, quaternionic multiplication, modular form, field of moduli Categories:11G18, 14G35 

11. CJM 2006 (vol 58 pp. 1095)
 Sakellaridis, Yiannis

A CasselmanShalika Formula for the Shalika Model of $\operatorname{GL}_n$
The CasselmanShalika method is a way to compute explicit
formulas for periods of irreducible unramified representations of
$p$adic groups that are associated to unique models (i.e.,
multiplicityfree induced representations). We apply this method
to the case of the Shalika model of $GL_n$, which is known to
distinguish lifts from odd orthogonal groups. In the course of our
proof, we further develop a variant of the method, that was
introduced by Y. Hironaka, and in effect reduce many such problems
to straightforward calculations on the group.
Keywords:CasselmanShalika, periods, Shalika model, spherical functions, Gelfand pairs Categories:22E50, 11F70, 11F85 

12. CJM 2004 (vol 56 pp. 1290)
 Scull, Laura

Equivariant Formality for Actions of Torus Groups
This paper contains a comparison of several
definitions of equivariant formality for actions of torus groups. We
develop and prove some relations between the definitions. Focusing on
the case of the circle group, we use $S^1$equivariant minimal models
to give a number of examples of $S^1$spaces illustrating the
properties of the various definitions.
Keywords:Equivariant homotopy, circle action, minimal model,, rationalization, formality Categories:55P91, 55P62, 55R35, 55S45 

13. CJM 2003 (vol 55 pp. 1264)
 Havin, Victor; Mashreghi, Javad

Admissible Majorants for Model Subspaces of $H^2$, Part II: Fast Winding of the Generating Inner Function
This paper is a continuation of Part I [6]. We consider the model
subspaces $K_\Theta=H^2\ominus\Theta H^2$ of the Hardy space $H^2$
generated by an inner function $\Theta$ in the upper half plane. Our
main object is the class of admissible majorants for $K_\Theta$,
denoted by Adm $\Theta$ and consisting of all functions $\omega$
defined on $\mathbb{R}$ such that there exists an $f \ne 0$, $f \in
K_\Theta$ satisfying $f(x)\leq\omega(x)$ almost everywhere on
$\mathbb{R}$. Firstly, using some simple Hilbert transform techniques,
we obtain a general multiplier theorem applicable to any $K_\Theta$
generated by a meromorphic inner function. In contrast with
[6], we consider the generating functions $\Theta$ such that
the unit vector $\Theta(x)$ winds up fast as $x$ grows from $\infty$
to $\infty$. In particular, we consider $\Theta=B$ where $B$ is a
Blaschke product with ``horizontal'' zeros, i.e., almost
uniformly distributed in a strip parallel to and separated from $\mathbb{R}$.
It is shown, among other things, that for any such $B$, any even
$\omega$ decreasing on $(0,\infty)$ with a finite logarithmic integral
is in Adm $B$ (unlike the ``vertical'' case treated in [6]),
thus generalizing (with a new proof) a classical result related to
Adm $\exp(i\sigma z)$, $\sigma>0$. Some oscillating $\omega$'s in
Adm $B$ are also described. Our theme is related to the
BeurlingMalliavin multiplier theorem devoted to Adm $\exp(i\sigma z)$,
$\sigma>0$, and to de Branges' space $\mathcal{H}(E)$.
Keywords:Hardy space, inner function, shift operator, model, subspace, Hilbert transform, admissible majorant Categories:30D55, 47A15 

14. CJM 2003 (vol 55 pp. 1231)
 Havin, Victor; Mashreghi, Javad

Admissible Majorants for Model Subspaces of $H^2$, Part I: Slow Winding of the Generating Inner Function
A model subspace $K_\Theta$ of the Hardy space $H^2 = H^2
(\mathbb{C}_+)$ for the upper half plane $\mathbb{C}_+$ is
$H^2(\mathbb{C}_+) \ominus \Theta H^2(\mathbb{C}_+)$ where $\Theta$
is an inner function in $\mathbb{C}_+$. A function $\omega \colon
\mathbb{R}\mapsto[0,\infty)$ is called an admissible
majorant for $K_\Theta$ if there exists an $f \in K_\Theta$, $f
\not\equiv 0$, $f(x)\leq \omega(x)$ almost everywhere on
$\mathbb{R}$. For some (mainly meromorphic) $\Theta$'s some parts
of Adm $\Theta$ (the set of all admissible majorants for
$K_\Theta$) are explicitly described. These descriptions depend on
the rate of growth of $\arg \Theta$ along $\mathbb{R}$. This paper
is about slowly growing arguments (slower than $x$). Our results
exhibit the dependence of Adm $B$ on the geometry of the zeros of
the Blaschke product $B$. A complete description of Adm $B$ is
obtained for $B$'s with purely imaginary (``vertical'') zeros. We
show that in this case a unique minimal admissible majorant exists.
Keywords:Hardy space, inner function, shift operator, model, subspace, Hilbert transform, admissible majorant Categories:30D55, 47A15 

15. CJM 1999 (vol 51 pp. 3)
 Allday, C.; Puppe, V.

On a Conjecture of Goresky, Kottwitz and MacPherson
We settle a conjecture of Goresky, Kottwitz and MacPherson related
to Koszul duality, \ie, to the correspondence between differential
graded modules over the exterior algebra and those over the
symmetric algebra.
Keywords:Koszul duality, HirschBrown model Categories:13D25, 18E30, 18G35, 55U15 

16. CJM 1998 (vol 50 pp. 1119)
 Anand, Christopher Kumar

Ward's solitons II: exact solutions
In a previous paper, we gave a correspondence between certain exact
solutions to a \((2+1)\)dimensional integrable Chiral Model and
holomorphic bundles on a compact surface. In this paper, we use
algebraic geometry to derive a closedform expression for those
solutions and show by way of examples how the algebraic data which
parametrise the solution space dictates the behaviour of the
solutions.
Dans un article pr\'{e}c\'{e}dent, nous avons d\'{e}montr\'{e} que
les solutions d'un mod\`{e}le chiral int\'{e}grable en dimension \(
(2+1) \) correspondent aux fibr\'{e}s vectoriels holomorphes sur
une surface compacte. Ici, nous employons la g\'{e}om\'{e}trie
alg\'{e}brique dans une construction explicite des solutions. Nous
donnons une formule matricielle et illustrons avec trois exemples
la signification des invariants alg\'{e}briques pour le
comportement physique des solutions.
Keywords:integrable system, chiral field, sigma model, soliton, monad, uniton, harmonic map Category:35Q51 

17. CJM 1997 (vol 49 pp. 855)
 Smith, Samuel Bruce

Rational Classification of simple function space components for flag manifolds.
Let $M(X,Y)$ denote the space of all continous functions
between $X$ and $Y$ and $M_f(X,Y)$ the path component
corresponding to a given map $f: X\rightarrow Y.$ When $X$ and
$Y$ are classical flag manifolds, we prove the components of
$M(X,Y)$ corresponding to ``simple'' maps $f$ are classified
up to rational homotopy type by the dimension of the kernel of
$f$ in degree two
cohomology. In fact, these components are themselves all products
of flag manifolds and odd spheres.
Keywords:Rational homotopy theory, SullivanHaefliger model. Categories:55P62, 55P15, 58D99. 
