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1201  Monodromy Action on Unknotting Tunnels in Fiber Surfaces Banks, Jessica; Rathbun, Matt
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.


1227  Eigenvarieties for Cuspforms over PEL Type Shimura Varieties with Dense Ordinary locus Brasca, Riccardo
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.


1257  Sharp Norm Estimates for the Bergman Operator from Weighted Mixednorm Spaces to Weighted Hardy Spaces Cascante, Carme; Fàbrega, Joan; Ortega, Joaquín M.
In this paper we give sharp norm estimates for the Bergman operator
acting from weighted
mixednorm spaces to weighted Hardy spaces in the ball,
endowed with natural norms.


1285  2row Springer Fibres and Khovanov Diagram Algebras for Type D Ehrig, Michael; Stroppel, Catharina
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.


1334  On the Neumann Problem for MongeAmpère Type Equations Jiang, Feida; Trudinger, Neil S; Xiang, Ni
In this paper, we study the global regularity for
regular
MongeAmpère type equations associated with semilinear Neumann
boundary conditions.
By establishing a priori estimates for second order derivatives,
the
classical solvability of the Neumann boundary value problem is
proved under natural conditions.
The techniques build upon the delicate and intricate treatment
of the standard MongeAmpère case
by Lions, Trudinger and Urbas in 1986 and the recent barrier
constructions and second derivative bounds
by Jiang, Trudinger and Yang for the Dirichlet problem. We also
consider more general oblique boundary
value problems in the strictly regular case.


1362  Optimal Quotients of Jacobians with Toric Reduction and Component Groups Papikian, Mihran; Rabinoff, Joseph
Let $J$ be a Jacobian variety with toric reduction
over a local field $K$.
Let $J \to E$ be an optimal quotient defined over $K$, where
$E$ is an elliptic curve.
We give examples in which the functorially induced map $\Phi_J
\to \Phi_E$
on component groups of the Néron models is not surjective.
This answers a question of Ribet and Takahashi.
We also give various criteria under which $\Phi_J \to \Phi_E$
is surjective, and discuss
when these criteria hold for the Jacobians of modular curves.


1382  La Variante infinitésimale de la formule des traces de JacquetRallis pour les groupes unitaires Zydor, Michał
We establish an infinitesimal version of the
JacquetRallis trace formula for unitary groups.
Our formula is obtained by integrating a
truncated kernel à 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
zêta functions.

