We discuss a simple model for D-brane transport in non-abelian GLSMs. The model is the elliptic curve version of a non-abelian GLSM introduced by Hori and Tong and has gauge group U(2). It has two geometric phases, both of which describe the same elliptic curve, once realised as a codimension five complete intersection in G(2,5) and once as a determinantal variety. The determinantal phase is strongly coupled with unbroken SU(2). There are two singular points in the moduli space where the theory has a Coulomb branch. Using grade restriction rules, we show how to transport B-branes between the two phases along paths avoiding the singular points. With the help of the GLSM hemisphere partition function we compute analytic continuation matrices and monodromy matrices, confirming results obtained by different methods.

Johanna Knapp

We discuss some of the most unusual active galactic nuclei (AGN) discovered to date by the Sloan Digital Sky Survey (SDSS): the first broad absorption line quasar seen to exhibit He II absorption, several quasars with extremely strong, narrow UV Fe II emission, and an AGN with an unexplained and very strange continuum shape.

Patrick B. Hall G. R. Knapp G. T. Richards M. A. Strauss S. F. Anderson D. P. Schneider D. A. Vanden Berk D. G. York K. S. J. Anderson J. Brinkmann S. A. Snedden

Let G be a reductive p-adic group. We study how a local Langlands correspondence for irreducible tempered G-representations can be extended to a local Langlands correspondence for all irreducible smooth representations of G. We prove that, under a natural condition involving compatibility with unramified twists, this is possible in a canonical way. To this end we introduce analytic R-groups associated to non-tempered essentially square-integrable representations of Levi subgroups of G. We establish the basic properties of these new R-groups, which generalize Knapp--Stein R-groups.

Anne-Marie Aubert Paul Baum Roger Plymen Maarten Solleveld

In 2009, G. Gr\"atzer and E. Knapp proved that every planar semimodular lattice has a rectangular extension. We prove that, under reasonable additional conditions, this extension is unique. This theorem naturally leads to a hierarchy of special diagrams of planar semimodular lattices. Besides that these diagrams are unique in a strong sense, we explore many of their further properties. Finally, we demonstrate the power of our new diagrams in two ways. First, we prove a simplified version of our earlier Trajectory Coloring Theorem, which describes the inclusion con(p)\supseteq\con(q) for prime intervals p and q in slim rectangular lattices. Second, we prove G. Gr\"atzer's Swing Lemma for the same lattices, which describes the same inclusion more simply.

Gábor Czédli

The Sloan Digital Sky Survey (SDSS) will provide the data to support detailed investigations of the distribution of luminous and non- luminous matter in the Universe: a photometrically and astrometrically calibrated digital imaging survey of pi steradians above about Galactic latitude 30 degrees in five broad optical bands to a depth of g' about 23 magnitudes, and a spectroscopic survey of the approximately one million brightest galaxies and 10^5 brightest quasars found in the photometric object catalog produced by the imaging survey. This paper summarizes the observational parameters and data products of the SDSS, and serves as an introduction to extensive technical on-line documentation.

D. G. York

For a symmetric pair $(G,H)$ of reductive groups we extend to a large class of generalized principal series representations our previous construction of meromorphic families of symmetry breaking operators. These operators intertwine between a possibly vector-valued principal series of $G$ and one for $H$ and are given explicitly in terms of their integral kernels. As an application we give a complete classification of symmetry breaking operators from spinors on a Euclidean space to spinors on a hyperplane, intertwining for a double cover of the conformal group of the hyperplane.

Jan Frahm Bent Ørsted

Following G.~Gr\"atzer and E.~Knapp, 2009, a planar semimodular lattice $L$ is \emph{rectangular}, if~the left boundary chain has exactly one doubly-irreducible element, $c_l$, and the right boundary chain has exactly one doubly-irreducible element, $c_r$, and these elements are complementary. The Cz\'edli-Schmidt Sequences, introduced in 2012, construct rectangular lattices. We use them to prove some structure theorems. In particular, we prove that for a slim (no $\mathsf{M}_3$ sublattice) rectangular lattice~$L$, the congruence lattice $\Con L$ has exactly $\length[c_l,1] + \length[c_r,1]$ dual atoms and a dual atom in $\Con L$ is a congruence with exactly two classes. We also describe the prime ideals in a slim rectangular lattice.

G. Grätzer

Menger's well-known theorem from 1927 characterizes when it is possible to find $k$ vertex-disjoint paths between two sets of vertices in a graph $G$. Recently, Georgakopoulos and Papasoglu and, independently, Albrechtsen, Huynh, Jacobs, Knappe and Wollan conjectured a coarse analogue of Menger's theorem, when the $k$ paths are required to be pairwise at some distance at least $d$. The result is known for $k\le 2$, but we will show that it is false for all $k\ge 3$, even if $G$ is constrained to have maximum degree at most three. We also give a simpler proof of the result when $k=2$.

Tung Nguyen Alex Scott Paul Seymour

Lov\'{a}sz and Cherkassky discovered independently that, if $G$ is a finite graph and $T\subseteq V(G)$ such that the degree $d_G(v)$ is even for every vertex $v\in V(G)\setminus T$, then the maximum number of edge-disjoint paths which are internally disjoint from~$T$ and connect distinct vertices of $T$ is equal to $\frac{1}{2} \sum_{t\in T}\lambda_G(t, T\setminus \{t\})$ (where $\lambda_G(t, T\setminus \{t\})$ is the size of a smallest cut that separates $t$ and $T\setminus\{t\}$). From another perspective, this means that for every vertex $t\in T$, in any optimal path-system there are $\lambda_G(t, T\setminus \{t\})$ many paths between $t$ and~$T\setminus\{t\}$. We extend the theorem of Lov\'{a}sz and Cherkassky based on this reformulation to all locally-finite infinite graphs and their ends. In our generalisation, $T$ may contain not just vertices but ends as well, and paths are one-way (two-way) infinite when they establish a vertex-end (end-end) connection.

Raphael W. Jacobs Attila Joó Paul Knappe Jan Kurkofka Ruben Melcher

We present a detailed, self-consistent model of radiatively driven stellar outflows which couples the radiative transfer and hydrodynamics equations. The circumstellar envelope, which consists of gas and dust, is described as a two-component fluid to account for relative drifts. Our results agree with both molecular line observations and infrared continuum spectra, and show that steady-state outflows driven by radiation pressure on dust grains adequately describe the surroundings of the majority of cool luminous evolved stars.

Z. Ivezic G. R. Knapp M. Elitzur