Locally Toric Manifolds and Singular Bohr-Sommerfeld Leaves
Author: Mark D. Hamilton
Publisher: American Mathematical Soc.
Published: 2010
Total Pages: 73
ISBN-13: 0821847147
DOWNLOAD EBOOK"Volume 207, number 971 (first of 5 numbers)."
Posts
The Moduli Space of Cubic Threefolds as a Ball Quotient
Author: Daniel Allcock
Publisher: American Mathematical Soc.
Published: 2011
Total Pages: 89
ISBN-13: 0821847511
DOWNLOAD EBOOK"Volume 209, number 985 (fourth of 5 numbers)."
Weighted Shifts on Directed Trees
Author: Zenon Jan Jablónski
Publisher: American Mathematical Soc.
Published: 2012
Total Pages: 122
ISBN-13: 0821868683
DOWNLOAD EBOOKA new class of (not necessarily bounded) operators related to (mainly infinite) directed trees is introduced and investigated. Operators in question are to be considered as a generalization of classical weighted shifts, on the one hand, and of weighted adjacency operators, on the other; they are called weighted shifts on directed trees. The basic properties of such operators, including closedness, adjoints, polar decomposition and moduli are studied. Circularity and the Fredholmness of weighted shifts on directed trees are discussed. The relationships between domains of a weighted shift on a directed tree and its adjoint are described. Hyponormality, cohyponormality, subnormality and complete hyperexpansivity of such operators are entirely characterized in terms of their weights. Related questions that arose during the study of the topic are solved as well.
The Generalized Fitting Subsystem of a Fusion System
Author: Michael Aschbacher
Publisher: American Mathematical Soc.
Published: 2011-01-20
Total Pages: 122
ISBN-13: 0821853031
DOWNLOAD EBOOKHere, the author seeks to build a local theory of fusion systems, analogous to the local theory of finite groups, involving normal subsystems and factor systems.
Metrics of Positive Scalar Curvature and Generalised Morse Functions, Part I
Author: Mark P. Walsh
Publisher: American Mathematical Soc.
Published: 2011
Total Pages: 105
ISBN-13: 082185304X
DOWNLOAD EBOOKIt is well known that isotopic metrics of positive scalar curvature are concordant. Whether or not the converse holds is an open question, at least in dimensions greater than four. The author shows that for a particular type of concordance, constructed using the surgery techniques of Gromov and Lawson, this converse holds in the case of closed simply connected manifolds of dimension at least five.
Affine Insertion and Pieri Rules for the Affine Grassmannian
Author: Thomas Lam
Publisher: American Mathematical Soc.
Published: 2010
Total Pages: 103
ISBN-13: 0821846582
DOWNLOAD EBOOKThe authors study combinatorial aspects of the Schubert calculus of the affine Grassmannian ${\rm Gr}$ associated with $SL(n,\mathbb{C})$.Their main results are: Pieri rules for the Schubert bases of $H^*({\rm Gr})$ and $H_*({\rm Gr})$, which expresses the product of a special Schubert class and an arbitrary Schubert class in terms of Schubert classes. A new combinatorial definition for $k$-Schur functions, which represent the Schubert basis of $H_*({\rm Gr})$. A combinatorial interpretation of the pairing $H^*({\rm Gr})\times H_*({\rm Gr}) \rightarrow\mathbb Z$ induced by the cap product.
Operator Algebras for Multivariable Dynamics
Author: Kenneth R. Davidson
Publisher: American Mathematical Soc.
Published: 2011
Total Pages: 68
ISBN-13: 0821853023
DOWNLOAD EBOOKLet $X$ be a locally compact Hausdorff space with $n$ proper continuous self maps $\sigma_i:X \to X$ for $1 \le i \le n$. To this the authors associate two conjugacy operator algebras which emerge as the natural candidates for the universal algebra of the system, the tensor algebra $\mathcal{A}(X,\tau)$ and the semicrossed product $\mathrm{C}_0(X)\times_\tau\mathbb{F}_n^+$. They develop the necessary dilation theory for both models. In particular, they exhibit an explicit family of boundary representations which determine the C*-envelope of the tensor algebra.|Let $X$ be a locally compact Hausdorff space with $n$ proper continuous self maps $\sigma_i:X \to X$ for $1 \le i \le n$. To this the authors associate two conjugacy operator algebras which emerge as the natural candidates for the universal algebra of the system, the tensor algebra $\mathcal{A}(X,\tau)$ and the semicrossed product $\mathrm{C}_0(X)\times_\tau\mathbb{F}_n^+$. They develop the necessary dilation theory for both models. In particular, they exhibit an explicit family of boundary representations which determine the C*-envelope of the tensor algebra.
Towards a Modulo $p$ Langlands Correspondence for GL$_2$
Author: Christophe Breuil
Publisher: American Mathematical Soc.
Published: 2012-02-22
Total Pages: 127
ISBN-13: 0821852272
DOWNLOAD EBOOKThe authors construct new families of smooth admissible $\overline{\mathbb{F}}_p$-representations of $\mathrm{GL}_2(F)$, where $F$ is a finite extension of $\mathbb{Q}_p$. When $F$ is unramified, these representations have the $\mathrm{GL}_2({\mathcal O}_F)$-socle predicted by the recent generalizations of Serre's modularity conjecture. The authors' motivation is a hypothetical mod $p$ Langlands correspondence.
Classification of Radial Solutions Arising in the Study of Thermal Structures with Thermal Equilibrium or No Flux at the Boundary
Author: Alfonso Castro
Publisher: American Mathematical Soc.
Published: 2010
Total Pages: 87
ISBN-13: 0821847260
DOWNLOAD EBOOKThe authors provide a complete classification of the radial solutions to a class of reaction diffusion equations arising in the study of thermal structures such as plasmas with thermal equilibrium or no flux at the boundary. In particular, their study includes rapidly growing nonlinearities, that is, those where an exponent exceeds the critical exponent. They describe the corresponding bifurcation diagrams and determine existence and uniqueness of ground states, which play a central role in characterizing those diagrams. They also provide information on the stability-unstability of the radial steady states.
Centres of Centralizers of Unipotent Elements in Simple Algebraic Groups
Author: Ross Lawther
Publisher: American Mathematical Soc.
Published: 2011
Total Pages: 201
ISBN-13: 0821847694
DOWNLOAD EBOOKLet G be a simple algebraic group defined over an algebraically closed field k whose characteristic is either 0 or a good prime for G, and let uEG be unipotent. The authors study the centralizer CG(u), especially its centre Z(CG(u)). They calculate the Lie algebra of Z(CG(u)), in particular determining its dimension; they prove a succession of theorems of increasing generality, the last of which provides a formula for dim Z(CG(u)) in terms of the labelled diagram associated to the conjugacy class containing u.
