Author: Dirk Kussin
Publisher: American Mathematical Soc.
ISBN: 0821844008
Category : Mathematics
Languages : en
Pages : 146
Get Book Here
Book Description
In these notes the author investigates noncommutative smooth projective curves of genus zero, also called exceptional curves. As a main result he shows that each such curve $\mathbb{X}$ admits, up to some weighting, a projective coordinate algebra which is a not necessarily commutative graded factorial domain $R$ in the sense of Chatters and Jordan. Moreover, there is a natural bijection between the points of $\mathbb{X}$ and the homogeneous prime ideals of height one in $R$, and these prime ideals are principal in a strong sense.
Author: Tohru Eguchi
Publisher: Cambridge University Press
ISBN: 1107056411
Category : Mathematics
Languages : en
Pages : 303
Get Book Here
Book Description
This volume contains seven chapters based on lectures given by invited speakers at two May 2010 workshops held at the Mathematical Sciences Research Institute.
Author: Gelu Popescu
Publisher: American Mathematical Soc.
ISBN: 0821847104
Category : Mathematics
Languages : en
Pages : 137
Get Book Here
Book Description
"Volume 205, number 964 (third of 5 numbers)."
Author: Yoshiaki Maeda
Publisher: Springer Science & Business Media
ISBN: 9401007047
Category : Science
Languages : en
Pages : 310
Get Book Here
Book Description
Noncommutative differential geometry is a new approach to classical geometry. It was originally used by Fields Medalist A. Connes in the theory of foliations, where it led to striking extensions of Atiyah-Singer index theory. It also may be applicable to hitherto unsolved geometric phenomena and physical experiments. However, noncommutative differential geometry was not well understood even among mathematicians. Therefore, an international symposium on commutative differential geometry and its applications to physics was held in Japan, in July 1999. Topics covered included: deformation problems, Poisson groupoids, operad theory, quantization problems, and D-branes. The meeting was attended by both mathematicians and physicists, which resulted in interesting discussions. This volume contains the refereed proceedings of this symposium. Providing a state of the art overview of research in these topics, this book is suitable as a source book for a seminar in noncommutative geometry and physics.
Author: Richard Montgomery
Publisher: American Mathematical Soc.
ISBN: 0821848186
Category : Mathematics
Languages : en
Pages : 154
Get Book Here
Book Description
Cartan introduced the method of prolongation which can be applied either to manifolds with distributions (Pfaffian systems) or integral curves to these distributions. Repeated application of prolongation to the plane endowed with its tangent bundle yields the Monster tower, a sequence of manifolds, each a circle bundle over the previous one, each endowed with a rank $2$ distribution. In an earlier paper (2001), the authors proved that the problem of classifying points in the Monster tower up to symmetry is the same as the problem of classifying Goursat distribution flags up to local diffeomorphism. The first level of the Monster tower is a three-dimensional contact manifold and its integral curves are Legendrian curves. The philosophy driving the current work is that all questions regarding the Monster tower (and hence regarding Goursat distribution germs) can be reduced to problems regarding Legendrian curve singularities.
Author: Ursula Carow-Watamura
Publisher: Springer Science & Business Media
ISBN: 9783540239000
Category : Mathematics
Languages : en
Pages : 316
Get Book Here
Book Description
This volume reflects the growing collaboration between mathematicians and theoretical physicists to treat the foundations of quantum field theory using the mathematical tools of q-deformed algebras and noncommutative differential geometry. A particular challenge is posed by gravity, which probably necessitates extension of these methods to geometries with minimum length and therefore quantization of space. This volume builds on the lectures and talks that have been given at a recent meeting on "Quantum Field Theory and Noncommutative Geometry." A considerable effort has been invested in making the contributions accessible to a wider community of readers - so this volume will not only benefit researchers in the field but also postgraduate students and scientists from related areas wishing to become better acquainted with this field.
Author: Leonid Positselski
Publisher: American Mathematical Soc.
ISBN: 0821852965
Category : Mathematics
Languages : en
Pages : 146
Get Book Here
Book Description
"July 2011, volume 212, number 996 (first of 4 numbers)."
Author: Adam Coffman
Publisher: American Mathematical Soc.
ISBN: 0821846574
Category : Mathematics
Languages : en
Pages : 105
Get Book Here
Book Description
"Volume 205, number 962 (first of 5 numbers)."
Author: Makoto Sakai
Publisher: American Mathematical Soc.
ISBN: 0821848100
Category : Mathematics
Languages : en
Pages : 282
Get Book Here
Book Description
For a given plane domain, the author adds a constant multiple of the Dirac measure at a point in the domain and makes a new domain called a quadrature domain. The quadrature domain is characterized as a domain such that the integral of a harmonic and integrable function over the domain equals the integral of the function over the given domain plus the integral of the function with respect to the added measure. The family of quadrature domains can be modeled as the Hele-Shaw flow with a free-boundary problem. The given domain is regarded as the initial domain and the support point of the Dirac measure as the injection point of the flow.
Author: Wilfrid Gangbo
Publisher: American Mathematical Soc.
ISBN: 0821849395
Category : Mathematics
Languages : en
Pages : 90
Get Book Here
Book Description
Let $\mathcal{M}$ denote the space of probability measures on $\mathbb{R}^D$ endowed with the Wasserstein metric. A differential calculus for a certain class of absolutely continuous curves in $\mathcal{M}$ was introduced by Ambrosio, Gigli, and Savare. In this paper the authors develop a calculus for the corresponding class of differential forms on $\mathcal{M}$. In particular they prove an analogue of Green's theorem for 1-forms and show that the corresponding first cohomology group, in the sense of de Rham, vanishes. For $D=2d$ the authors then define a symplectic distribution on $\mathcal{M}$ in terms of this calculus, thus obtaining a rigorous framework for the notion of Hamiltonian systems as introduced by Ambrosio and Gangbo. Throughout the paper the authors emphasize the geometric viewpoint and the role played by certain diffeomorphism groups of $\mathbb{R}^D$.
