1st ed. 2017, XIII, 460 p. 151 illus., 61 illus. in color.
Printed book
Hardcover
ISBN 978-3-319-68102-3
Series: Springer Proceedings in Mathematics & Statistics, Vol. 219
This interdisciplinary book covers a wide range of subjects, from pure mathematics (knots,
braids, homotopy theory, number theory) to more applied mathematics (cryptography,
algebraic specification of algorithms, dynamical systems) and concrete applications
(modeling of polymers and ionic liquids, video, music and medical imaging). The main
mathematical focus throughout the book is on algebraic modeling with particular
emphasis on braid groups.
The research methods include algebraic modeling using topological structures, such as
knots, 3-manifolds, classical homotopy groups, and braid groups. The applications address
the simulation of polymer chains and ionic liquids, as well as the modeling of natural
phenomena via topological surgery. The treatment of computational structures, including
finite fields and cryptography, focuses on the development of novel techniques. These
techniques can be applied to the design of algebraic specifications for systems modeling
and verification.
This book is the outcome of a workshop in connection with the research project Thales on
Algebraic Modeling of Topological and Computational Structures and Applications, held
at the National Technical University of Athens, Greece in July 2015. The reader will benefit
from the innovative approaches to tackling difficult questions in topology, applications
and interrelated research areas, which largely employ algebraic tools.
1st ed. 2017, VII, 290 p. 13 illus., 9 illus. in color.
Printed book
Hardcover
ISBN 978-3-319-68030-9
November 5, 2017
Series: Springer Proceedings in Mathematics & Statistics, Vol. 220
* Collates recent advances in combinatorial and additive number
theory from distinguished mathematicians in the field
* Points to future areas of research
* All papers feature original, peer-reviewed content
Based on talks from the 2015 and 2016 CANT workshops at the City University of New
York, these proceedings offer 19 peer-reviewed and edited papers on current topics
in number theory. The volume features subjects such as sumsets, partitions, convex
polytopes and discrete geometry, Ramsey theory, primality testing, and cryptography.
Held every year since 2003, this workshop series aims to survey state-of-the-art, open
problems, and future colleagues of combinatorial and additive number theory and related
parts of mathematics. Each contribution in this volume is dedicated to a specific topic
and reflects the latest results by eminent experts in the field. Researchers and graduate
students interested in the latest progress in number theory will find this selection of
articles relevant and compelling.
1st ed. 2017, XX, 676 p. 22 illus., 7 illus. in color.
Printed book
Hardcover
ISBN 978-3-319-68375-1
Series: Springer Proceedings in Mathematics & Statistics, Vol. 221
* Offers numerous and diverse articles on the latest research in number
theory
* Expands on Krishna Alladi's recent contributions on partitions and qseries
Gathered from the 2016 Gainesville Number Theory Conference honoring Krishna Alladi
on his 60th birthday, these proceedings present recent research in number theory.
Extensive and detailed, this volume features 40 articles by leading researchers on topics
in analytic number theory, probabilistic number theory, irrationality and transcendence,
Diophantine analysis, partitions, basic hypergeometric series, and modular forms. Readers
will also find detailed discussions of several aspects of the path-breaking work of Srinivasa
Ramanujan and its influence on current research. Many of the papers were motivated
by Alladi's own research on partitions and q-series as well as his earlier work in number
theory.
Alladi is well known for his contributions in number theory and mathematics. His research
interests include combinatorics, discrete mathematics, sieve methods, probabilistic and
analytic number theory, Diophantine approximations, partitions and q-series identities.
Graduate students and researchers will find this volume a valuable resource on new
developments in various aspects of number theory.
1st ed. 2018, Approx. 220 p.
Printed book
Hardcover
ISBN 978-3-319-68902-9
November 5, 2017
Series: Operator Theory: Advances and Applications, Vol. 264
* Develops basic vector-bundle-valued objects of geometric analysis
from scratchGives a detailed proof of the Feynman-Kac fomula with
singular potentials on manifolds
* Includes previously unpublished results
This monograph discusses covariant Schrodinger operators and their heat semigroups
on noncompact Riemannian manifolds and aims to fill a gap in the literature, given the
fact that the existing literature on Schrodinger operators has mainly focused on scalar
Schrodinger operators on Euclidean spaces so far. In particular, the book studies operators
that act on sections of vector bundles. In addition, these operators are allowed to have
unbounded potential terms, possibly with strong local singularities. The results presented
here provide the first systematic study of such operators that is sufficiently general to
simultaneously treat the natural operators from quantum mechanics, such as magnetic
Schrodinger operators with singular electric potentials, and those from geometry, such
as squares of Dirac operators that have smooth but endomorphism-valued and possibly
unbounded potentials.
Up to by now classical results on the heat kernel of the Laplace-Beltrami operator,
the book is essentially self-contained. Thus, it should be accessible to graduate and
postgraduate students. However, since the book includes unpublished facts as well as
new proofs of recently published facts, it will also be interesting for researchers from
geometric analysis, stochastic analysis, spectral theory, and mathematical physics.
1st ed. 2018, Approx. 530 p.
Printed book
Hardcover
ISBN 978-3-319-68848-0
November 5, 2017
Series: Linear Operators and Linear Systems, Vol. 263
* Collects state-of-the-art papers on central domains in operator
theory
* Features several illustrations
* Includes the full "Laudatio" of the celebration of Heinz Langer's
honorary doctoral degree
This is a volume dedicated to Heinz Langer. It includes some biographical material and
papers related to his research interests.
Heinz Langer has made fundamental contributions to operator theory. In particular, he
studied the domains of operator pencils and nonlinear eigenvalue problems, the theory
of indefinite inner product spaces, operator theory in Pontryagin and Krein spaces, and
applications to mathematical physics. His works include studies on and applications of
Schur analysis in the indefinite setting, where the factorization theorems of Krein and
Langer for generalized Schur functions and of Dijksma-Langer-Luger-Shondin play a key
role.