Part of Encyclopedia of Mathematics and its Applications
FORMAT: Hardback ISBN: 9781316512036
LENGTH: 425 pages DIMENSIONS: 234 x 156 mm
AVAILABILITY: Not yet published - available from January 2022
Strongly regular graphs lie at the intersection of statistical design, group theory, finite geometry,
nformation and coding theory, and extremal combinatorics. This monograph collects all the major
known results together for the first time in book form, creating an invaluable text that researchers
in algebraic combinatorics and related areas will refer to for years to come. The book covers
the theory of strongly regular graphs, polar graphs, rank 3 graphs associated to buildings and
Fischer groups, cyclotomic graphs, two-weight codes and graphs related to combinatorial configurations
such as Latin squares, quasi-symmetric designs and spherical designs. It gives the complete classification
of rank 3 graphs, including some new constructions. More than 100 graphs are treated individually.
Some unified and streamlined proofs are featured, along with original material including a new approach to the
(affine) half spin graphs of rank 5 hyperbolic polar spaces.
The first treatment of the subject in book form, comprehensively structured with unified proofs
Gives the complete classification of rank 3 graphs, previously scattered in the literature
Treats over 100 graphs individually, demonstrating their uses e.g. to test hypotheses, make conjectures
or check properties
1. Graphs
2. Polar spaces
3. Graphs related to polar spaces
4. Buildings
5. Fischer spaces
6. Golay codes, Witt designs, and Leech lattice
7. Cyclotomic constructions
8. Combinatorial constructions
9. p-Ranks
10. Individual graph descriptions
11. Classification of rank 3 graphs
12. Parameter table
References
Parameter Index
Author Index
Subject Index
Part of Cambridge Studies in Advanced Mathematics
FORMAT: Hardback
ISBN: 9781108832496
LENGTH: 260 pagesDIMENSIONS: 229 x 152 mm
AVAILABILITY: Not yet published - available from April 2022
The past decade has seen numerous major mathematical breakthroughs for topics such as
the finite field Kakeya conjecture, the cap set conjecture, Erd?s's distinct distances problem,
the joints problem, as well as others, thanks to the introduction of new polynomial methods.
There has also been significant progress on a variety of problems from additive combinatorics,
discrete geometry, and more. This book gives a detailed yet accessible introduction to these
new polynomial methods and their applications, with a focus on incidence theory. Based on
the author's own teaching experience, the text requires a minimal background, allowing graduate
and advanced undergraduate students to get to grips with an active and exciting research front.
The techniques are presented gradually and in detail, with many examples, warm-up proofs, and
exercises included. An appendix provides a quick reminder of basic results and ideas.
Requires a minimal background and includes numerous examples, warm-up proofs, figures, and intuitive
ways of thinking about complex ideas
Contains over 100 exercises that can be used by instructors in courses or by readers for extra practice
Discusses the main open problems in polynomial methods and incidence theory to encourage further research
Introduction
1. Incidences and classical discrete geometry
2. Basic real algebraic geometry in R^2
3. Polynomial partitioning
4. Basic real algebraic geometry in R^d
5. The joints problem and degree reduction
6. Polynomial methods in finite fields
7. The Elekeshariruthatz framework
8. Constant-degree polynomial partitioning and incidences in C^2
9. Lines in R^3
10. Distinct distances variants
11. Incidences in R^d
12. Incidence applications in R^d
13. Incidences in spaces over finite fields
14. Algebraic families, dimension counting, and ruled surfaces
Appendix. Preliminaries
References
Index.
Part of London Mathematical Society Lecture Note Series
FORMAT: Paperback
ISBN: 9781108792509
LENGTH: 431 pagesDIMENSIONS: 228 x 152 mm
AVAILABILITY: Not yet published - available from May 2022
Written to honor the 80th birthday of William Fulton, the articles collected in this volume
(the first of a pair) present substantial contributions to algebraic geometry and related fields,
with an emphasis on combinatorial algebraic geometry and intersection theory. Featured topics include:
commutative algebra, representation theory, tropical geometry, moduli spaces, Schubert calculus,
quantum cohomology. The range of these contributions is a testament to the breadth and depth of
Fulton's mathematical influence. The authors are all internationally recognized experts,
and include well-established researchers as well as rising stars of a new generation of mathematicians.
The text aims to stimulate progress and provide inspiration to graduate students and researchers in the field.
Covers a wide range of topics in modern algebraic geometry reflecting William Fulton's broad range of interests
Written by a combination of well-established researchers and rising stars of a new generation of mathematicians
Suitable for graduate students and researchers in algebraic geometry and related fields
1. Positivity of Segre-MacPherson classes Paolo Aluffi, Leonardo C. Mihalcea, Jrg Schrmann and Changjian Su
2. Brill?Noether special cubic fourfolds of discriminant 14 Asher Auel
3. Automorphism groups of almost homogeneous varieties Michel Brion
4. Topology of moduli spaces of tropical curves with marked points Melody Chan, Soren Galatius and Sam Payne
5. Mirror symmetry and smoothing Gorenstein toric affine 3-folds Alessio Corti, Matej Filip and Andrea Petracci
6. Vertex algebras of CohFT-type Chiara Damiolini, Angela Gibney and Nicola Tarasca
7. The cone theorem and the vanishing of Chow cohomology Dan Edidin and Ryan Richey
8. Cayley?Bacharach theorems with excess vanishing Lawrence Ein and Robert Lazarsfeld
9. Effective divisors on Hurwitz spaces Gavril Farkas
10. Chow quotients of Grassmannians by diagonal subtori Noah Giansiracusa and Xian Wu
11. Quantum Kirwan for quantum K-theory E. Gonzalez and C. Woodward
12. Toric varieties and a generalization of the Springer resolution William Graham
13. Toric surfaces, linear and quantum codes ?Esecret sharing and decoding Johan P. Hansen
Part of London Mathematical Society Lecture Note Series
FORMAT: Paperback
ISBN: 9781108792516
LENGTH: 408 pages DIMENSIONS: 228 x 152 mm
AVAILABILITY: Not yet published
Written to honor the 80th birthday of William Fulton, the articles collected in this volume
(the second of a pair) present substantial contributions to algebraic geometry and related fields,
with an emphasis on combinatorial algebraic geometry and intersection theory. Featured topics include:
commutative algebra, representation theory, tropical geometry, moduli spaces, Schubert calculus,
quantum cohomology. The range of these contributions is a testament to the breadth and depth of
Fulton's mathematical influence. The authors are all internationally recognized experts, and include
well-established researchers as well as rising stars of a new generation of mathematicians.
The text aims to stimulate progress and provide inspiration to graduate students and researchers in the field.
Covers a wide range of topics in modern algebraic geometry reflecting William Fulton's broad range of interests
Written by a combination of well-established researchers and rising stars of a new generation of mathematicians
Suitable for graduate students and researchers in algebraic geometry and related fields
14. Stability of tangent bundles on smooth toric Picard-rank-2 varieties and surfaces Milena Hering, Benjamin Nill and Hendrik SuAE
15. Tropical cohomology with integral coefficients for analytic spaces Philipp Jell
16. Schubert polynomials, pipe dreams, equivariant classes, and a co-transition formula Allen Knutson
17. Positivity certificates via integral representations Khazhgali Kozhasov, Mateusz Micha?ek and Bernd Sturmfels
18. On the coproduct in affine Schubert calculus Thomas Lam, Seung Jin Lee and Mark Shimozono
19. Bost?Connes systems and F1-structures in Grothendieck rings, spectra, and Nori motives Joshua F. Lieber, Yuri I. Manin, and Matilde Marcolli
20. Nef cycles on some hyperkahler fourfolds John Christian Ottem
21. Higher order polar and reciprocal polar loci Ragni Piene
22. Characteristic classes of symmetric and skew-symmetric degeneracy loci Sutipoj Promtapan and Richard Rimanyi
23. Equivariant cohomology, Schubert calculus, and edge labeled tableaux Colleen Robichaux, Harshit Yadav and Alexander Yong
24. Galois groups of composed Schubert problems Frank Sottile, Robert Williams and Li Ying
25. A K-theoretic Fulton class Richard P. Thomas.
Part of Encyclopedia of Mathematics and its Applications
FORMAT: Hardback
ISBN: 9781316519677
LENGTH: 1080 pages DIMENSIONS: 244 x 170 mm
AVAILABILITY: Not yet published - available from May 2022
The authors explain in this work a new approach to observing and controlling linear systems whose
inputs and outputs are not fixed in advance. They cover a class of linear time-invariant state/signal
system that is general enough to include most of the standard classes of linear time-invariant
dynamical systems, but simple enough that it is easy to understand the fundamental principles.
They begin by explaining the basic theory of finite-dimensional and bounded systems in a way suitable
for graduate courses in systems theory and control. They then proceed to the more advanced
infinite-dimensional setting, opening up new ways for researchers to study distributed parameter systems,
including linear port-Hamiltonian systems and boundary triplets. They include the general non-passive
part of the theory in continuous and discrete time, and provide a short introduction to the passive situation.
Numerous examples from circuit theory are used to illustrate the theory.
Written by leading experts in the field, incorporating years of research
Includes over 60 worked examples to illustrate the theory
Contains a number of new results for linear time-invariant input/state/output systems
Table of Contents
1. Introduction and overview
2. State/signal systems: trajectories, transformations, and interconnections
3. State/signal systems: dynamic and frequency domain properties
4. Input/state/output representations
5. Input/state/output systems: dynamic and frequency domain properties
6. Bounded input/state/output systems in continuous and discrete time
7. Bounded state/signal systems in continuous and discrete time
8. Semi-bounded input/state/output systems
9. Semi-bounded state/signal systems
10. Resolvable input/state/output and state/signal nodes
11. Frequency domain input/state/output systems
12. Frequency domain state/signal systems
13. Internally well-posed systems
14. Well-posed input/state/output systems
15. Well-posed state/signal systems
Appendix
Operators and analytic vector bundles in H-spaces
References
Index.