Part of London Mathematical Society Lecture Note Series
PUBLICATION PLANNED FOR: September 2021AVAILABILITY: Not yet published - available from September 2021
FORMAT: Paperback ISBN: 9781108710947
Robert Langlands formulated his celebrated conjectures, initiating the Langlands Program, at the age of 31, profoundly changing the landscape of mathematics. Langlands, recipient of the Abel Prize, is famous for his insight in discovering links among seemingly dissimilar objects, leading to astounding results. This book is uniquely designed to serve a wide range of mathematicians and advanced students, showcasing Langlands' unique creativity and guiding readers through the areas of Langlands' work that are generally regarded as technical and difficult to penetrate. Part 1 features non-technical personal reflections, including Langlands' own words describing how and why he was led to formulate his conjectures. Part 2 includes survey articles of Langlands' early work that led to his conjectures, and centers on his principle of functoriality and foundational work on the Eisenstein series, and is accessible to mathematicians from other fields. Part 3 describes some of Langlands' contributions to mathematical physics.
Features a non-technical interview with Robert Langlands
Select chapters in part 2 can be taught in graduate courses on the Langlands Program
Includes contributions from Langlands' friends, colleagues, and students
Part I. Remembrance of Things Past:
1. A glimpse at the genesis of the Langlands program Julia Mueller
2. The early Langlands program ?Epersonal reflections Steve Gelbart
Part II. Langlands as Mentor:
3. Langlands and Turkey Cihan Saclioglu
4. Reminiscences by a student of Langlands Thomas Hales
5. Graduate school with Langlands Ali Altug
6. An unforgettable year at the Institute (Enstitu'de unutulmaz bir y?l) Dinakar Ramakrishnan
Part III. Langlands as Friend:
7. My reminiscences of Bob Langlands at the University of British Columbia Alan Goodacre
8. Robert P. Langlands: l'homme derriere le Mathematicien Claude Levesque
9. un homme de culture et de nature Claude Pichet
Part IV. Surveys of the Langlands Program Early Years:
10. An introduction to Langlands functoriality James Arthur
11. In the beginning Langlands' doctoral thesis Derek W. Robinson
12. The Langlands spectral decomposition Jean-Pierre Labesse
13. Automorphic representations and L-functions for the group GL(n) Dorian Goldfeld and Hervei Jacquet
14. Automorphic L-functions Freydoon Shahidi
15. Langlands reciprocity: L-functions, automorphic forms, and Diophantine equations Matthew Emerton
16. On some early sources for the notion of transfer in Langlands functoriality Diana Shelstad
Part V. Langlands' Contributions to Mathematical Physics:
17. Robert Langlands' work in mathematical physics Thomas Spencer
18. L'invariance conforme et l'universalite au point critique des modeles bidimensionnels Yvan Saint-Aubin.
Part of London Mathematical Society Lecture Note Series
PUBLICATION PLANNED FOR: September 2021AVAILABILITY: Not yet published - available from September 2021
FORMAT: Paperback ISBN: 9781108746120
The language of ends and (co)ends provides a natural and general way of expressing many phenomena in category theory, in the abstract and in applications. Yet although category-theoretic methods are now widely used by mathematicians, since (co)ends lie just beyond a first course in category theory, they are typically only used by category theorists, for whom they are something of a secret weapon. This book is the first systematic treatment of the theory of (co)ends. Aimed at a wide audience, it presents the (co)end calculus as a powerful tool to clarify and simplify definitions and results in category theory and export them for use in diverse areas of mathematics and computer science. It is organised as an easy-to-cite reference manual, and will be of interest to category theorists and users of category theory alike.
The first comprehensive account of the (co)end calculus
Presents some hard to find material from the literature in a modern form
Includes an appendix summarising the necessary basic category theory
Preface
1. Dinaturality and (co)ends
2. Yoneda and Kan
3. Nerves and realisations
4. Weighted (co)limits
5. Profunctors
6. Operads
7. Higher dimensional (co)ends
Appendix A. Review of category theory
Appendix B
References
Index.
Part of Cambridge Studies in Advanced Mathematics
PUBLICATION PLANNED FOR: September 2021AVAILABILITY: Not yet published - available from September 2021
FORMAT: HardbackISBN: 9781108843966
Over the past 25 years, there has been an explosion of interest in the area of random tilings. The first book devoted to the topic, this timely text describes the mathematical theory of tilings. It starts from the most basic questions (which planar domains are tileable?), before discussing advanced topics about the local structure of very large random tessellations. The author explains each feature of random tilings of large domains, discussing several different points of view and leading on to open problems in the field. The book is based on upper-division courses taught to a variety of students but it also serves as a self-contained introduction to the subject. Test your understanding with the exercises provided and discover connections to a wide variety of research areas in mathematics, theoretical physics, and computer science, such as conformal invariance, determinantal point processes, Gibbs measures, high-dimensional random sampling, symmetric functions, and variational problems.
Introduces the theory of random lozenge tilings step by step, starting from the very basics and reaching advanced results
Covers in detail almost all aspects of mathematics of random tilings
Outlines numerous connections of tilings to other areas of mathematics, theoretical physics, and computer science
Preface
1. Lecture 1: introduction and tileability
2. Lecture 2: counting tilings through determinants
3. Lecture 3: extensions of the Kasteleyn theorem
4. Lecture 4: counting tilings on large torus
5. Lecture 5: monotonicity and concentration for tilings
6. Lecture 6: slope and free energy
7. Lecture 7: maximizers in the variational principle
8. Lecture 8: proof of the variational principle
9. Lecture 9: Euler-Lagrange and Burgers equations
10. Lecture 10: explicit formulas for limit shapes
11. Lecture 11: global Gaussian fluctuations for the heights
12. Lecture 12: heuristics for the Kenyon-kounkov conjecture
13. Lecture 13: ergodic translation-invariant Gibbs measures
14. Lecture 14: inverse Kasteleyn matrix for trapezoids
15. Lecture 15: steepest descent method for asymptotic analysis
16. Lecture 16: bulk local limits for tilings of hexagons
17. Lecture 17: bulk local limits near straight boundaries
18. Lecture 18: edge limits of tilings of hexagons
19. Lecture 19: the Airy line ensemble and other edge limits
20. Lecture 20: GUE-corners process and its discrete analogues
21. Lecture 21: discrete log-gases
22. Lecture 22: plane partitions and Schur functions
23. Lecture 23: limit shape and fluctuations for plane partitions
24. Lecture 24: discrete Gaussian component in fluctuations
25. Lecture 25: sampling random tilings
References
Index.
ISBN 9780367187330
Published August 11, 2020
340 Pages
Format : Hardback
[This book] reflects the extensive experience and significant contributions of the author to non-linear and non-Gaussian modeling. [It] is a valuable book, especially with its broad and accessible introduction of models in the state-space framework.
Statistics in Medicine
What distinguishes this book from comparable introductory texts is the use of state-space modeling. Along with this come a number of valuable tools for recursive filtering and smoothing, including the Kalman filter, as well as non-Gaussian and sequential Monte Carlo filters.
AA Reviews
Introduction to Time Series Modeling with Applications in R, Second Edition covers numerous stationary and nonstationary time series models and tools for estimating and utilizing them. The goal of this book is to enable readers to build their own models to understand, predict and master time series. The second edition makes it possible for readers to reproduce examples in this book by using the freely available R package TSSS to perform computations for their own real-world time series problems.
This book employs the state-space model as a generic tool for time series modeling and presents the Kalman filter, the non-Gaussian filter and the particle filter as convenient tools for recursive estimation for state-space models. Further, it also takes a unified approach based on the entropy maximization principle and employs various methods of parameter estimation and model selection, including the least squares method, the maximum likelihood method, recursive estimation for state-space models and model selection by AIC.
Along with the standard stationary time series models, such as the AR and ARMA models, the book also introduces nonstationary time series models such as the locally stationary AR model, the trend model, the seasonal adjustment model, the time-varying coefficient AR model and nonlinear non-Gaussian state-space models.
Genshiro Kitagawa is a project professor at the University of Tokyo, the former Director-General of the Institute of Statistical Mathematics, and the former President of the Research Organization of Information and Systems.
ISBN 9780367782504
March 31, 2021 Forthcoming
364 Pages
Request Inspection Copy
Format : Paperback
The theory of algebras, rings, and modules is one of the fundamental domains of modern mathematics. General algebra, more specifically non-commutative algebra, is poised for major advances in the twenty-first century (together with and in interaction with combinatorics), just as topology, analysis, and probability experienced in the twentieth century. This is the second volume of Algebras, Rings and Modules: Non-commutative Algebras and Rings by M. Hazewinkel and N. Gubarenis, a continuation stressing the more important recent results on advanced topics of the structural theory of associative algebras, rings and modules.
Rings related to finite posets. Distributive and semidistributive rings. The group of extensions. Modules over semiperfect rings. Representations of primitive posets. Representations of quivers, species and finite dimensional algebras. Artinian rings of finite representation type. O-species and SPSD-rings of bounded representation type.
ISBN 9780367779344
March 31, 2021 Forthcoming
296 Pages
Format : Paperback
This book presents, in an integrated form, both the analysis and synthesis of three different types of hidden Markov models. Unlike other books on the subject, it is generic and does not focus on a specific theme, e.g. speech processing. Moreover, it presents the translation of hidden Markov models?Econcepts from the domain of formal mathematics into computer codes using MATLABR. The unique feature of this book is that the theoretical concepts are first presented using an intuition-based approach followed by the description of the fundamental algorithms behind hidden Markov models using MATLABR. This approach, by means of analysis followed by synthesis, is suitable for those who want to study the subject using a more empirical approach.
Presents a broad range of concepts related to Hidden Markov Models (HMM), from simple problems to advanced theory
Covers the analysis of both continuous and discrete Markov chains
Discusses the translation of HMM concepts from the realm of formal mathematics into computer code
Offers many examples to supplement mathematical notation when explaining new concepts