Advanced Lectures in Mathematics Volume 47
Published: 2 March 2020
Publisher: International Press of Boston, Inc.
Paperback
558 pages
In algebraic geometry and theoretical physics, mirror symmetry refers to the relationship between two Calabi?Yau manifolds
which appear very different geometrically but are nevertheless equivalent when employed as extra dimensions of string theory.
Mathematicians became interested in mirror symmetry around 1990, when it was shown that mirror symmetry could be used to
count rational curves on a Calabi?Yau manifold, thus solving a long-standing problem.
Today, mirror symmetry is a fundamental tool for doing calculations in string theory, and it has been used to understand
aspects of quantum field theory, the formalism that physicists use to describe elementary particles. Major approaches to
mirror symmetry include the homological mirror symmetry program of Maxim Kontsevich and the SYZ conjecture of Andrew
Strominger, Shing-Tung Yau, and Eric Zaslow.
This handbook surveys recent developments in mirror symmetry. It presents papers based on selected lectures given at a 2014
Taipei conference on “Calabi-Yau Geometry and Mirror Symmetry,” along with
other contributions from invited authors.
Advanced Lectures in Mathematics Volume 48
Published: 20 March 2020
Publisher: International Press of Boston, Inc.
Paperback
498 pages
Groups are fundamental objects in mathematics, as they are responsible for the symmetries of any object or system under
consideration. The presence of symmetry makes a problem more interesting and, as a general rule, easier to solve. In all
cases, it is group action which makes groups useful and important. This is not surprising, since the notion of group was
first introduced through group actions as permutation groups on roots of algebraic equations. On the other hand, the single
notion of group action includes many different actions arising from various sources.
All of which is amply illustrated by the papers collected in this volume, the fifth Handbook of Group Actions. Topics
include: classical geometric groups, geometric group theory, diffeomorphism groups of manifolds, mapping class groups, three
-dimensional topology, hyperbolic manifolds, automorphism groups of complex manifolds, dynamics, and number theory.
April 2020
Pages: 400
Quantum information and contemporary smart network domains are so large and complex as to be beyond the reach of current
research approaches. Hence, new theories are needed for their understanding and control. Physics is implicated as smart
networks are physical systems comprised of particle-many items interacting and reaching criticality and emergence across
volumes of macroscopic and microscopic states. Methods are integrated from statistical physics, information theory, and
computer science. Statistical neural field theory and the AdS/CFT correspondence are employed to derive a smart network field
theory (SNFT) and a smart network quantum field theory (SNQFT) for the orchestration of smart network systems. Specifically,
a smart network field theory (conventional or quantum) is a field theory for the organization of particle-many systems from a
characterization, control, criticality, and novelty emergence perspective.
This book provides insight as to how quantum information science as a paradigm shift in computing may influence other high-
impact digital transformation technologies, such as blockchain and machine learning. Smart networks refer to the idea that
the internet is no longer simply a communications network, but rather a computing platform. The trajectory is that of
communications networks becoming computing networks (with self-executing code), and perhaps ultimately quantum computing
networks. Smart network technologies are conceived as autonomous self-operating computing networks. This includes blockchain
economies, deep learning neural networks, autonomous supply chains, self-piloting driving fleets, unmanned aerial vehicles,
industrial robotics cloudminds, real-time bidding for advertising, high-frequency trading networks, smart city IoT sensors,
and the quantum internet.
Introduction
Smart Networks and Quantum Computing:
Smart Networks: Classical and Quantum Field Theory
Quantum Computing: Basic Concepts
Advanced Quantum Computing: Interference and Entanglement
Blockchain and Zero-Knowledge Proofs:
Classical Blockchain
Quantum Blockchain
Zero-Knowledge Proof Technology
Post-quantum Cryptography and Quantum Proofs
Machine Learning and Artificial Intelligence:
Classical Machine Learning
Quantum Machine Learning
Smart Network Field Theories:
Model Field Theories: Neural Statistics and Spin Glass
Smart Network Field Theory Specification and Examples
The AdS/CFT Correspondence and Holographic Codes:
The AdS/CFT Correspondence
Holographic Quantum Error-Correcting Codes
Quantum Smart Networks:
AdS/Smart Network Correspondence and Conclusion
Glossary
Index
Thought-leaders, executives, industry strategists, research scientists, graduate students, advanced undergraduate students,
policy-makers, government regulators, corporate practitioners, and entrepreneurs in the areas of computer science,
blockchain, machine learning, quantum information science, and theoretical physics.
July 2020
Pages: 300
ISBN: 978-981-121-066-2 (hardcover)
Professor Roman Jackiw is a theoretical physicist renowned for his many fundamental contributions and discoveries in quantum
and classical field theories, ranging from high energy physics and gravitation to condensed matter and the physics of fluids.
Among his major achievements is the establishment of the presence of the famous Adler?Bell?Jackiw anomalies in quantum field
theory, a discovery with far-reaching implications for the structure of the Standard Model of particle physics and all
attempts to go beyond it. Other important contributions, among many, that one may mention here are the topological mass term
in gravity and gauge theories, and the fractionalization of fermion number and charge in the presence of topological objects.
Roman Jackiw, a Professor Emeritus at the MIT Center for Theoretical Physics, is the recipient of several international
awards including the Dannie Heineman Prize for Mathematical Physics and the Dirac Medal of the ICTP. He is a member of the US
National Academy of Sciences and honorary doctor of Kiev, Montreal, Tours, Turin and Uppsala universities.
To celebrate his 80th birthday, many students and colleagues of Professor Jackiw have come together to share interesting
anecdotes of working with him as well as their latest research, some of it inspired by his work. Edited by his former
students Antti Niemi and Terry Tomboulis together with his long-time friend KK Phua, this festschrift volume is a must-have
collection for all theoretical physicists.
Personal Recollections:
Recent Path Crossings with Roman and Anomalies (Stephen L Adler)
Roman Jackiw and the Family Structure (Luis Alvarez-Gaume)
Romaniana: A Student's Appreciation of Roman Jackiw, on His 80th Birthday (Michael Bos)
Electron Fractionalization in Celebration of Roman Jackiw's 80th Birthday (Claudio Chamon)
Roman Jackiw and Our Physics in Common (John Mike Cornwall)
Fun in 2+1 (Stanley Deser)
Roman Jackiw and Gauge Field Theory: Reminiscences of MIT Postdoc Days (Nicholas Manton)
Recollections of a Most Fruitful and Enjoyable Collaboration: Looking Back at My Work with Roman Jackiw (Claudio Rebbi)
Roman Jackiw and My MIT Days (Paolo Rossi)
Roman Jackiw: A Beacon in a Golden Period of Theoretical Physics (Luc Vinet)
Roman Jackiw (Steven Weinberg)
Tribute to a Mentor (Rohana Wijewardhana)
Scientific Contributions:
Entanglement in Fermionic Chains and Bispectrality (Nicolas Crampe, Rafael I Nepomechie and Luc Vinet)
Gravitational Wilson Lines in AdS? (Eric D'Hoker and Per Kraus)
Bions and Instantons in Triple-Well and Multi-Well Potentials (Gerald V Dunne, Tin Sulejmanpasic and Mithat Unsal)
On the Sudakov Form Factor, and a Factor of Two (Stefano Forte)
Emerging Majorana Modes in Junctions of One-Dimensional Spin Systems (Domenico Giuliano, Andrea Trombettoni and Pasquale
Sodano)
Anomalies and Bose Symmetry (Daniel Kabat)
Sasakians and the Geometry of a Mass Term (V Parameswaran Nair)
Celestial Operator Products of Gluons and Gravitons (Monica Pate, Ana-Maria Raclariu, Andrew Strominger and Ellis Ye Yuan)
How to Split the Electron in Half (Gordon W Semenoff)
Anomalies and Topologies in Quantum Field Theories (Gerard 't Hooft)
Superinsulators, a Toy Realization of QCD in Condensed Matter (Carlo Trugenberger and Maria Cristina Diamantini)
Three Easy Pieces (in Tribute to Roman Jackiw) (Frank Wilczek)
A Note on Boundary Conditions in Euclidean Gravity (Edward Witten)
Physics students and theoretical physicists.
The 5th Franco-Japanese-Vietnamese Symposium on Singularities, Kagoshima, Japan, 27 October - 3 November 2017
June 2020
Pages: 250
ISBN: 978-981-120-602-3 (hardcover)
The main theme of the symposium was Singularity Theory in a broad sense, including complex and real algebraic varieties,
functions and mappings, and topology of singularities. The symposium was based on long-term interaction of singularity
theorists in France, Japan, Vietnam and other countries. The reader can find recent trends and progresses in Singularity
Theory. The volume is especially useful for those who would like to overview recent topics in these areas. In particular, the
three surveys will serve as good introductions to the topics for young researchers. All the papers in the volume are original
and have been carefully peer-reviewed
Preface (Shoji Yokura)
Smooth and Global Versions of the Lojasiewicz Inequality (Ha Huy Vui)
Topology of Real Algebraic Varieties and Tropical Homology (Ilia Itenberg)
On Continuous Rational Functions (Wojciech Kucharz)
On the Higher Topological Complexity of Configuration Spaces on Riemann Surfaces (Nguyen Viet Dung and Nguyen Van Ninh)
Substitution Property for the Ring of Continuous Rational Functions (Goulwen Fichou, Ronan Quarez and Jean-Philippe Monnier)
Milnor fibration, A'Campo's divide and Turaev's shadow (Masaharu Ishikawa and Hironobu Naoe)
On (2; p) Quasi Torus Curves and Weak Zariski Pairs (Masayuki Kawashima)
Key Polynomials in Dimension 2 (Wael Mahboub and Mark Spivakovsky)
Tropical Analogies of the Delta Invariant and Degree-Genus Formula (Takuhiro Takahashi)
Maximal Ideal Cycles and Multiplicities for Cyclic Coverings Over Normal Surface Singularities (Tadashi Tomaru)
Notes on the Motivic Mckay Correspondence for the Group Scheme α_p (Fabio Tonini and Takehiko Yasuda)
Singular Patterns of Generic Maps of Surfaces w Boundary Into the Plane (Dominik Wrazidlo)
Motivic Milnor?Hirzebruch Classes Revisited (Shoji Yokura)
Graduate students and researchers.
(In 4 Volumes)
Volume I. Memristors: New Circuit Element with Memory
Volume II. Memristors and CNN: The Right Stuff for AI and Brain-Like Computers
Volume III. Chaos: Chua's Circuit and Complex Nonlinear Phenomena
Volume IV. Local Activity Principle: Chua's Riddle, Turing Machine, and Universal Computing Rule 137
December 2020
Pages: 1062
ISBN: 978-981-121-537-7 (hardcover)
This 4-volume compendium contains the verbatim hard copies of all color slides from the Chua Lecture Series presented at HP
in Palo Alto, during the period from September 22 to November 24, 2015. Each lecture consists of 90 minutes, divided into a
formal lecture, a discussion session, and an Encore of special trivia that the audience found mesmerizing.
These lectures share some unique features of the classic Feynman Lectures on Physics, as much of the materials are presented
in the unique style of the author, and the content is original as discovered or invented by the author himself. Unlike most
technical books that suffer a notoriously short life span as their features could be superseded by superior models, this
series of Chua lectures are intended to never be obsolete ? many concepts and principles introduced are in fact new laws of
nature, written in the language of sophomore-level mathematics, providing the foundation and the elan vital for initiating
and nurturing future concepts and inventions.
Volume I covers everything that a researcher may want to know about memristors but is too afraid to ask.
Volume II shows that memristors can be either volatile or non-volatile, and effectively proving that synapses are non-
volatile memristors, while action potentials are generated by locally-active memristors.
Volume III presents an overview of the fascinating phenomenon called chaos, while immersing the audience with the sights and
sound of chaos from the Chua Circuit, invented in 1984 by Leon Chua, and has now become the standard textbook example of
chaos exhibited by a real nonlinear electronic circuit, and not by computer simulations.
Volume IV surprises the audience with a new law of nature ? dubbed the local activity principle, as discovered and proved
mathematically in 1996 by Leon Chua. In particular, a Corollary of Chua's local activity theorem, dubbed the edge of chaos,
is shown via insightful examples to be the originator of most complex phenomena, including intelligence, creativity, and deep
learning. The edge of chaos is Mother Nature's tool for overcoming the tyranny of the second law of thermodynamics by
providing an escape hatch for entropy to decrease over time. Indeed, the local activity principle which is profusely
illustrated in the final volume, is widely recognized as a new law of thermodynamics, and is identified as the sine qua non
of all complex phenomena, including life itself.
Graduate students and researchers interested in memristors and circuits.