Series: London Mathematical Society Lecture Note Series
Published: November 2025
Format: Paperback
ISBN: 9781009497190
The present volume features contributions from the 2022 BIRS-CMO workshop 'Moduli, Motives and Bundles – New Trends in Algebraic Geometry' held at the Casa Matemática Oaxaca (CMO), in partnership with the Banff International Research Station for Mathematical Innovation and Discovery (BIRS). The first part presents overview articles on enumerative geometry, moduli stacks of coherent sheaves, and torsors in complex geometry, inspired by related mini course lecture series of the workshop. The second part features invited contributions by experts on a diverse range of recent developments in algebraic geometry, and its interactions with number theory and mathematical physics, offering fresh insights into this active area. Students and young researchers will appreciate this text's accessible approach, as well as its focus on future research directions and open problems.
Provides a panorama of new inter-disciplinary relations between algebraic geometry with number theory and mathematical physics
Makes recent techniques and methods accessible to doctoral students and young researchers as well as to researchers in adjacent fields of algebraic geometry
Emphasizes future research directions and open problems
Preface
1. On the stack of 0-dimensional coherent sheaves: structural aspects Barbara Fantechi and Andrea T. Ricolfi
2. Three lectures on quadratic enumerative geometry Marc Levine
3. Flat torsors in complex geometry Juan Sebastián Numpaque-Roa and Florent Schaffhauser
4. Universal chern classes on the moduli of bundles Donu Arapura
5. Linear stability of coherent systems and applications to Butler's conjecture Abel Castorena, George H. Hitching, and Erick Luna
6. A Kobayashi-Hitchin correspondence for general coherent systems Cesare Goretti
7. On the injectivity and non-injectivity of the l-adic cycle class maps Bruno Kahn
8. A primer on zeta functions and decomposition spaces Andrew Kobin
9. Atiyah-Bott localization in equivariant Witt cohomology Marc Levine
10. Base loci, semiampleness, and parallelizable manifolds Ernesto C. Mistretta
11. Recent developments on compactifications of stacks of shtukas Tuan Ngo Dac and Yakov Varshavsky
12. A common generalisation of the André-Oort and André-Pink-Zannier conjectures Rodolphe Richard and Andrei Yafaev.
Format: Hardback
ISBN: 9781009561297
'An excellent exposition of proof search as a vehicle for realizing computations that, in the process, provides a novel view of structural proof theory through the prism of logic programming. Another strength is the presentation of linear logic and its use in modelling computational systems. Ideal for a graduate-level course on logic and its role in specification and programming.' Gopalan Nadathur, University of Minnesota
'Proof Theory and Logic Programming: Computation as Proof Search by Dale Miller is a refreshing look at the role that logic, specifically proof theory, plays in the foundation of computation. The book takes the perspective of a less-traveled route of applications of proof theory to computation - through the lens of proof search, a systematic and disciplined approach for searching for proofs of logical propositions. The book assumes minimal prerequisites, which makes it accessible to novices and experts alike. Its comprehensive coverage of decades of work in the field should make this an excellent reference textbook.' Alwen Tiu, The Australian National University
'This book is a clear and elegant journey through the connections between proof theory and programming. With a rigorous treatment of logic programming via sequent calculus and focused proof systems, Miller shows how logic can shape the way we think about computation without losing sight of practical relevance. Proof Theory and Logic Programming is a great resource for students, researchers, and anyone interested in exploring the theoretical foundations of logic-based programming languages.' Elaine Pimentel, University College London
'This book takes the reader on a rigorous, yet accessible journey starting from fundamental proof theoretic principles to understanding proof search as the computational foundation of logic programming. It is a joy to read and a valuable resource for anyone interested in the intersection of logic, computation, and language design.' Brigitte Pientka, McGill University
'Miller's book represents a long-awaited authoritative source on the proof-theoretic account of logic programming. It is ideal for students, educators, and researchers seeking to understand logic programming from a principled standpoint. Miller develops this account via the theoretical lens of sequent calculus, carefully illustrating how the choice of logic and search strategy affects operational properties of computation and structural properties of proofs. The material is interleaved with examples and exercises, providing a first-of-its-kind resource for learners on subjects such as focused proof systems, linear logic programming, and higher-order logic programming. The book concludes with two case studies, showcasing how a logic programming language incorporating the book's earlier developments can be used for modeling communication protocols and operational semantics.' Chris Martens, Northeastern University
Preface
1. Introduction
2. Terms, formulas, and sequents
3. Sequent calculus proof rules
4. Classical and intuitionistic logics
5. Two abstract logic programming languages
6. Linear logic
7. Formal properties of linear logic focused proofs
8. Linear logic programming
9. Higher-order quantification
10. Specifying computations using multisets
11. Collection analysis for Horn clauses
12. Encoding security pro
13. Formalizing operational semantics
Solutions to selected exercises
References
Index.
When you see a paper crane, what do you think of? A symbol of hope, a delicate craft, The Karate Kid? What you might not see, but is ever present, is the fascinating mathematics underlying it. Origami is increasingly applied to engineering problems, including origami-based stents, deployment of solar arrays in space, architecture, and even furniture design. The topic is actively developing, with recent discoveries at the frontier (e.g., in rigid origami and in curved-crease origami) and an infusion of techniques and algorithms from theoretical computer science. The mathematics is often advanced, but this book instead relies on geometric intuition, making it accessible to readers with only a high school geometry and trigonometry background. Through careful exposition, more than 150 color figures, and 49 exercises all completely solved in an Appendix, the beautiful mathematics leading to stunning origami designs can be appreciated by students, teachers, engineers, and artists alike.
Allows readers to visualize folding in action with 3D animations and to try techniques themselves with downloadable templates
Introduces mathematical topics in asides to bring unfamiliar readers up to speed while advanced readers can skip ahead
Reinforces concepts through 49 solved exercises graded into three categories
Gives a glimpse of unsolved problems beyond the frontier
Preface
1. Introduction
2. Stamp folding
3. Flat vertex folds
4. Flat folding is hard
5. Rigid origami and degree-4 vertices
6. Origami design
7. Fold & 1-cut
8. Curved crease origami
9. Self-folding origami
10. Origamizer
11. Beyond: topics not covered
12. Solutions to exercises
References
Index.
The study of smooth embeddings of 3-manifolds in 4-space has been hampered by difficulties with the simplest case, that of homology spheres. This book presents some advantages of working with locally flat embeddings. The first two chapters outline the tools used and give general results on embeddings of 3-manifolds in S4. The next two chapters consider which Seifert manifolds may embed, with criteria in terms of Seifert data. After summarizing results on those Seifert manifolds that embed smoothly, the following chapters determine which 3-manifolds with virtually solvable fundamental groups embed. The final three chapters study the complementary regions. When these have 'good' fundamental groups, topological surgery may be used to find homeomorphisms. Figures throughout help illustrate links representing embeddings and open questions are further discussed in the appendices, making this a valuable resource for graduate students and research workers in geometric topology.
Highlights the advantages of working with locally flat rather than smooth embeddings
Demonstrates the applicability of 4-dimensional TOP surgery to problems relating to 3-manifolds
Consolidates most known relevant work not involving gauge-theoretic ideas whilst presenting open problems
1. Preliminaries
2. Invariants and constructions
3. 3-manifolds with S1-actions
4. Seifert manifolds with non-orientable base orbifolds
5. Smooth embeddings
6. 3-manifolds with restrained fundamental group
7. The complementary regions
8. Abelian embeddings
9. Nilpotent embeddings
Appendix A. The linking pairings of orientable Seifert manifolds
Appendix B. Homologically balanced nilpotent groups
Appendix C. Some questions
References
Index.
Published: February 2026
Format: Paperback
ISBN: 9781009710930
Providing comprehensive yet accessible coverage, this is the first graduate-level textbook dedicated to the mathematical theory of risk measures. It explains how economic and financial principles result in a profound mathematical theory that allows us to quantify risk in monetary terms, giving rise to risk measures. Each chapter is designed to match the length of one or two lectures, covering the core theory in a self-contained manner, with exercises included in every chapter. Additional material sections then provide further background and insights for those looking to delve deeper. This two-layer modular design makes the book suitable as the basis for diverse lecture courses of varying length and level, and a valuable resource for researchers.
Provides a systematic account of basic theory of risk measures with emphasis on duality results
Includes a range of exercises, for use in class or for self-study
Requires an understanding of measure-theoretic probability and basic concepts from functional analysis
Introduction
1. Gains, quantiles and Value-at-Risk
2. Monetary property and acceptance sets
3. Diversification, convexity and coherence
4. Average-Value-at-Risk
5. Dual representation of convex and coherent risk measures
6. Representation theorems for risk measures on $L_p$-spaces
7. Constructions of risk measures
8. Law-determined risk measures
9. Law-determined risk measures on $L_p$-spaces
10. Comonotonicity and Choquet integrals
11. Coherent comonotonic additive risk measures
12. Multivariate risk measures
List of representations of coherent risk measures
List of important law-determined risk measures
References
Index.