Softcover ISBN: 978-1-4704-8015-8
Product Code: ULECT/81
Expected availability date: June 25, 2026
University Lecture SeriesVolume: 81;
2026; Estimated: 218 pp
MSC: Primary 14; 13
Over the past forty years, a substantial body of work has appeared centered around the syzygies of algebraic varieties. Classical results about defining equations have emerged as the first cases of a much more general picture involving higher syzygies. Moreover, as computer-assisted computations have become practical, Castelnuovo-Mumford regularity has come into focus as a measure of algebraic complexity. This research has touched on a wide array of topics in algebraic geometry, and the time seemed ripe for a survey of some of these ideas. The present monograph attempts to provide this.
Conceived as an introduction to the theory rather than a comprehensive survey, the authors focus on the geometric side of the story. A first course in algebraic geometry and some exposure to commutative algebra are sufficient background for most of the material, although facility with coherent cohomology is assumed. The presentation is pitched at the level of an intermediate or advanced graduate course.
Graduate students and research mathematicians interested in commutative algebra and algebraic geometry.
Hilbert’s theorem on syzygies
An introduction to Boij-Söderberg theory
Castelnuovo-Mumford regularity
Regularity bounds and constructions
Koszul cohomology
Linearity of syzygyies: Property
Syzygies of curves
Asymptotic syzygies in higher dimensions
Bibliography
Index
*
Softcover ISBN: 978-1-4704-7844-5
Product Code: CONM/838
Expected availability date: June 10, 2026
Contemporary Mathematics Volume: 838;
2026; 331 pp
MSC: Primary 05; 16; 19; 53; 18
This volume contains the proceedings of the Workshop on Higher Segal Spaces and their Applications to Algebraic
-Theory, Hall Algebras, and Combinatorics, held from January 21 to 26, 2024, at the Banff International Research Station, Banff (AB), Canada.
This book is a collection of ten expository papers providing an introduction to the theory and applications of higher Segal spaces, a rather new topic in the interface between homotopy theory and higher category theory, finding applications in homological algebra, representation theory, geometry, combinatorics, algebraic
-theory, and other areas. The papers are written by experts on the various topics, in an engaging style welcoming newcomers to the field, and are also designed to help specialists in one application area make the transition to another.
Graduate students and research mathematicans interested in homotopy theory, category theory, representation theory, and combinatorics.
Walker H. Stern — Perspectives on the 2-Segal conditions
Philip Hackney — The decomposition space perspective
Viktoriya Ozornova and Martina Rovelli — Waldhausen’s
-construction
Martina Rovelli — The
-construction as an equivalence between
-Segal spaces and stable augmented double Segal spaces
Benjamin Cooper and Matthew B. Young — Hall algebras via
-Segal spaces
Tobias Dyckerhoff — Cyclic polytopes, orientals, and correspondences: some aspects of higher Segal spaces
Maru Sarazola, Brandon T. Shapiro and Inna Zakharevich — A combinatorial construction of homology via ACGW categories
Hiro Lee Tanaka — Wrapped Fukaya categories and the 2-Segal conditions
Julia E. Bergner and Walker H. Stern — Cyclic Segal spaces
Imma Gálvez-Carrillo, Joachim Kock and Andrew Tonks — Decomposition spaces in combinatorics
Softcover ISBN: 978-1-4704-7947-3
Product Code: CONM/839
Expected availability date: June 10, 2026
Contemporary Mathematics Volume: 839;
2026; 233 pp
MSC: Primary 37; 60; 46; 47
Articles in this volume are based on talks given at the special session “Dynamical Systems: Statistical Properties, Spectral Theory, and Fractal Geometry” at the AMS Sectional Meeting held at University of Texas at San Antonio on September 14–15, 2024.
The authors discuss topics at the intersection of dynamical systems, ergodic theory, fractal geometry, operator theory, and symbolic dynamics. Key features include the introduction of relative topological pressure for nonautonomous systems, a novel dual-operator framework for analyzing diffusion equations with self-similar measures, and generalized fractal interpolation functions. Several articles offer new methods that extend classical theories to more intricate contexts.
Readers will benefit from a wide range of fresh perspectives, including asymptotic complexity in billiards, ergodic Hilbert transform inequalities, symbolic zeta function poles, and new transformations in measurable dynamics. The unique blend of topological, combinatorial, probabilistic, and analytical tools offers a valuable resource for researchers seeking to explore or expand contemporary methods in complex dynamical systems.
Graduate students and research mathematicians interested in fractal geometry, analysis, and dynamical systems.
Baimei Shi, Bilel Selmi and Zhiming Li — Relative topological pressure of nonautonomous dynamical systems
Andrew Vince — Self-similar GIFS tilings of Euclidean space
Leonid A. Bunimovich and Yaofeng Su — Statistics of weakly chaotic systems
Md. Abdul Aziz, Brittany E. Duncan and John C. Mayer — Fixed flowers in hyperbolic laminations
Doğan Çömez — Maximal inequalities for the ergodic Hilbert transform along sequences with cone condition and a local moving ergodic theorem
Yunping Jiang — Orders of oscillation motivated by Sarnak’s conjecture—Part II
Chris Johnson — Reciprocal transformations and their discrete Maharam extensions
Chenxi Wu — Concatenations of periodic words in subshifts defined by linear orders and poles of the Artin-Mazur zeta function
Efstathios-K. Chrontsios-Garitsis — Dimensions and metric dyadic cubes
Nandor Simanyi — Asymptotic homotopical complexity of an infinite sequence of dispersing
billiards
Palle E. T. Jorgensen and James Tian — Operator theory of diffusion equations governed by self-similar measures
Gwang-Jin O and Vasileios Drakopoulos — Generalised fractal interpolation functions with partial self-similarity using Rakotch contraction mappings
Softcover ISBN: 978-1-4704-8380-7
Product Code: MBK/156
Expected availability date: July 16, 2026
Miscellaneous Books
2026; Estimated: 446 pp
MSC: Primary 11; Secondary 60; 62; 65
This book presents a rich, insightful exploration of the interplay between randomness, the Riemann Hypothesis, and analytic number theory. Written for readers with a moderate background in mathematics (preferably having some familiarity with probability theory and complex analysis), it offers a deeper and more comprehensive account of the Riemann Hypothesis and its far-reaching consequences than is typically available in books aimed at general audiences.
The book takes a relaxed and engaging approach, highlighting the beauty and intuition behind the key ideas. Technical proofs are kept to a minimum, with accessible arguments presented fully, while deeper results are described in context and supported by historical background and comprehensive references. This combination allows readers to appreciate the elegance of the subject and to navigate their own path toward more advanced study.
Bringing together a wealth of material that is otherwise widely scattered across the literature, the book serves as an indispensable reference for researchers and enthusiasts alike. Throughout, it illuminates the crucial role that randomness plays in modern number theory—inspiring conjectures, guiding proofs, and opening new directions of inquiry. Six valuable appendices round out the volume, providing opportunities to review—or learn—essential background material across a range of mathematical topics.
Undergraduate and graduate students and researchers interested in recent advances in number theory, including probabilistic results and results that use tools from statistics.
The prime numbers
Interlude on arithmetic functions
The heuristic of Harald Cramér
The zeta function
Statistics of the zeros
Statistics of the critical line
Million dollar questions
Frontiers of chance and chaos
The zeta distributions
Random multiplicative functions
Further topics
Appendix A. Analytic functions
Appendix B. The Gamma and related functions
Appendix C. Dirichlet series
Appendix D. The statistical limit laws
Appendix E. Approximations for sums and products in powers of
, log
, and log
Appendix F. Some mathematical points
Acknowledgments
Bibliography
Index
Softcover ISBN: 978-1-4704-8514-6
Product Code: HMATH/51
Expected availability date: July 26, 2026
History of Mathematics Volume: 51;
2026; Estimated: 230 pp
MSC: Primary 01; 37; 53; 57; 58
The Floer Jungle traces the development of Floer theory while portraying the life of mathematician Andreas Floer (1956–1991), whose ideas transformed geometry and topology. Blending mathematical exposition with biography, it reconstructs the existing ideas, and introduces the main characters, describing their interactions, their judgements and attempts, wrong or right. Aimed at graduate students, researchers, and scientifically curious readers, it emphasizes examples over formalism and offers appendices and references for deeper study. The book is both an engaging introduction to sophisticated mathematics and an intimate portrait of the people who pursue it.
The mathematical narrative is aimed at readers with a strong foundation—graduate students in mathematics, physics, and engineering; researchers across disciplines; and, more broadly, those with a serious scientific curiosity.
Foundation
Birth-death
The (bad) action functional
Moser’s error and beyond
Progress
From Duisburg to Berkeley
The magic
Smuggling ideas
Breakthrough
Floer between Berkeley, Bochum, and beyond
World premiere
Getting inside Floer’s head
Symplectic lift-off
Thereafter
Epilogue
Floer’s bibliography
Qualifying exam
Arbeitstagung, June 14 1986
Progress report
The (PS) extension
There’s a lot of room in infinite dimensions
Analysis of $\mathcal{A}_{{\mathbb{R}^{2n}}$
Arnold’s motiviation
Details for the magic
From cartoon to theory
Notes
Acknowledgments
Image credits
Bibliography
Index of names
General index
Softcover ISBN: 978-1-4704-8507-8
Product Code: ULECT/80
Expected availability date: July 16, 2026
University Lecture Series Volume: 80;
2026; Estimated: 180 pp
MSC: Primary 81; 18; 57
Topological quantum field theories lie at the intersection of algebra, topology, and quantum field theory. The area is highly active, driven by recent developments in representation theory and topology, as well as developments in theoretical physics, including the study of topological phases of matter and topological symmetries. This book provides an accessible introduction to topological quantum field theories, along with basic notions of category theory—the natural mathematical setting for topological field theories—by describing these theories as a symmetric monoidal functor from a cobordism category to the category of vector spaces.
Using Dijkgraaf–Witten theories as a recurring example, the book introduces key tools such as category theory, Hopf algebras, and tensor categories, providing a solid foundation for students aiming to pursue a more advanced study in quantum topology and related areas. The book concludes with an outlook connecting the foundational theory to recent developments and current research directions.
The text is intended for advanced undergraduates and beginning graduate students in mathematics and theoretical physics. It is largely self-contained and assumes no specific background beyond standard undergraduate algebra and topology. While some familiarity with basic ideas from quantum theory is helpful, it is not a prerequisite.
Undergraduate and graduate students and researchers interested in the mathematical and physical aspects of topological quantum field theories (TQFTs).
An invitation to topological field theories
Categories
Tensor products, duals, and braidings
Topological field theories in dimension 1 and 2
Dijkgraaf-Witten topological field theories
Extended topological field theories
More about TFTs: a few appetizers
Bibliography
Index
Softcover ISBN: 978-1-4704-8032-5
Product Code: CONM/840
Expected availability date: June 25, 2026
Contemporary Mathematics Volume: 840;
2026; Estimated: 348 pp
MSC: Primary 11; 14; 08
This volume contains the proceedings of the LMFDB, Computation, and Number Theory (LuCaNT) 2025 conference, held at the Institute for Computational and Experimental Research in Mathematics (ICERM), from July 7–11, 2025, in Providence, Rhode Island.
This conference provided an opportunity for researchers, scholars, and practitioners to exchange ideas, share advances, and collaborate in the fields of computation, mathematical databases, number theory, and arithmetic geometry. The papers that appear in this volume record recent advances in these areas, with special focus on the LMFDB (the L-Functions and Modular Forms Database), an online resource for mathematical objects arising in the Langlands program and the connections between them.
Graduate students and research mathematicians interested in computations in number theory, in particular, modular forms.
ordi Guàrdia-Rubies, John W. Jones, Kevin Keating, Sebastian Pauli, David P. Roberts and David Roe — Families of
-adic fields
Fabian Gundlach — Sampling cubic rings
Noam D. Elkies — A Shimura-Belyi map of degree 33, and number fields with Galois group 33T55 =
David W. Farmer, Sally Koutsoliotas, Stefan Lemurell and David P. Roberts — Fine structure in some landscapes of L-functions
David Lowry-Duda — Computing a database of rigorous Maass forms
Taha Hedayat, Sarah Arpin and Renate Scheidler — The spine of a supersingular
-isogeny graph
Edgar Costa, Andreas-Stephan Elsenhans, Jörg Jahnel and John Voight — Explicit modularity of K3 surfaces with complex multiplication of large degree
Sven Cats, John Michael Clark, Charlotte Dombrowsky, Mar Curcó Iranzo, Krystal Maughan and Eli Orvis — Experimental investigations on Lehmer’s conjecture for elliptic curves
Lewis Combes, John Jones, Jennifer Paulhus, David Roe, Manami Roy and Sam Schiavone — Creating a dynamic database of finite groups
Steven Clontz — Database-Driven Mathematical Inquiry and the
-Base Model for Small Semantic Databases
Stevan Gajović, Jeroen Hanselman and Angelos Koutsianas — Local-global principle for 11-isogenies of elliptic curves is true over quadratic fields
Kate Finnerty — Quadratic Chabauty Experiments on Genus 2 Bielliptic Modular Curves in the LMFDB
Pitchayut Saengrungkongka and Noah Walsh — Gluing genus 1 and genus 2 curves along
-torsion
Yongyuan Huang, Kiran S. Kedlaya and Jun Bo Lau — A Census of Genus 6 Curves over
Adam Logan — The Kodaira dimension of Hilbert modular threefolds
Shiva Chidambaram — Computing the mod-
Galois image of a principally polarized abelian surface over the rationals
Jennifer Paulhus and Andrew V. Sutherland — Completely decomposable modular Jacobians
Edgar Costa, Taylor Dupuy, Stefano Marseglia, David Roe and Christelle Vincent — Labeling abelian varieties over finite fields
Craig Costello and Gaurish Korpal — On pairs of primes with small order reciprocity
Asimina S. Hamakiotes and Jun Bo Lau — Genus formulas for families of modular curves
Maria Corte-Real Santos, Jonathan Komada Eriksen, Antonin Leroux, Michael Meyer and Lorenz Panny — Evaluation of Modular Polynomial from Supersingular Elliptic Curves
Marco Streng — Explicit supersingular cyclic curves
Raymond van Bommel, Edgar Costa, Bjorn Poonen and Padmavathi Srinivasan — Curve equations from expansions of 1-forms at a nonrational point
Softcover ISBN: 978-1-4704-8194-0
Product Code: CONM/841
Expected availability date: June 25, 2026
Contemporary Mathematics Volume: 841;
2026; Estimated: 283 pp
MSC: Primary 18; 14; 81; 16
This volume contains the proceedings of the Homotopical Methods in Geometry and Physics Conference in honor of the 60th birthday of Ezra Getzler held at Northwestern University in Evanston, Illinois, on March 21–25, 2022.
It includes papers on geometry and topology of moduli spaces and configuration spaces, on theory of operads, and on noncommutative geometry, as well as on various connections between these topics and on their role in mathematical physics. These topics have been extensively studied during the last forty years. One prominent feature of the subject is that various invariants of spaces, noncommutative algebras, etc. carry classical algebraic structures but only up to homotopy. Operations that are part of these structures form topological spaces (from polyhedra to configuration or moduli spaces) whose homotopy theory is of central importance. The same spaces can be viewed as configuration spaces in mathematical physics.
Graduate students and research mathematicians interested in homotopy theory methods in geometry and applications to mathematical physics.
Konstanin Aleshkin and Chiu-Chu Melissa Liu — Open/closed correspondence and extended LG/CY correpondence for quintic threefolds
André Beuckelmann and Ieke Moerdijk — A small catalogue of
-operads
Indranil Biswas and Eduard Looijenga — Characteristic forms for holomorphic families of local systems
Nathaniel Bottman and Dylan Mavrides — The 2-aassociahedra are Eulerian
Zsuzsanna Dancso, Tamara Hogan, and Marcy Robertson — A knot-theoretic approach to comparing the Grothendieck-Teichmüller and Kashiwara-Verge groups
Ben Davison — Affine BPS algebras, W algebras, and the cohomological Hall algebra of
Mikhail Kapranov and Vadim Schechtman — PROBs and perverse sheaves II. Ran spaces and 0-cycles with coefficients
Boris Tsygan — Gauss-Manin connection in noncommutative geometry
Jesse Wolfson — On simplicial principal bundles in descent categories