Format: Hardback, 124 pages, height x width: 235x155 mm, 2 Illustrations, color
Series: Trends in Mathematics
Pub. Date: 01-Jul-2026
ISBN-13: 9783032224927
This volume presents contributions of modern developments in analysis, PDEs and geometric analysis by leading experts, as well as distinguished junior and senior researchers.
The book includes contributions from speakers at the Methusalem Colloquium, Methusalem Junior Seminar, and Geometric Analysis Seminar, all of which were held at the Department of Mathematics, Ghent University from 2023 to 2024. Additionally, it features colloquia and mini-courses delivered by visiting and invited guests.
The book has two main directions:
Analysis and PDEs: Covers topics in noncommutative analysis and geometry, functional and harmonic analysis, geometry and spectral methods, and applications to mathematical physics. Geometric Analysis: Covers topics in modern analytic techniques applied to elliptic, hypoelliptic, and subelliptic PDEs. A central theme of this book is the role of pseudo-differential operators in spectral analysis of geometric structures, with direct implications for index theory, noncommutative geometry, and quantization.
Global existence result for a semilinear wave equation on quantum tori.-
Bergman Spaces on Homogeneous.- Logarithmic convexity of evolution equations
and application to inverse problems.- Existence of Least Energy Nodal
Solutions for p-Laplace Equations Involving Singularity.- Existence and
Uniqueness Theorems for One Class of Hammerstein-Type Nonlinear Integral
Equations.- A spatial dependent inverse source problem for a fractional
pseudoparabolic equation.- Lp- Lq multipliers for the Weyl transform.-
Schatten properties of commutators on twisted crossed product.
Format: Paperback / softback, 225 pages, height x width: 235x155 mm, XIII, 225 p.
Pub. Date: 01-Jul-2026
ISBN-13: 9783032262714
This open access book is intended to give a bird's-eye view of ellipses and planetary orbits. The only background required is secondary-school Euclidean geometry, analytic geometry, and trigonometry. That doesn't mean that the theorems and proofs are easy; to the contrary, many are very challenging.
Although Isaac Newton invented the calculus and used it to study motion, from the time of the Greeks, proof meant proof by geometry. The book contains Newton's detailed geometric proof of the inverse-square law of orbits, based on Conic Sections Treated Geometrically, a widely used textbook from the nineteenth century written by William H. Besant. An important feature of the book is the numerous diagrams that are much more detailed than those appearing in the textbooks from the nineteenth century.
Turning to planetary orbits, the book presents Kepler's equation for computing the position, speed and direction of a planet in its orbit, followed by the computation of Lagrange points, which are points in the solar system where a spacecraft can be placed so that the period of its orbit is the same as the Earth's.
The history of mathematics has (or should have) an important place in mathematics education. Euclid is well-known but mathematicians were equally familiar with Conics by Apollonius of Perga. Some of his results are given in modern notation, although the presentation is faithful to his style. In addition, Kepler's own geometric proof of his First Law is given.
The final chapter presents challenging theorems on ellipses: the Steiner inellipse, Marden's Theorem, the theorems of Pascal and Brianchon, and Newton's Ellipse Theorem.
1. Ellipses: Definitions and Properties.-
2. Before Newton.-
3. Gravitation and Elliptical Orbits.-
4. The Euclidean Geometry of Ellipses.-
5. Constructing an Ellipse.-
6. Orbital Calculations.-
7. Apollonius and Conic Sections.-
8. Advanced Topics.-
9. Fun with Ellipses.- A. Theorems of Euclidean Geometry.- B. The Principia.- References.- Index.
Format: Hardback, 346 pages, height x width: 235x155 mm, 27 Illustrations, color; 4 Illustrations, black and white
Series: Trends in Mathematics
Pub. Date: 03-Jul-2026
ISBN-13: 9783032215772
This volume collects papers based on lectures given at the XLII Workshop on Geometric Methods in Physics, held in Biaystok, Poland in June-July 2025. These chapters provide readers an overview of cutting-edge research in quantum field theories, infinite-dimensional groups, integrable systems, noncommutative geometry, and a wide variety of other areas. Specific topics include:
Twisted ArakiWoods Algebras Monoidal actions in Lie-algebraic context Introductory course to quantum formalism in low dimensions Gelfand triplets in Quantum Mechanics Riemann Hypothesis in terms of the continuous Newton flow
Geometric Methods in Physics XLII are a valuable resource for mathematicians and physicists interested in recent developments at the intersection of these areas.
Address of the Chairman of the Wigner Medal Board at the Wigner Medal
Ceremony 2025.- Wigner Medal 2024.- Laudatio for Professor S.L. Woronowicz
Recipient of the Wigner Medal 2024.- Arno Bohm: Main Scientific
Contributions.- On the use of Gelfand triplets in Quantum Mechanics.- The No
U-Turn Rule in the Riemann Hypothesis.- Topological Feynman integrals and
the odd graph complex.- Electromagnetic field from affine symmetry of
punctured plane.- Variational principles in physics (how to use them and how
not to use).- On the electron spin origin, its Hamiltonian operator and the
related SU(2) × SU(2)-symmetry structure.- Affine symplectic structures in
gauge systems .
Format: Paperback / softback, 312 pages, height x width: 235x155 mm, 5 Illustrations, color; 9 Illustrations, black and white
Pub. Date: 16-Sep-2026
ISBN-13: 9783032272850
Large Language Models (LLMs) are reshaping how people write, communicate, and conduct research. ChatGPT, one of the most widely used tools in OpenAIs GPT series, can serve as a practical assistant when used thoughtfully and responsibly. ChatGPT for Math is a concise, hands-on guide to applying ChatGPT in mathematical work. It shows how to clarify arguments, debug proofs, generate diagrams, support LaTeX workflows, and improve both research writing and teaching materials. The book emphasizes a disciplined approach: ChatGPT is treated as an assistant, not an oracle, and its limitations are addressed openly. Each chapter includes carefully designed exercises to help readers build skill, judgment, and confidence in using ChatGPT effectively.
Preface.- Introduction.- I Foundations.- 1 What can ChatGPT actually
do?.- How ChatGPT interacts with Math.- Verification: trust but verify.- II
Core Mathematical Workflows.- 4 Mathematical computation and small case
experimentation.- 5 Proofs with ChatGPT.- 6 Examples and small structures.- 7
Computations and experiments.- 8 Diagrams beyond lattices.- 9 Teaching with
ChatGPT.- 10 Prompt patterns for math.- 11 Bibliographies.- 12 Index.- 13
Notation and terminological consistency.- 14 AI-assisted research.- 15
Explaining math.- 16 LaTeX, diagrams, and writing.- III Limits and outlook.-
17 Limits of ChatGPT for Mathematics.- 18 Reflections and future directions.-
A. Prompt Patterns for Mathematics.
Format: Paperback / softback, 442 pages, height x width: 235x155 mm, 1 Illustrations, black and white
Series: Universitext
Pub. Date: 02-Aug-2026
ISBN-13: 9783032292094
Functional analysis can be understood as a shift, within mathematical analysis, from the study of individual functions to the study of function spaces, their structures, and the mappings between them. Developed primarily during the 20th century, this theory continues to be essential for the study of partial differential equations.
This textbook begins with the general theory: Banach spaces, Hilbert spaces, and the spectral theory of operators. It then proceeds to a thorough account of Schwartzs Theory of Distributions and some of its applications, such as the fundamental solutions of classical operators in physics, the MalgrangeEhrenpreis Theorem, hypoelliptic operators, and the Schrödinger equation. An extensive chapter is dedicated to the study of Sobolev spaces, including functions of bounded variation. These spaces provide the appropriate framework for the study of elliptic boundary value problems, which form the focus of the final chapter.
Drawing on years of teaching experience, this textbook is ideal for introductory graduate courses, featuring historical notes and numerous exercises that reinforce learning and complement the core material.
Chapter 1. Brief Historical Notes.
Chapter 2. Banach Spaces.-
Chapter 3. Hilbert Spaces.
Chapter 4. Spectral Theory of Operators.-
Chapter 5. Theory of Distributions.
Chapter 6. Sobolev Spaces.
Chapter 7. Elliptic Boundary Value Problems.
Format: Hardback, 608 pages, height x width: 235x155 mm, 9 Illustrations, color
Pub. Date: 21-Jul-2026
ISBN-13: 9789819598168
Mikio Sato (19282023) is one of the most original and influential mathematicians of the twentieth century, whose ideas continue to shape modern mathematics. He initiates the theories of hyperfunctions and D-modules, laying the foundations of what he later called algebraic analysis. These innovations establish a unifying framework for analysis, algebra, and geometry, while revealing deep connections with theoretical physics. His work profoundly influences developments in analysis, number theory, holonomic quantum field theory, and integrable systems.
This three-volume collected edition presents a representative and authoritative selection of Satos writings, reflecting both the breadth of his vision and the coherence of his thought. Volume I focuses on algebraic analysis, especially hyperfunction theory and microlocal analysis. Volume II centers on mathematical physics, notably holonomic quantum field theory. Volume III gathers works on prehomogeneous vector spaces, number theory, exact WKB analysis, and integrable systems, including soliton equations, highlighting the unity of Satos mathematics across diverse domains.
Each volume opens with substantial scholarly commentaries by leading experts. These commentaries place Satos work in historical and intellectual context, clarify the state of the subject before his contributions, and elucidate his conceptual innovations. Together, they comprise over one hundred pages of critical assessment and reflection, offering insight into the enduring impact of Satos ideas on later developments.
To document the full scope of his research and influence, the edition includes a comprehensive bibliography encompassing informal materials not reproduced in these volumes.
This collection stands as both a definitive record of Satos achievements and an enduring source of inspiration, demonstrating how bold conceptual thinking can open new directions in mathematics and providing a model for future generations.
1 On a generalization of the concept of functions, Proc. Japan Acad. 34
(1958), no. 3, 126130.- 2 On a generalization of the concept of functions.
II, Proc. Japan Acad. 34 (1958), no. 9, 604608.- 5 Theory of hyperfunctions.
I, J. Fac. Sci. Univ. Tokyo. Sect. I 8 (1959), 139193.-
6. Theory of
hyperfunctions. II, J. Fac. Sci. Univ. Tokyo. Sect. I 8 (1960), 387437.- 12
Hyperfunctions and partial differential equations, in Proceedings of the
International Conference on Functional Analysis and Related Topics (Tokyo,
1969), Univ. Tokyo Press, Tokyo, 1970, 9194.- 16 (the same as [ 17])
Regularity of hyperfunctions solutions of partial differential equations,
RIMS Kōkyūroku, No. 114 (1971), 105123.- 17 Regularity of hyperfunctions
solutions of partial differential equations, in Actes du Congrčs
International des Mathématiciens (Nice, 1970), Tome 2, 785794,
Gauthier-Villars Éditeur, Paris, 1971.- 21 (with T. Kawai and M. Kashiwara)
On pseudo-differential equations in hyperfunction theory, RIMS Kōkyūroku, No.
162 (1972), 136144.- 22 (with T. Kawai and M. Kashiwara) On the structure of
single linear pseudo-differential equations, Proc. Japan Acad. 48 (1972), no.
9, 643646.- 23 Microlocal structure of a single linear pseudodifferential
equation, in Séminaire Goulaouic-Schwartz 19721973: Équations aux dérivées
partielles et analyse fonctionnelle, Exp. 18, 9 École Polytech., Paris,
1973.- 24 (with T. Kawai and M. Kashiwara) Microfunctions and
pseudo-differential equations, in Hyperfunctions and pseudo-differential
equations (Proceedings of a Conference at Katata, 1971; dedicated to the
memory of André Martineau), 265529, Lecture Notes in Math., Vol. 287,
Springer, Berlin-New York, 1973.- 26 Pseudo-differential equations and theta
functions, in Colloque International CNRS sur les Equations aux Derivees
Partielles Lineaires (Univ. Paris-Sud, Orsay, 1972), 286291, Astérisque, 2
et 3, Soc. Math. France, Paris, 1973.- 27 (the same as [ 26])
Pseudo-differential equations and theta functions, RIMS Kōkyūroku, No. 201
(1974), 247252.- 30 (with M. Kashiwara) The determinant of matrices of
pseudo-differential operators, Proc. Japan Acad. 51 (1975), no. 1, 1719.- 33
Recent development in hyperfunction theory and its application to physics
(microlocal analysis of S-matrices and related quantities), in International
Symposium on Mathematical Problems in Theoretical Physics (Kyoto Univ.,
1975), 1329, Lecture Notes in Phys., Vol. 39, Springer, Berlin-New York,
1975.- 36 (with T. Miwa and M. Jimbo) Dimension formula for the Landau
singularity, RIMS Kōkyūroku, No. 266 (1976), 91107.- 38 (with T. Miwa, M.
Jimbo and T. Oshima) Holonomy structure of Landau singularities and Feynman
integrals, Publ. Res. Inst. Math. Sci., 12 (1976/77), no. suppl, supplement,
387439.- 76 (with M. Kashiwara and T. Kawai) Linear differential equations
of infinite order and theta functions, Adv. in Math. 47 (1983), no. 3,
300325.- 80 (with M. Kashiwara and T. Kawai) Microlocal analysis of theta
functions, in Group representations and systems of differential equations
(Tokyo, 1982), 267289, Adv. Stud. Pure Math., Vol. 4, NorthHolland,
Amsterdam, 1984.- 86 D-modules and nonlinear systems, in Integrable systems
in quantum field theory and statistical mechanics, 417434, Adv. Stud. Pure
Math., Vol. 19, Academic Press, Boston, 1989.
Format: Hardback, 192 pages, height x width: 235x155 mm, 1 Illustrations, color
Series: Progress in Nonlinear Differential Equations and Their Applications
Pub. Date: 15-Aug-2026
ISBN-13: 9783032284914
This monograph explores feedback stabilization of bilinear control systems evolving in Hilbert and Banach spaces, with particular emphasis on unbounded control operators arising in PDE models. It develops a unified and comprehensive framework for weak, strong, robust, and exponential stabilization, incorporating nonlinear feedback laws, such as homogeneous, normalized, and switching feedbacks. By combining tools from functional analysis, semigroup theory, and control theory, this book bridges linear and nonlinear stabilization strategies and highlights the robustness of feedback mechanisms in infinite-dimensional systems. Feedback Stabilization of Bilinear Systems will serve as an ideal resource for researchers, graduate students, and practitioners who seek deeper insight into the stabilization of PDEgoverned systems as well as applications where bilinear dynamics naturally arise.
Preliminaries.- Weak and strong stabilization of bilinear systems in
Hilbert spaces.- Feedback stabilization for a bilinear control system under
weak observability inequalities.- Robust stabilization for affine control
systems under weak observability inequalities.- Robust stabilization for
affine control systems in reflexive state spaces.- Exponential stabilization
of unstable bilinear systems in finite and infinite dimensional spaces.-
Uniform exponential stabilization of nonlinear systems in Banach spaces.-
Exponential stability of linear and bilinear systems under Miyadera
perturbations.- Exponential stability of linear systems under
Desch-Schappacher perturbations.- Exponential stability of linear systems
under Weiss-Staffans perturbations.
Format: Hardback, 504 pages, height x width: 235x155 mm, XIII, 504 p.
Series: Operator Theory: Advances and Applications
Pub. Date: 01-Aug-2026
ISBN-13: 9783032286970
This volume contains translations of six of the original papers of Moshe Livsic on the characteristic operator function, together with a collection of contributions devoted to MosheLivsics theory of the characteristic operator function and its impact on the spectral analysis of nonselfadjoint operators, a theory first introduced in the 1940s. This theory provides a framework for the spectral analysis of non-selfadjoint and non-unitary operators and has since become a cornerstone of modern operator theory. Over the past seventyfive years, Livsics theory has exerted a lasting influence on analysis, complex analysis, linear systems theory, and a broad range of related topics. The volume examines how Livsics theory has shaped the study of pairs of commuting operators, a research direction initiated in the early 1970s with the aim of linking systems theory, nonselfadjoint operator theory, and Riemannian geometry.
The contributions collected here reflect the scope and depth of Livsics work at the intersection of operator theory, geometry, and systems theory. This book will be a valuable resource for researchers and advanced graduate students working in operator theory, analysis, systems theory and related areas.
A number of recollections from colleagues, students and friends of Moshe Livsic are also included.
Part I Translations.-
1. On an Application of the Theory of Hermitian Operators to the Generalized
Moment Problem by M.S. Livshits.-
2. A Theorem cation of Characteristic Matrix-Functions by M.S. Livshits.-
3. The Application of Non-Self-Adjoint Operators to Scattering Theory by
M.SLivshits.-
4. On Linear Physical Systems Connected with the External World by Coupling
Channels by M.S. Livshits.-
5. Open Systems as Linear Automata by M.S. Livshits.-
6. Open Geometry and Operator Colligations by L.L. Vaksman and M.S. Livshits.-
Part II Research paper.-
7. Characteristic Function of M.S. Livsic and Triangular Models of Bounded
Linear Operators by Vladimir K.Dubovoy, Bernd Kirstein, Conrad Madler and
Karsten Mueller.-
8. Characteristic Function, Schur Interpolation Problem and Darlington
Synthesis by Sergey S. Boiko,Vladimir K. Dubovoy,Bernd Fritzsche,Bernd
Kirstein,Conrad
Madler and Karsten Mueller.-
9. Characteristic Function, Schur Parameters and Pseudocontinuation of
Schur Functions by Vladimir K. Dubovoy,Bernd Fritzsche,Bernd Kirstein,Conrad
Madler and Karsten Mueller.-
10. Characteristic Function of M. Livsic and some Developments by Lev Sakhnovich.-
11. The Sine Kernel, Two Corresponding Operator Identities, and Random
Matrices by Lev Sakhnovich.-
12. Characteristic Function of Pencils. Model Representations of a Quadratic
Operator Pencil by V.A. Zolotarev.- Part III Recollections.-
13. M.S. Livsic (19172007) by V.A. Marchenko,E.R. Tsekanovski,V.K. Dubovoy
and V.A. Zolotarev.-
14. The Bravery of a Scientist by B.S. Pavlov.-
15. M.S. Livsic (19172007) L.L. Vaksman (19512007) by V.K. Dubovoy, V.A.
Zolotarev, A.A. Yantsevich and A.G. Rutkas.
Format: Paperback / softback, 86 pages, height x width: 235x155 mm, 20 Illustrations, color; 2 Illustrations, black and white
Series: Springer Proceedings in Mathematics & Statistics
Pub. Date: 01-Aug-2026
ISBN-13: 9783032231451
This book gathers written notes from three lecture series presented at the PIMSIFDSNSF Summer School on Optimal Transport, held at the University of Washington in June 2022. The summer school was the first major event organized by the Kantorovich Initiative, a nascent research consortium linking several universities in the Pacific Northwest and dedicated to advancing the mathematics of MongeKantorovich transport problems and their many applications. The mini-courses offered during the summer schooland the lecture notes collected hereare poised to have a substantial impact on the next generation of optimal transport researchers. The range of topics included in this volume reflects the remarkable breadth of contemporary research in the field. Felix Otto and Lukas Kochs contribution, based on Ottos mini-course, presents a variational perspective on the regularity theory of optimal transport. Alfred Galichon and Antoine Jacquets notes, drawn from Galichons mini-course, explore the links between optimal transport and matching models in economics. Finally, Geoffrey Schiebingers notes survey his mini-course on applications of optimal transport in developmental biology.
Preface.- Lecture notes on the harmonic approximation to quadratic
optimal transport (Koch, Ott).- Substitutability, equilibrium transport, and
matching models (Galichon, Jacquet).- The optimal transport principle for
developmental biology (Schiebinger).