## H. Holden, R. Piene (eds.): The Abel Prize 2018–2022

Springer Nature Switzerland AG, 2024, pp. xi+883.

The book presents the winners of the Abel Prize in mathematics for the period 2018–2022: Robert P. Langlands (2018), Karen K. Uhlenbeck (2019), Hillel Furstenberg and Gregory Margulis (2020), Lászlo Lóvász and Avi Wigderson (2021), Dennis P. Sullivan (2022).

Springer (eBook): https://link.springer.com/book/10.1007/978-3-031-33973-8

## H. Holden, R. Piene (eds.): The Abel Prize 2013–2017

Springer Nature Switzerland AG, 2019. pp. xi+774.

The book presents the winners of the Abel Prize in mathematics for the period 2013–17: Pierre Deligne (2013); Yakov G. Sinai (2014); John Nash Jr. and Louis Nirenberg (2015); Sir Andrew Wiles (2016); and Yves Meyer (2017).

The profiles feature autobiographical information as well as a scholarly description of each mathematician’s work. In addition, each profile contains a Curriculum Vitae, a complete bibliography, and the full citation from the prize committee.

The book also includes photos for the period 2003–2017 showing many of the additional activities connected with the Abel Prize.

As an added feature, video interviews with the Laureates as well as videos from the prize ceremony are provided at an accompanying website (http://extras.springer.com/).

Springer: https://www.springer.com/gp/book/9783319990279

Springer (eBook): https://link.springer.com/book/10.1007%2F978-3-319-99028-6

Reviews:

Notices of the AMS (Jan 2021)

## H. Holden, R. Piene (eds.): The Abel Prize 2008–2012

Springer-Verlag Berlin Heidelberg, 2014. pp. xvii+571.

Covering the years 2008-2012, this book profiles the life and work of recent winners of the Abel Prize:

John G. Thompson and Jacques Tits, 2008

Mikhail Gromov, 2009

John T. Tate Jr., 2010

John W. Milnor, 2011

Endre Szemerédi, 2012.

The profiles feature autobiographical information as well as a description of each mathematician's work. In addition, each profile contains a complete bibliography, a curriculum vitae, as well as photos — old and new. As an added feature, interviews with the Laureates are presented on an accompanying web site (http://extras.springer.com/).

The book also presents a history of the Abel Prize written by the historian Kim Helsvig, and includes a facsimile of a letter from Niels Henrik Abel, which is transcribed, translated into English, and placed into historical perspective by Christian Skau.

Springer: https://www.springer.com/gp/book/9783642394485

Springer (eBook): https://link.springer.com/book/10.1007%2F978-3-642-39449-2

Reviews:

Mathematical Association of America

## H. Holden, R. Piene (eds.): The Abel Prize 2003–2007. The First Five Years

Springer-Verlag Berlin Heidelberg, 2010. pp. xi+329.

The book presents the winners of the first five Abel Prizes in mathematics: 2003 Jean-Pierre Serre; 2004 Sir Michael Atiyah and Isadore Singer; 2005 Peter D. Lax; 2006 Lennart Carleson; and 2007 S.R. Srinivasa Varadhan.

Each laureate provides an autobiography or an interview, a curriculum vitae, and a complete bibliography. This is complemented by a scholarly description of their work written by leading experts in the field and by a brief history of the Abel Prize. Interviews with the laureates can be found at http://extras.springer.com

Springer: https://www.springer.com/gp/book/9783642013720

Springer (eBook): https://link.springer.com/book/10.1007%2F978-3-642-01373-7

Reviews:

## P.C. Hemmer, H. Holden, S. Kjelstrup Ratkje (eds.): The Collected Works of Lars Onsager (With Commentary)

World Scientific, Singapore, 1996, pp. 1088.

This volume contains the collected works of the eminent chemist and physicist Lars Onsager, one of the most influential scientists of the 20th Century.

The volume includes Onsager's previously unpublished PhD thesis, a biography by H C Longuet-Higgins and M E Fisher, an autobiographical commentary, selected photographs, and a list of Onsager discussion remarks in print.

Onsager's scientific achievements were characterized by deep insights into the natural sciences. His two best-known accomplishments are his reciprocal relations for irreversible processes, for which he received the 1968 Nobel Prize in Chemistry, and his explicit solution of the two-dimensional Ising model, a mathematical tour de force that created a sensation when it appeared. In addition, he made significant theoretical contributions to other fields, including electrolytes, colloids, superconductivity, turbulence, ice, electrons in metals, and dielectrics.

In this volume, Onsager's contributions are divided into the following fields: irreversible processes; the Ising model; electrolytes; colloids; helium II and vortex quantization; off-diagonal long-range order and flux quantization; electrons in metal; turbulence; ion recombination; fluctuation theory; dielectrics; ice and water; biology; Mathieu functions. The different fields are evaluated by leading experts. The commentators are P W Anderson, R Askey, A Chorin, C Domb, R J Donnelly, W Ebeling, J-C Justice, H N W Lekkerkerker, P Mazur, H P McKean, J F Nagle, T Odijk, A B Pippard, G Stell, G H Weiss, and C N Yang.

World Scientific: https://www.worldscientific.com/worldscibooks/10.1142/3027

## P. Exner, R.L. Frank, F. Gesztesy, H. Holden, T. Weidl (eds.): Partial Differential Equations, Spectral Theory, and Mathematical Physics. The Ari Laptev Anniversary Volume

EMS Press, 2011, pp. 481.

This volume is dedicated to Ari Laptev on the occasion of his 70th birthday. It collects contributions by his numerous colleagues sharing with him research interests in analysis and spectral theory.

In brief, the topics covered include Friedrichs, Hardy, and Lieb–Thirring inequalities, eigenvalue bounds and asymptotics, Feshbach–Schur maps and perturbation theory, scattering theory and orthogonal polynomials, stability of matter, electron density estimates, Bose–Einstein condensation, Wehrl-type entropy inequalities, Bogoliubov theory, wave packet evolution, heat kernel estimates, homogenization, d-bar problems, Brezis–Nirenberg problems, the nonlinear Schrödinger equation in magnetic fields, classical discriminants, and the two-dimensional Euler–Bardina equations. In addition, Ari’s multifaceted service to the mathematical community is also touched upon.

Altogether the volume presents a collection of research articles which will be of interest to any active scientist working in one of the above mentioned fields.

Keywords: Friedrichs inequality, Hardy inequality, Lieb–Thirring inequality, Feshbach–Schur map, scattering theory, Wehrl-type entropy inequalities, electron density estimates, stability of matter, Bose–Einstein condensation, heat kernel estimates, Euler–Bardina equations, nonlinear Schrödinger equation, Brezis–Nirenberg problem, d-bar problem, Bogoliubov theory, wave packet evolution

EMS Press: https://www.ems-ph.org/books/book.php?proj_nr=265

## G.-Q. G. Chen, H. Holden, K. H. Karlsen (eds.): Hyperbolic Conservation Laws and Related Analysis with Applications. Edinburgh, September 2011.

Springer-Verlag Berlin Heidelberg, 2014. pp. x+384.

This book presents thirteen papers, representing the most significant advances and current trends in nonlinear hyperbolic conservation laws and related analysis with applications. Topics covered include a survey on multidimensional systems of conservation laws as well as novel results on liquid crystals, conservation laws with discontinuous flux functions, and applications to sedimentation. Also included are articles on recent advances in the Euler equations and the Navier-Stokes-Fourier-Poisson system, in addition to new results on collective phenomena described by the Cucker-Smale model.

The Workshop on Hyperbolic Conservation Laws and Related Analysis with Applications at the International Centre for Mathematical Sciences (Edinburgh, UK) held in Edinburgh, September 2011, produced this fine collection of original research and survey articles. Many leading mathematicians attended the event and submitted their contributions for this volume. It is addressed to researchers and graduate students interested in partial differential equations and related analysis with applications.

Springer: https://www.springer.com/gp/book/9783642390067

Springer (eBook): https://link.springer.com/book/10.1007%2F978-3-642-39007-4

## H. Holden, B. Simon, G. Teschl (eds.): Spectral Analysis, Differential Equations and Mathematical Physics: A Festschrift in Honor of Fritz Gesztesy’s 60th Birthday

Proceedings of Symposia in Pure Mathematics, American Mathematical Society, Providence. Volume: 87. 2013; 376 pp.

This volume contains twenty contributions in the area of mathematical physics where Fritz Gesztesy made profound contributions.

There are three survey papers in spectral theory, differential equations, and mathematical physics, which highlight, in particular, certain aspects of Gesztesy's work. The remaining seventeen papers contain original research results in diverse areas reflecting his interests. The topics of these papers range from stochastic differential equations; operators on graphs; elliptic partial differential equations; Sturm-Liouville, Jacobi, and CMV operators; semigroups; to inverse problems.

## H. Holden, K.H. Karlsen (eds.): Nonlinear Partial Differential Equations. The Abel Symposium 2010.

Springer-Verlag Berlin Heidelberg, 2012. pp. xvi+360.

The topic of the 2010 Abel Symposium, hosted at the Norwegian Academy of Science and Letters, Oslo, was Nonlinear Partial Differential Equations, the study of which is of fundamental importance in mathematics and in almost all of natural sciences, economics, and engineering.

This area of mathematics is currently in the midst of an unprecedented development worldwide. Differential equations are used to model phenomena of increasing complexity, and in areas that have traditionally been outside the realm of mathematics. New analytical tools and numerical methods are dramatically improving our understanding of nonlinear models. Nonlinearity gives rise to novel effects reflected in the appearance of shock waves, turbulence, material defects, etc., and offers challenging mathematical problems. On the other hand, new mathematical developments provide new insight in many applications.

These proceedings present a selection of the latest exciting results by world leading researchers.

Springer: https://www.springer.com/gp/book/9783642253607

Springer (eBook): https://link.springer.com/book/10.1007%2F978-3-642-25361-4

## H. Holden, K.H. Karlsen (eds.): Nonlinear Partial Differential Equations and Hyperbolic Wave Phenomena.

Contemporary Mathematics, American Mathematical Society, Providence. Volume: 526; 2010; 389 pp.

This volume presents the state of the art in several directions of research conducted by renowned mathematicians who participated in the research program on Nonlinear Partial Differential Equations at the Centre for Advanced Study at the Norwegian Academy of Science and Letters, Oslo, Norway, during the academic year 2008–09.

The main theme of the volume is nonlinear partial differential equations that model a wide variety of wave phenomena. Topics discussed include systems of conservation laws, compressible Navier-Stokes equations, Navier-Stokes-Korteweg type systems in models for phase transitions, nonlinear evolution equations, degenerate/mixed type equations in fluid mechanics and differential geometry, nonlinear dispersive wave equations (Korteweg-de Vries, Camassa-Holm type, etc.), and Poisson interface problems and level set formulations.

## F. Gesztesy, H. Holden, J. Jost, S. Paycha, M. Röckner, S. Scarlatti (eds.): Stochastic Processes, Physics and Geometry: New Interplays. I: A Volume in Honor of Sergio Albeverio

Conference Proceedings, Canadian Mathematical Society, American Mathematical Society. Volume: 28; 2000; 333 pp;

A co-publication of the AMS and Canadian Mathematical Society

This volume and Stochastic Processes, Physics and Geometry: New Interplays. II present state-of-the-art research currently unfolding at the interface between mathematics and physics. Included are select articles from the international conference held in Leipzig (Germany) in honor of Sergio Albeverio's sixtieth birthday. The theme of the conference, “Infinite Dimensional (Stochastic) Analysis and Quantum Physics”, was chosen to reflect Albeverio's wide-ranging scientific interests. The articles in these books reflect that broad range of interests and provide a detailed overview highlighting the deep interplay among stochastic processes, mathematical physics, and geometry.

The contributions are written by internationally recognized experts in the fields of stochastic analysis, linear and nonlinear (deterministic and stochastic) PDEs, infinite dimensional analysis, functional analysis, commutative and noncommutative probability theory, integrable systems, quantum and statistical mechanics, geometric quantization, and neural networks. Also included are applications in biology and other areas.

Most of the contributions are high-level research papers. However, there are also some overviews on topics of general interest. The articles selected for publication in these volumes were specifically chosen to introduce readers to advanced topics, to emphasize interdisciplinary connections, and to stress future research directions. Volume I contains contributions from invited speakers; Volume II contains additional contributed papers.

## F. Gesztesy, H. Holden, J. Jost, S. Paycha, M. Röckner, S. Scarlatti (eds.): Stochastic Processes, Physics and Geometry: New Interplays. II: A Volume in Honor of Sergio Albeverio

Conference Proceedings, Canadian Mathematical Society, American Mathematical Society. Volume: 29; 2000; 647 pp;

A co-publication of the AMS and Canadian Mathematical Society

This volume and Stochastic Processes, Physics and Geometry: New Interplays. I present state-of-the-art research currently unfolding at the interface between mathematics and physics. Included are select articles from the international conference held in Leipzig (Germany) in honor of Sergio Albeverio's sixtieth birthday. The theme of the conference, “Infinite Dimensional (Stochastic) Analysis and Quantum Physics”, was chosen to reflect Albeverio's wide-ranging scientific interests. The articles in these books reflect that broad range of interests and provide a detailed overview highlighting the deep interplay among stochastic processes, mathematical physics, and geometry.

The contributions are written by internationally recognized experts in the fields of stochastic analysis, linear and nonlinear (deterministic and stochastic) PDEs, infinite dimensional analysis, functional analysis, commutative and noncommutative probability theory, integrable systems, quantum and statistical mechanics, geometric quantization, and neural networks. Also included are applications in biology and other areas.

Most of the contributions are high-level research papers. However, there are also some overviews on topics of general interest. The articles selected for publication in these volumes were specifically chosen to introduce readers to advanced topics, to emphasize interdisciplinary connections, and to stress future research directions. Volume I contains contributions from invited speakers; Volume II contains additional contributed papers.

## S. Albeverio, J.E. Fenstad, H. Holden, T. Lindstrøm (eds.): Ideas and Methods in Quantum and Statistical Physics. In Memory of Raphael Høegh-Krohn

Cambridge University Press, Cambridge, 1992. pp. 558 .

These volumes contain a collection of essays by many of the closest co-workers of Raphael Høegh-Krohn, 1938–88, one of the outstanding mathematical physicists of our age. The contributions vary in style, purpose and content - some are surveys where leading experts sum up and clarify a subject area, others are new and adventurous expeditions into unknown territory. The topics cover most aspects of modern mathematical physics with special emphasis on methods from operator theory and stochastic analysis. Many of the papers are based on talks given at a symposium in honour of Høegh-Krohn at the University of Oslo; however the final volumes are far more than proceedings and great care has been taken to attract contributions from the leading researchers.

## S. Albeverio, J.E. Fenstad, H. Holden, T. Lindstrøm (eds.): Ideas and Methods in Quantum and Statistical Physics. In Memory of Raphael Høegh-Krohn

Cambridge University Press, Cambridge, 1992. pp. 524.

These volumes contain a collection of essays by many of the closest co-workers of Raphael Høegh-Krohn, 1938–88, one of the outstanding mathematical physicists of our age. The contributions vary in style, purpose, and content - some are surveys where leading experts sum up and clarify a subject area, others are new and adventurous expeditions into unknown territory. The topics cover most aspects of modern mathematical physics with special emphasis on methods from operator theory and stochastic analysis. Many of the papers are based on talks given at a symposium in honor of Høegh-Krohn at the University of Oslo: however the final volumes are far more than proceedings and great care has been taken to attract contributions from the leading researchers.

## H. Holden, A. Jensen (eds.): Schrödinger Operators. Proceedings of the Nordic Summer School in Mathematics Held at Sandbjerg Slot, Sønderborg, Denmark, August 1–12, 1988.

Lecture Notes in Physics, vol. 345. Springer-Verlag Berlin Heidelberg, 1989. pp. V+458.

Understanding quantum mechanics inevitably leads to an in-depth study of the Schrödinger operator. This set of review lectures informs researchers and advanced students of the most recent developments in the analysis of the Schrödinger operator occurring in solid-state physics, nuclear physics, etc. The topics covered are nonlinear and random potentials, magnetic fields, and many-body problems. Inverse spectral theory is also treated. The results are mathematically rigorous and many physical implications are discussed. The book is suitable for advanced courses in mathematical physics.

## H. Holden, K. Overskaug (eds.): Høydepunkter i Skrifter og Forhandlinger. Et utvalg artikler fra perioden 1761–2011.

DKNVS Skrifter, Trondheim, 2011. pp. 256.

Det første nummeret i Skrifter kom ut i 1761, alt året etter stiftinga av Det Trondhiemske Selskab som selskapet heitte fram til det vart approbert 1767, og er dermed ein av verdas eldste laupande vitskaplege publikasjonsseriar.

Utanom stiftarane av selskapet Gunnerus, Schøning og Suhm, har mange andre skrive artiklar til Skrifter. Mellom desse finn vi prest, naturforskar og topograf Hans Strøm, og komponist, overbranndirektør og meteorolog Johan Daniel Berlin.

Matematikar Niels Henrik Abel, filosof Arthur Schopenhauer, diktarane Henrik Wergeland, Johan Sebastian Welhaven og Henrik Ibsen, zoolog Michael Sars samt språkforskar, botanikar og diktar Ivar Aasen har óg medverka i skriftserien.

Skrifter har hatt eit godt fotfeste i grunnforskinga, og skal attspegla samtlege disiplinar som er representerte innan Vitenskapsselskapet sine humanistiske og naturvitskaplege klassar. Artiklane i skriftserien representerer såleis eit breidt emneval, som spenner frå naturvitskap i vidaste forstand, til matematiske fag, teknologi, samfunnsvitskap, teologi, filosofi, historie, litteratur, språkvitskap og kunst.

## Book published on the occasion of my 60th birthday:

## F. Gesztesy, H. Hanche-Olsen, E.R. Jakobsen, Y.I. Lyubarskii, N. H. Risebro, K. Seip (eds.): Non-Linear Partial Differential Equations, Mathematical Physics, and Stochastic Analysis. The Helge Holden Anniversary Volume

EMS Publishing House, Zurich, 2018, 502 pp,

This volume is dedicated to Helge Holden on the occasion of his 60th anniversary. It collects contributions by numerous scientists with expertise in non-linear partial differential equations (PDEs), mathematical physics, and stochastic analysis, reflecting to a large degree Helge Holden’s longstanding research interests. Accordingly, the problems addressed in the contributions deal with a large range of topics, including, in particular, infinite-dimensional analysis, linear and nonlinear PDEs, stochastic analysis, spectral theory, completely integrable systems, random matrix theory, and chaotic dynamics and sestina poetry. They represent to some extent the lectures presented at the conference Non-linear PDEs, Mathematical Physics and Stochastic Analysis, held at NTNU, Trondheim, July 4–7, 2016 (https://wiki.math.ntnu.no/holden60).

The mathematical tools involved draw from a wide variety of techniques in functional analysis, operator theory, and probability theory.

This collection of research papers will be of interest to any active scientist working in one of the above mentioned areas.