Vol.88 　 　 McKay Correspondence, Mutation and Related Topics Edited by Y. Ito, A. Ishii and O. Iyama 　 　 This volume is the proceedings of the online conference "McKay correspondence, Mutation and Related Topics," which was held at Kavli Institute for the Physics and Mathematics of the Universe (IPMU) in Japan in Summer in 2020. This volume consists of 15 peer-reviewed articles written by speakers who lead currently active research fields of McKay correspondence, crepant resolution, singularities, quiver and cluster algebra. The editors believe that this volume is quite useful for all researchers and students who are interested in these fruitful research fields.

Vol.87 　 　 Stochastic Analysis, Random Fields and Integrable Probability --- Fukuoka 201 Edited by Y. Inahama, H. Osada and T. Shirai 　 　 This volume is the proceedings of the 12th Mathematical Society of Japan, Seasonal Institute (MSJ-SI) "Stochastic Analysis, Random Fields and Integrable Probability," which was held at Kyushu University in Fukuoka, Japan from July 31 to August 9, 2019. This volume consists of 18 peer-reviewed articles written by speakers who lead currently active research fields of probability theory such as stochastic analysis, integrable probability, random fields and discrete probability. The editors believe that this volume is quite useful for all researchers and students who are interested in these fruitful research fields.

Vol.86 　 　 Development of Iwasawa Theory --- the Centennial of K. Iwasawa's Birth Edited by M. Kurihara, K. Bannai, T. Ochiai and T. Tsuji 　 　 This volume is edited as the proceedings of the international conference “Iwasawa 2017”, which was held at the University of Tokyo from July 19th through July 28th, 2017, in order to commemorate the 100th anniversary of Kenkichi Iwasawa's birth. In total 236 participants attended the conference including 98 participants from 15 countries outside Japan, and enjoyed the talks and the discussions on several themes flourishing in Iwasawa theory. This volume consists of 3 survey papers and of 15 research papers submitted from the speakers and the organizers of the conference. We also included 4 essays on memories of Iwasawa to celebrate the Centennial of Iwasawa's birth. We recommend this volume to all researchers and graduate students who are interested in Iwasawa theory, number theory and related fields.

Vol.85 　 　 The Role of Metrics in the Theory of Partial Differential Equations Edited by Y. Giga, N. Hamamuki, H. Kubo, H. Kuroda and T. Ozawa 　 　 This volume is edited as the proceedings of the 11th Mathematical Society of Japan, Seasonal Institute (MSJ-SI) “The Role of Metrics in the Theory of Partial Differential Equations”, held for the period of July 2 - 13, 2018 in Hokkaido University, Sapporo, Japan. This volume consists of peer-reviewed articles written by speakers who actively lead the fields of partial differential equations, numerical analysis, harmonic analysis, and geometric analysis. It should be underlined that 3 survey articles provided by course lecturers show an interesting direction of analysis under various metrics. This volume is suitable for any graduate students and young researchers to motivate the research on these fields from the viewpoint of metrics.

Vol.84 　 　 Various Aspects of Multiple Zeta Functions --- in honor of Professor Kohji Matsumoto's 60th birthday Edited by H. Mishou, T. Nakamura, M. Suzuki and Y. Umegaki 　 　 This volume is the proceedings of the international conference "Various Aspects of Multiple Zeta Functions" in honor of Professor Kohji Matsumoto's 60th birthday held at Nagoya University, Japan, during August 21 to 25, 2017. The present volume consists of 15 research papers on various recent topics about multiple zeta-functions, which include not only actually multivariate cases but also single-variable cases, additive and multiplicative number theory, and poly-Bernoulli numbers and polynomials. The editors believe that this volume represents the major part of the contributions presented in the conference, and hope that the volume is useful for all researchers and students who are interested in this fruitful research field.

Vol.83 　 　 Primitive Forms and Related Subjects---Kavli IPMU 2014 Edited by K. Hori, C. Li, S. Li and K. Saito 　 　 This is the proceedings of the conference "Primitive Forms and Related Subjects" held at Kavli IPMU, the University of Tokyo in February 10-14, 2014. The principal aim of the conference was to discuss the current status of rapidly developing subjects related to primitive forms. In particular, Fukaya category, Gromov-Witten and FJRW invariants, mathematical formulation of Landau-Ginzburg models, and mirror symmetry were discussed. The conference had three introductory courses by　experts, and 12 lectures on more advanced topics. The present volume contains two survey articles and 11 research articles based on them. Thus the volume is recommended both to researchers who are already experts in the subjects, and also to graduate students who are interested in and want to start study the subjects.

Vol.82 　 　 Differential Geometry and Tanaka Theory---Differential Systems and Hypersurface Theory--- Edited by T. Shoda and K. Shibuya 　 　 This volume is published in honor of the sixtieth birthdays of Professors Reiko Miyaoka and Keizo Yamaguchi, contributed by international researchers. On January 2011, the international conference "Differential Geometry and Tanaka Theory --Differential System and Hypersurface Theory--'' was held at the Research Institute for Mathematical Sciences (RIMS), Kyoto University in honor of their sixtieth birthdays. With deep admiration and respect, we dedicate the present volume to the two Professors. This volume contains one survey article and six research articles, recommended to researchers in related fields.

Vol.81 　 　 Asymptotic Analysis for Nonlinear Dispersive and Wave Equations Edited by K. Kato, T. Ogawa and T. Ozawa 　 　 This volume is edited as the proceedings of the international conference "Asymptotic Analysis for Nonlinear Dispersive and Wave Equations" held in September, 2014 at Department of Mathematics, Osaka University, Osaka, Japan. The conference was devoted to the honor of Professor Nakao Hayashi (Osaka University) on the occasion of his 60th birth year, and includes the newest results up to 2017 related to the fields of nonlinear partial differential equations of hyperbolic and dispersive type. In particular, the asymptotic expansion of solutions for those equations has been the main contribution of Professor Hayashi and his collaborators. The contents is 18 papers related to the asymptotic analysis and qualitative research paper concerning the problems of nonlinear wave equations and nonlinear dispersive equations such as nonlinear Schrödinger equations, the Hartree equation, the Camassa--Holm equation, the Ginzburg--Landau equations. Among others, the outstanding method developed by Professor Hayashi and his collaborators is introduced by one of his main collaborator, Professor P.I. Naumkin. This volume is suitable for any students and young researchers who are starting the research on the asymptotic analysis of nonlinear wave and dispersive equations for knowing the out-lined theory of these fields.

Vol.80 　 　 Operator Algebras and Mathematical Physics Edited by M. Izumi, Y. Kawahigashi, M. Kotani, H. Matui and N. Ozawa 　 　 This is a proceedings volume of an international conference "Operator Algebras and Mathematical Physics" held at Tohoku University in August, 2016. This meeting was the 9th MSJ-Seasonal Institute of the Mathematical Society of Japan. Twenty-eight researchers gave lectures on a wide range of topics on operator algebras and their applications to mathematical physics. This volume contains one survey article and 11 research articles based on the lectures given. We recommend this to researchers and graduate students in related fields strongly.

Vol.79 　 　 Mathematics of Takebe Katahiro and History of Mathematics in East Asia Edited by T. Ogawa and M. Morimoto 　 　 This volume is a collection of papers contributed by participants at the "International Conference on Traditional Mathematics in East Asia and Related Topics" held August 25 -- 30, 2014 at Ochanomizu University, Tokyo, Japan, which was one of the satellite conferences of the Seoul ICM 2014. The year 2014 also coincides with the 350th anniversary of the birth of Takebe Katahiro (1664 -- 1739), one of the great mathematicians of the Edo period. In his honor, the conference was called the "Takebe Conference 2014." This volume is divided into four parts and an appendix. Part one is concerned with Takebe Katahiro, his mathematics and his times. The editors believe that wasan represents one phase of the mathematics of East Asia, especially of China, Japan and Korea, for which ancient Chinese mathematics served as a basis, and Chinese characters as a lingua franca. Part two concerns the old mathematics of Korea in the Joseon Dynasty. Part three treats the mathematics of Ancient China. Part four, finally, follows the subsequent development of Japanese mathematics and mathematical education after the Meiji Restoration (1868). The very substantial appendix contains English translations of three volumes (12, 17 and 19) of the Taisei Sankei (twenty volumes, 1711), a monograph written by the master mathematician Seki Takakazu and the two Takebe brothers, Kata’akira and Katahiro.

Vol.78 　 　 Singularities in Generic Geometry Edited by S. Izumiya, G. Ishikawa, M. Yamamoto, K. Saji, T. Yamamoto and M. Takahashi 　 　 This volume is the proceedings of the workshop“Singularities in Generic Geometry and Applications--Kobe-Kyoto 2015 (Valencia IV)--”which was held at Kobe University June 3-6 and RIMS, Kyoto University June 8-10, 2015. The workshop was the fourth in a sequence of biennial workshops, which had been started in Valencia (Spain, 2009). The volume consists fifteen original research articles and three survey articles by specialists in Singularity theory and its applications to Differential Topology and Differential Geometry. It is highly recommended to researchers and graduate students who are interested in these areas.

Vol.77 　 　 The 50th Anniversary of Gröbner Bases Edited by T. Hibi 　 　 The discovery of the algorithm by Bruno Buchberger on July 1965, so-called the Buchberger algorithm, to compute Gröbner bases of ideals of the polynomial ring had led the birth of the exciting research area called "Computer Algebra" in the modern mathematics. The 8th Mathematical Society of Japan Seasonal Institute (MSJ SI 2015) entitled "The 50th Anniversary of Gröbner Bases" was held on July 2015, which is the 50th year following the discovery of the Buchberger algorithm. This volume is the proceedings of MSJ SI 2015 and consists of 14 papers related with computer algebra, algebraic statistics, D-modules, convex polytopes and toric ideals. These papers enable the reader to look over the current trends on Gröbner bases. Especially, young researchers can reach a treasury of fascinating research problems which are pending. Foreword was contributed by Bruno Buchberger, where a secret story on the discovery of the Buchberger algorithm is stated.

Vol.76 　 　 Representation Theory, Special Functions and Painlevé Equations --- RIMS 2015 Edited by H. Konno, H. Sakai, J. Shiraishi, T. Suzuki and Y. Yamada 　 　 To celebrate Professor Masatoshi Noumi's 60th Birthday, we held the international conference "Representation Theory, Special Functions and Painlevé Equations" at the Research Institute for Mathematical Sciences, Kyoto University from March 3 to March 6 in 2015. This volume is the proceedings of the conference. It contains 15 papers covering a variety of topics in the research fields where Prof. Noumi has made many significant contributions over the years -- representation theory, special functions, Painlevé equations and so on. We hope that readers interested in those subjects will find exciting and stimulating insights from excellent papers of this volume.

Vol.75 　 　 Algebraic Varieties and Automorphism Groups Edited by K. Masuda, T. Kishimoto, H. Kojima, M. Miyanishi and M. Zaidenberg 　 　 This volume is the proceedings of the workshop on "Algebraic Varieties and Automorphism Groups" which was held at RIMS, Kyoto University during July 7--11, 2014. The volume consists of fifteen original research articles by specialists in fast developing areas of algebraic geometry including various aspects of algebraic varieties (singularities, toric surfaces, weak positivity of log canonical pairs, Fano threefolds with cylinders, etc.), algebraic group actions on algebraic varieties (actions of additive group, unipotent group, semi-abelian variety, etc.) , automorphism groups of affine varieties and Cremona groups. Highly recommended to researchers and graduate students interested in research trends in affine and projective algebraic geometry and algebraic group actions.

Vol.74 　 　 Higher Dimensional Algebraic Geometry in honour of Professor Yujiro Kawamata's sixtieth birthday Edited by K. Oguiso, C. Birkar, S. Ishii and S. Takayama 　 　 This is the proceedings of the conference "Higher dimensional algebraic geometry - in honour of Professor Yujiro Kawamata's sixtieth birthday". This volume consists of 20 inspiring research papers on birational algebraic geometry, minimal model program, derived algebraic geometry, classification of algebraic varieties, transcendental methods and so on, by very active top level of mathematicians all over the worlds. We believe that this volume will be useful for researchers in these area as well as those who are studying algebraic geometry.

Vol.73 　 　 Hyperbolic Geometry and Geometric Group Theory Edited by K. Fujiwara, S. Kojima and K. Ohshika 　 　 The 7th Seasonal Institute of the Mathematical Society of Japan (MSJ-SI meeting) under the title ‘Hyperbolic geometry and geometric group theory’ was held from 30 July to 5 August 2014 at the University of Tokyo. This volume is the proceedings of the meeting, and collects survey and research articles in this fast-growing field by international specialists. Recommended for researchers and graduate students interested in hyperbolic geometry, geometric group theory, and low-dimensional topology.

Vol.72 　 　 Geometry, Dynamics, and Foliations 2013 In honor of Steven Hurder and Takashi Tsuboi on the occasion of their 60th birthdays Edited by T. Asuke, S. Matsumoto and Y. Mitsumatsu 　 　 This volume is an outcome of the conference 'Geometry and Foliations 2013' held in Tokyo in September 2013 and associated meetings, aimed for providing a good overview of the present studies as well as some perspective for further studies. The aspects and quality of the volume is represented by B. Deroin's survey on Brownian motions on foliated complex surfaces which contains many essential results and ideas. Other articles cover wide topics of foliations and groups of diffeomorphisms old and new; some discuss characteristic classes such as Godbillon-Vey class or homotopy theory of foliations while others deal with topological and differential geometrical aspects, particularly in the holomorphic setting. Also, several articles shows relationship to the geometric group theory. Highly recommended to researchers and graduate students who are interested in and going to study the theories of foliations and related topics such as diffeomorphism groups, geometric group theory.

Vol.71 　 　 Schubert Calculus --- Osaka 2012 Edited by H. Naruse, T. Ikeda, M. Masuda and T. Tanisaki 　 　 This volume is the proceedings of the 5th MSJ Seasonal Institute "Schubert Calculus" held at Osaka City University, September 17th--27th, 2012. It is recommended for all researchers and graduate students who are interested in Schubert calculus and its many connections and applications to related areas of mathematics, such as geometric representation theory, combinatorial aspects of algebraic varieties arising in Lie theory, and equivariant topology. Alain Lascoux, who is one of the pioneers of modern Schubert calculus, and a contributor of this volume, passed away during the time of editing process of the proceedings. The volume is dedicated to him.

Vol.70 　 　 Minimal Models and Extremal Rays (Kyoto, 2011) Edited by J. Kollár, O. Fujino, S. Mukai and N. Nakayama 　 　 Since the appearance of extremal rays and the minimal model program around 1980, we have seen the tremendous development of Algebraic Geometry. With this in mind, the conference "Minimal Models and Extremal Rays" was held at RIMS Kyoto University in June 2011. The purpose was to review the past, examine the present and enjoy discussing the future. This volume is the outcome of this conference and consists of one survey article on the mathematical work of Professor Shigefumi Mori, who turned sixty in 2011, and thirteen research papers given by the authors: L. Ein--S. Ishii--M. Mustaţă, J. Kollár, S. Kovács--K. Schwede, D. Greb--S. Kebekus--T. Peternell, H. Kawanoue--K. Matsuki, A-S. Kaloghiros--A. Küronya--V. Lazić, J-M. Hwang--K. Oguiso, M. Lehn--Y. Namikawa--Ch. Sorger--D. van Straten, O. Fujino, J. Chen, C. Hacon--C. Xu, S. Mukai, Y. Prokhorov--M. Reid.

Vol.69 　 　 Development of Moduli Theory --- Kyoto 2013 Edited by O. Fujino, S. Kondô, A. Moriwaki, M.-H. Saito and K. Yoshioka 　 　 The present volume is the proceedings of the meeting "Development of Moduli theory" which was held as the Seasonal Institute 2013 (The 6th MSJ-SI), the Mathematical Society of Japan and the 2013 Research Project of Research Institute of Mathematical Science, Kyoto University. This volume is dedicated to Professor Shigeru Mukai on the occasion of his sixtieth birthday. The volume consists of five survey articles and eight research articles given by the authors: I. Dolgachev, E. Looijenga, N. Mestrano--C. Simpson, H. Nakajima, I. Nakamura, V. Alexeev, M. Aprodu--G. Farkas--A. Ortega, I. Ciocan-Fontanine--B. Kim, B. Hassett--A. Kresch--Y. Tschinkel, D. Huybrechts, J.H. Keum, V. Nikulin, K. Yoshioka.

Vol.68 　 　 School on Real and Complex Singularities in São Carlos, 2012 Edited by R. N. Araújo dos Santos, V. H. Jorge Pérez, O. Saeki and T. Nishimura 　 　 This volume is a collection of 6 lecture notes presented at the School on Singularity Theory, São Carlos, Brazil, July 16-21, 2012, or at the 12th International Workshop on Real and Complex Singularities, São Carlos, Brazil, July 22-27, 2012. Topics treated in the 6 lecture notes written by established authors cover, reflecting authors' expertise, a wide range including Topology and Geometry of real singularities, Singularities of holomorphic map-germs, Singularities of complex algebraic sets, Algorithms of the computer algebra "SINGULAR", Singularities of maps and characteristic classes, Limit cycles of systems of ordinary differential equations. Each lecture note is extremely well-written with plentiful examples and may be considered as one of the most excellent readings in the relevant topic. This book is suitable for being kept at one's desk-side and widely recommended for graduate students studying singularity theory, and researchers in various fields who would like to enjoy the world of singularities.

Vol.67 　 　 Variational Methods for Evolving Objects Edited by L. Ambrosio, Y. Giga, P. Rybka and Y. Tonegawa 　 　 This volume consists of eight original survey papers written by invited lecturers in connection with a conference “Variational Methods for Evolving Objects” held at Hokkaido University, Sapporo, Japan, July 30--August 3, 2012. The topics of papers vary widely from problems in image processing to dynamics of topological defects, and all involve some nonlinear phenomena of current major research interests. These papers are carefully prepared so that they serve as a good starting point of investigation for graduate students and new comers to the field and are strongly recommended.

Vol.66 　 　 Singularities in Geometry and Topology 2011 Edited by V. Blanlœil and O. Saeki 　 　 This book collects original and survey papers on Singularities in Geometry and Topology, which resulted from the 6th Franco--Japanese Symposium on Singularities, held in Fukuoka, during September 5--10, 2011. Though singularity theory was born in the XIXth century, this field of research became more popular in France after Prof. Heisuke Hironaka came to Paris. Then, a lot of collaborations between Japanese and French mathematicians started, and the conferences on Singularities in Geometry and Topology continue to develop this collaboration between France and Japan. This volume consists of 2 survey articles and 12 research articles, whose topics include algebraic curves and varieties, line arrangements, mixed polynomials, algebraic local cohomology classes, stable maps, and mirror symmetry. This book is recommended to any researcher or graduate student interested in singularity theory.

Vol.65 　 　 Algebraic Geometry in East Asia --- Taipei 2011 Edited by J. A. Chen, M. Chen, Y. Kawamata and J. Keum 　 　 Algebraic geometry in a traditional and fast developing research area in east Asia. There were many world leading algebraic geometers and there are remarkably increasing active mathematicians in the related area in the East Asia area including China, Japan, Korea, Taiwan and Vietnam. The purpose of the conference series “Algebraic Geometry in East Asia” is to provide a platform for algebraic geometers in or closely related to East Asia. This volume is the proceeding of the conference “Algebraic Geometry in East Asia, Taipei” which was held in November of 2011 in NCTS at Taipei. It contains two survey articles together with nine research articles. It provides the up-to-date advances of the research of algebraic geometry in East Asia.

Vol.64 　 　 Nonlinear Dynamics in Partial Differential Equations Edited by S.-I. Ei, S. Kawashima, M. Kimura and T. Mizumachi 　 　 This volume grew out from the 4th MSJ-SI international conference "NONLINEAR DYNAMICS IN PARTIAL DIFFERENTIAL EQUATIONS" held at Kyushu University, Kyushu, Japan, September 12th--21st, 2011. It consists of more than fifty peer-reviewed articles which are survey and research papers by participants of the conference. Nonlinear partial differential equations describing nonlinear dynamics are indispensable objects in many fields including technology and social science. This book covers recent mathematical theories and techniques to analyze such nonlinear partial differential equations. The book is recommended to any researcher or graduate student who is interested in them.