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.