Hiroaki Nakamura – författare

This volume is an outgrowth of the research project "The Inverse Ga­ lois Problem and its Application to Number Theory" which was carried out in three academic years from 1999 to 2001 with the support of the Grant-in-Aid for Scientific Research (B) (1) No. 11440013. In September, 2001, an international conference "Galois Theory and Modular Forms" was held at Tokyo Metropolitan University after some preparatory work­ shops and symposia in previous years. The title of this book came from that of the conference, and the authors were participants of those meet­ All of the articles here were critically refereed by experts. Some of ings. these articles give well prepared surveys on branches of research areas, and many articles aim to bear the latest research results accompanied with carefully written expository introductions. When we started our re~earch project, we picked up three areas to investigate under the key word "Galois groups"; namely, "generic poly­ nomials" to be applied to number theory, "Galois coverings of algebraic curves" to study new type of representations of absolute Galois groups, and explicitly described "Shimura varieties" to understand well the Ga­ lois structures of some interesting polynomials including Brumer's sextic for the alternating group of degree 5. The topics of the articles in this volume are widely spread as a result. At a first glance, some readers may think this book somewhat unfocussed.

This volume is an outgrowth of the research project "The Inverse Ga­ lois Problem and its Application to Number Theory" which was carried out in three academic years from 1999 to 2001 with the support of the Grant-in-Aid for Scientific Research (B) (1) No. 11440013. In September, 2001, an international conference "Galois Theory and Modular Forms" was held at Tokyo Metropolitan University after some preparatory work­ shops and symposia in previous years. The title of this book came from that of the conference, and the authors were participants of those meet­ All of the articles here were critically refereed by experts. Some of ings. these articles give well prepared surveys on branches of research areas, and many articles aim to bear the latest research results accompanied with carefully written expository introductions. When we started our re~earch project, we picked up three areas to investigate under the key word "Galois groups"; namely, "generic poly­ nomials" to be applied to number theory, "Galois coverings of algebraic curves" to study new type of representations of absolute Galois groups, and explicitly described "Shimura varieties" to understand well the Ga­ lois structures of some interesting polynomials including Brumer's sextic for the alternating group of degree 5. The topics of the articles in this volume are widely spread as a result. At a first glance, some readers may think this book somewhat unfocussed.

This book is the result of research initiatives formed during the workshop "Low Dimensional Topology and Number Theory XIII" at Kyushu University in 2022. It is also dedicated to the memory of Professor Toshie Takata, who has been a main figure of the session chairs for the series of annual workshops since 2009.The activity was aimed at understanding and deepening recent developments of lively and fruitful interactions between low-dimensional topology and number theory over the past decades.In this volume of proceedings, the reader will find research papers as well as survey articles, including open problems, at the interface between classical and quantum topology, and algebraic and analytic number theory,  written by leading experts and active researchers in the respective fields.Topics include, among others, the strong slope conjecture; Kashiwara–Vergne Lie algebra; braids and fibered double branched covers of 3-manifolds; Temperley–Lieb–Jones category andconformal blocks; WRT invariants and false theta functions; the colored Jones polynomial of the figure-eight knot; potential functions and A-polynomials; l-adic Galois polylogarithms; Dijkgraaf–Witten invariants in Bloch groups; analogies between knots and primes in arithmetic topology; normalized Jones polynomials for rational links; Iwasawa main conjecture; Weber’s class number problem.The book provides a valuable resource for researchers and graduate students interested in topics related to both low-dimensional topology and number theory.