As the interaction of mathematics and theoretical physics continues to intensify, the theories developed in mathematics are being applied to physics, and conversely. This book centers around the theory of primitive forms which currently plays an active and key role in topological field theory (theoretical physics), but was originally developed as a mathematical notion to define a "good period mapping" for a family of analytic structures. The invited papers in this volume are expository in nature by participants of the Taniguchi Symposium on "Topological Field Theory, Primitive Forms and Related Topics" and the RIMS Symposium bearing the same title, both held in Kyoto. The papers reflect the broad research of some of the world's leading mathematical physicists, and should serve as an excellent resource for researchers as well as graduate students of both disciplines.

This volume contains the proceedings of the conference ``Primitive Forms and Related Subjects'', held at the Kavli Institute for the Physics and Mathematics of the Universe (IPMU), University of Tokyo, 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. This volume volume contains two survey articles and 11 research articles based on the conference presentations.

As the interaction of mathematics and theoretical physics continues to intensify, the theories developed in mathematics are being applied to physics, and conversely. This book centers around the theory of primitive forms which currently plays an active and key role in topological field theory (theoretical physics), but was originally developed as a mathematical notion to define a "good period mapping" for a family of analytic structures. The invited papers in this volume are expository in nature by participants of the Taniguchi Symposium on "Topological Field Theory, Primitive Forms and Related Topics" and the RIMS Symposium bearing the same title, both held in Kyoto. The papers reflect the broad research of some of the world's leading mathematical physicists, and should serve as an excellent resource for researchers as well as graduate students of both disciplines.

This book collects the papers presented at the Conference on Number Theory, held at the Kerala School of Mathematics, Kozhikode, Kerala, India, from December 10–14, 2018. The conference aimed at bringing the active number theorists and researchers in automorphic forms and allied areas to demonstrate their current research works. This book benefits young research scholars, postdoctoral fellows, and young faculty members working in these areas of research.

This volume contains the proceedings of the conference on Lie Algebras, Vertex Operator Algebras, and Related Topics, celebrating the 70th birthday of James Lepowsky and Robert Wilson, held from August 14–18, 2015, at the University of Notre Dame, Notre Dame, Indiana. Since their seminal work in the 1970s, Lepowsky and Wilson, their collaborators, their students, and those inspired by their work, have developed an amazing body of work intertwining the fields of Lie algebras, vertex algebras, number theory, theoretical physics, quantum groups, the representation theory of finite simple groups, and more. The papers presented here include recent results and descriptions of ongoing research initiatives representing the broad influence and deep connections brought about by the work of Lepowsky and Wilson and include a contribution by Yi-Zhi Huang summarizing some major open problems in these areas, in particular as they pertain to two-dimensional conformal field theory.

This volume contains the proceedings of the Building Bridges: 3rd EU/US Summer School and Workshop on Automorphic Forms and Related Topics, which was held in Sarajevo from July 11–22, 2016. The articles summarize material which was presented during the lectures and speed talks during the workshop. These articles address various aspects of the theory of automorphic forms and its relations with the theory of L-functions, the theory of elliptic curves, and representation theory. In addition to mathematical content, the workshop held a panel discussion on diversity and inclusion, which was chaired by a social scientist who has contributed to this volume as well. This volume is intended for researchers interested in expanding their own areas of focus, thus allowing them to “build bridges” to mathematical questions in other fields.

In her essay collection First, Second, and Other Selves: Essays on Friendship and Personal Identity, well-known scholar of ancient philosophy Jennifer Whiting gathers her previously published essays taking Aristotle's theories on friendship as a springboard to engage with contemporary philosophical work on personal identity and moral psychology. Whiting examines three themes throughout the collection, the first being psychic contingency, or the belief that the psychological structures characteristic of human beings may in fact vary, not just from one cultural (or socio-historical) context to another, but also from one individual to another. The second theme is the belief that friendship informs an understanding of the nature of the self, an idea that springs from Whiting's uncommon reading of Aristotle's writings on friendship. Specifically, Whiting explains a scenario in which a "virtuous agent" adopts a kind of impersonal attitude both towards herself and towards her "character" friends, loving both because they are virtuous; this scenario ties in with an examination of the Aristotelian concept of the ideal friend as an "other self," or a friendship that evolves from character rather than ego, as well as Whiting's meditation on whether or not a virtuous individual should have a "special" sort of concern for her own future self, distinct in kind from the concern that she has for others. The third theme is that of rational egoism, a concept that Whiting critiques, especially in the context of Aristotle's eudaimonism. The central tenet of the collection is the message that taking "ethocentric" (or character-based) attitudes both towards ourselves and towards our friends sheds light on the nature of personal identity and helps to combat ethnocentric and other objectionable forms of bias, a message that is becoming increasingly urgent in light of the recent deaths of Trayvon Martin and Michael Brown.

This volume uses a unified approach to representation theory and automorphic forms. It collects papers, written by leading mathematicians, that track recent progress in the expanding fields of representation theory and automorphic forms and their association with number theory and differential geometry. Topics include: Automorphic forms and distributions, modular forms, visible-actions, Dirac cohomology, holomorphic forms, harmonic analysis, self-dual representations, and Langlands Functoriality Conjecture, Both graduate students and researchers will find inspiration in this volume.

This proceedings volume documents the contributions presented at the conference held at Fairfield University and at the Graduate Center, CUNY in 2018 celebrating the New York Group Theory Seminar, in memoriam Gilbert Baumslag, and to honor Benjamin Fine and Anthony Gaglione. It includes several expert contributions by leading figures in the group theory community and provides a valuable source of information on recent research developments.

Robert A. Rankin, one of the world's foremost authorities on modular forms and a founding editor of The Ramanujan Journal, died on January 27, 2001, at the age of 85. Rankin had broad interests and contributed fundamental papers in a wide variety of areas within number theory, geometry, analysis, and algebra. To commemorate Rankin's life and work, the editors have collected together 25 papers by several eminent mathematicians reflecting Rankin's extensive range of interests within number theory. Many of these papers reflect Rankin's primary focus in modular forms. It is the editors' fervent hope that mathematicians will be stimulated by these papers and gain a greater appreciation for Rankin's contributions to mathematics. This volume would be an inspiration to students and researchers in the areas of number theory and modular forms.