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What Mathematics Can Do for You
Japan is a tiny country that occupies only 0.25% of the world’s total land area. However, this small country is the world’s third largest in economy: the Japanese GDP is roughly equivalent to the sum of any two major countries in Europe as of 2012. This book is a first attempt to ask leaders of top Japanese companies, such as Toyota, about their thoughts on mathematics. The topics range from mathematical problems in specific areas (e.g., exploration of natural resources, communication networks, finance) to mathematical strategy that helps a leader who has to weigh many different issues and make decisions in a timely manner, and even to mathematical literacy that ensures quality control. ...
What Mathematics Can Do for You
Japan is a tiny country that occupies only 0.25% of the world’s total land area. However, this small country is the world’s third largest in economy: the Japanese GDP is roughly equivalent to the sum of any two major countries in Europe as of 2012. This book is a first attempt to ask leaders of top Japanese companies, such as Toyota, about their thoughts on mathematics. The topics range from mathematical problems in specific areas (e.g., exploration of natural resources, communication networks, finance) to mathematical strategy that helps a leader who has to weigh many different issues and make decisions in a timely manner, and even to mathematical literacy that ensures quality control. ...
Symmetry in Geometry and Analysis, Volume 1
Symmetry in Geometry and Analysis is a Festschrift honoring Toshiyuki Kobayashi. The three volumes feature 35 selected contributions from invited speakers of twin conferences held in June 2022 in Reims, France, and in September 2022 in Tokyo, Japan. These contributions highlight the profound impact of Prof. Kobayashi's pioneering ideas, groundbreaking discoveries, and significant achievements in the development of analytic representation theory, noncommutative harmonic analysis, and the geometry of discontinuous groups beyond the Riemannian context, among other areas, over the past four decades. The first volume of the Festschrift includes a survey article on Kobayashi's innovative contribut...
Symmetry in Geometry and Analysis, Volume 3
Symmetries in Geometry and Analysis is a Festschrift honouring Toshiyuki Kobayashi. The three volumes feature 35 selected contributions from invited speakers of twin conferences held in June 2022 in Reims, France, and in September 2022 in Tokyo, Japan. These contributions highlight the profound impact of Prof. Kobayashi’s pioneering ideas, groundbreaking discoveries, and significant achievements in the development of analytic representation theory, noncommutative harmonic analysis, and the geometry of discontinuous groups beyond the Riemannian context, among other areas, over the past four decades. This third volume of the Festschrift contains original articles on branching problems in representation theory of reductive Lie groups and related topics. Contributions are by Ali Baklouti, Hidenori Fujiwara, Dmitry Gourevitch, Masatoshi Kitagawa, Salma Nasrin, Yoshiki Oshima, and Petr Somberg.
Symmetry in Geometry and Analysis, Volume 2
Symmetries in Geometry and Analysis is a Festschrift honouring Toshiyuki Kobayashi. The three volumes feature 35 selected contributions from invited speakers of twin conferences held in June 2022 in Reims, France, and in September 2022 in Tokyo, Japan. These contributions highlight the profound impact of Prof. Kobayashi’s pioneering ideas, groundbreaking discoveries, and significant achievements in the development of analytic representation theory, noncommutative harmonic analysis, and the geometry of discontinuous groups beyond the Riemannian context, among other areas, over the past four decades. This second volume of the Festschrift contains original articles on analytic methods in representation theory of reductive Lie groups and related topics. Contributions are by Salem Ben Saïd, Valentina Casarino, Paulo Ciatti, Jean-Louis Clerc, Jan Frahm, Joachim Hilgert, Toshihisa Kubo, Khalid Koufany, Quentin Labriet, Karl-Hermann Neeb, Yuri Neretin, Gestur Òlafsson, Bent Ørsted, Toshio Oshima, Birgit Speh, Jorge Vargas, and Clemens Weiske.
Conformal Symmetry Breaking Differential Operators on Differential Forms
We study conformal symmetry breaking differential operators which map dif-ferential forms on Rn to differential forms on a codimension one subspace Rn−1. These operators are equivariant with respect to the conformal Lie algebra of the subspace Rn−1. They correspond to homomorphisms of generalized Verma mod-ules for so(n, 1) into generalized Verma modules for so(n+1, 1) both being induced from fundamental form representations of a parabolic subalgebra. We apply the F -method to derive explicit formulas for such homomorphisms. In particular, we find explicit formulas for the generators of the intertwining operators of the re-lated branching problems restricting generalized Verma modules...
Singular Unitary Representations and Discrete Series for Indefinite Stiefel Manifolds $U(p,q;{\mathbb F})/U(p-m,q;{\mathbb F})$
This memoir examines the basic problem of finding vanishing theorems for Harish-Chandra modules. The results of these difficult problems contribute in a meaningful way to the singular unitary representation theory of reductive groups.
Representation Theory and Automorphic Forms
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.
The Schrodinger Model for the Minimal Representation of the Indefinite Orthogonal Group $O(p,q)$
The authors introduce a generalization of the Fourier transform, denoted by $\mathcal{F}_C$, on the isotropic cone $C$ associated to an indefinite quadratic form of signature $(n_1,n_2)$ on $\mathbb{R}^n$ ($n=n_1+n_2$: even). This transform is in some sense the unique and natural unitary operator on $L^2(C)$, as is the case with the Euclidean Fourier transform $\mathcal{F}_{\mathbb{R}^n}$ on $L^2(\mathbb{R}^n)$. Inspired by recent developments of algebraic representation theory of reductive groups, the authors shed new light on classical analysis on the one hand, and give the global formulas for the $L^2$-model of the minimal representation of the simple Lie group $G=O(n_1+1,n_2+1)$ on the other hand.
