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Integral Fourier Operators
This volume of contributions based on lectures delivered at a school on Fourier Integral Operators held in Ouagadougou, Burkina Faso, 14–26 September 2015, provides an introduction to Fourier Integral Operators (FIO) for a readership of Master and PhD students as well as any interested layperson. Considering the wide spectrum of their applications and the richness of the mathematical tools they involve, FIOs lie the cross-road of many a field. This volume offers the necessary background, whether analytic or geometric, to get acquainted with FIOs, complemented by more advanced material presenting various aspects of active research in that area.
Regularised Integrals, Sums and Traces
``Regularization techniques'' is the common name for a variety of methods used to make sense of divergent series, divergent integrals, or traces of linear operators in infinite-dimensional spaces. Such methods are often indispensable in problems of number theory, geometry, quantum field theory, and other areas of mathematics and theoretical physics. However arbitrary and noncanonical they might seem at first glance, regularized sums, integrals, and traces often contain canonical concepts, and the main purpose of this book is to illustrate and explain this. This book provides a unified and self-contained mathematical treatment of various regularization techniques. The author shows how to deri...
African Doctorates in Mathematics
This volume presents a catalogue of over 2000 doctoral theses by Africans in all fields of mathematics, including applied mathematics, mathematics education and history of mathematics. The introduction contains information about distribution by country, institutions, period, and by gender, about mathematical density, and mobility of mathematicians. Several appendices are included (female doctorate holders, doctorates in mathematics education, doctorates awarded by African universities to non-Africans, doctoral theses by non-Africans about mathematics in Africa, activities of African mathematicians at the service of their communities). Paulus Gerdes compiled the information in his capacity of Chairman of the African Mathematical Union Commission for the History of Mathematics in Africa (AMUCHMA). The book contains a preface by Mohamed Hassan, President of the African Academy of Sciences (AAS) and Executive Director of the Academy of Sciences for the Developing World (TWAS). (383 pp.)
Fifty Years of Women in Mathematics
The Association for Women in Mathematics (AWM), the oldest organization in the world for women in mathematics, had its fiftieth anniversary in 2021. This collection of refereed articles, illustrated by color photographs, reflects on women in mathematics and the organization as a whole. Some articles focus on the situation for women in mathematics at various times and places, including other countries. Others describe how individuals have shaped AWM, and, in turn, how the organization has impacted individuals as well as the broader mathematical community. Some are personal stories about careers in mathematics. Fifty Years of Women in Mathematics: Reminiscences, History, and Visions for the Fu...
La saga des mathématiciennes - Tome 1
La saga des mathématiciennes est une odyssée, dans le temps et dans l’espace, de la vie de quarante-cinq femmes méconnues ou célèbres, au surplus mathématiciennes. En dehors de tous les clichés attribués aux activités féminines, elles ont, la plupart du temps, navigué à contre-courant dans leur environnement pour faire émerger des connaissances mathématiques innovantes et prometteuses. De l’antiquité à nos jours, il faut « se promener » et ne pas hésiter à « s’aventurer au hasard » dans cet ouvrage atypique. En effet, il recense, pour chacune de ces « Drôles de Dames », non seulement leurs péripéties personnelles, familiales et leurs travaux mathématiques ma...
Mobilités d'Afrique en Europe. Récits et figures de l'aventure
Tandis que s’érige et se renforce la « forteresse Europe », aux avant-postes d’une guerre aux migrations, de nombreux récits – fictions, documents ou témoignages – émanent de l’Afrique subsaharienne, du Maghreb et d’Europe, voire d’Amérique du Nord, qui donnent à lire les conséquences tragiques de cette édification. Ils rendent compte également des multiples formes de mobilités par lesquelles les migrants d’Afrique persistent à résister à ce processus de clôture et d’exclusion. C’est ce pan de littérature contemporaine que le présent ouvrage tente d’analyser, en partant d’un ample corpus. Les oeuvres écrites de part et d’autre de la Méditerranée...
Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes)
The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.
Framing Global Mathematics
This open access book is about the shaping of international relations in mathematics over the last two hundred years. It focusses on institutions and organizations that were created to frame the international dimension of mathematical research. Today, striking evidence of globalized mathematics is provided by countless international meetings and the worldwide repository ArXiv. The text follows the sinuous path that was taken to reach this state, from the long nineteenth century, through the two wars, to the present day. International cooperation in mathematics was well established by 1900, centered in Europe. The first International Mathematical Union, IMU, founded in 1920 and disbanded in 1...
Geometric and Topological Methods for Quantum Field Theory
Aimed at graduate students in physics and mathematics, this book provides an introduction to recent developments in several active topics at the interface between algebra, geometry, topology and quantum field theory. The first part of the book begins with an account of important results in geometric topology. It investigates the differential equation aspects of quantum cohomology, before moving on to noncommutative geometry. This is followed by a further exploration of quantum field theory and gauge theory, describing AdS/CFT correspondence, and the functional renormalization group approach to quantum gravity. The second part covers a wide spectrum of topics on the borderline of mathematics and physics, ranging from orbifolds to quantum indistinguishability and involving a manifold of mathematical tools borrowed from geometry, algebra and analysis. Each chapter presents introductory material before moving on to more advanced results. The chapters are self-contained and can be read independently of the rest.
