The Genesis Of The Langlands Program
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The Genesis of the Langlands Program
Author: Julia Mueller
language: en
Publisher: Cambridge University Press
Release Date: 2021-08-05
A step-by-step guide to Langlands' early work leading up the Langlands Program for mathematicians and advanced students.
Mathematical Unity
An Exploration of Mathematical Cohesion Embark on a journey through the intricate realms of mathematics with "Mathematical Unity: The Langlands Programme and Beyond". This groundbreaking work delves into one of the most profound and ambitious pursuits in modern mathematics. Seamlessly weaving through centuries of mathematical thought and discovery, this book takes you deep into the quest for mathematical harmony. At the heart of this narrative lies the Langlands Programme, a monumental theory that seeks to bridge diverse areas such as algebra, number theory, and geometry. Discover the origins and ambitions of this fascinating framework, as the book illuminates the pathways towards unifying seemingly disparate mathematical concepts. Covering both historical developments and the latest advancements, readers will be captivated by how ancient problems have crossed new frontiers under the Langlands lens. Engage with the minds that have contributed to this evolving field, from the pioneers who first glimpsed the potential for unity to the modern-day mathematicians pushing the boundaries of knowledge. Through detailed case studies and real-world applications, see firsthand the tangible impact this programme has had, not only within mathematics but across interdisciplinary collaborations with fields like theoretical physics. Aspiring mathematicians, academics, and enthusiasts alike will find immense value in the rich narrative that presents complex ideas with clarity and elegance. Explore how emerging technologies and innovative methods are paving the way for future developments, and delve into the philosophical questions that challenge our perception of mathematics itself. Whether you're seeking to deepen your understanding or ignite your curiosity, "Mathematical Unity: The Langlands Programme and Beyond" offers a compelling exploration of the past, present, and future of mathematical unity, enticing readers into a domain where numbers, geometry, and theory converge in harmony.
String-Math 2022
Author: Ron Donagi
language: en
Publisher: American Mathematical Society
Release Date: 2024-04-18
This is a proceedings volume from the String-Math conference which took place at the University of Warsaw in 2022. This 12th String-Math conference focused on several research areas actively developing these days. They included generalized (categorical) symmetries in quantum field theory and their relation to topological phases of matter; formal aspects of quantum field theory, in particular twisted holography; various developments in supersymmetric gauge theories, BPS counting and Donaldson–Thomas invariants. Other topics discussed at this conference included new advances in Gromov–Witten theory, curve counting, and Calabi–Yau manifolds. Another broad topic concerned algebraic aspects of conformal field theory, vertex operator algebras, and quantum groups. Furthermore, several other recent developments were presented during the conference, such as understanding the role of operator algebras in the presence of gravity, derivation of gauge-string duality, complexity of black holes, or mathematical aspects of the amplituhedron. This proceedings volume contains articles summarizing 14 conference lectures, devoted to the above topics.