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Representations of Reductive Groups
This volume contains the proceedings of the Conference on Representation Theory and Algebraic Geometry, held in honor of Joseph Bernstein, from June 11–16, 2017, at the Weizmann Institute of Science and The Hebrew University of Jerusalem. The topics reflect the decisive and diverse impact of Bernstein on representation theory in its broadest scope. The themes include representations of p -adic groups and Hecke algebras in all characteristics, representations of real groups and supergroups, theta correspondence, and automorphic forms.
Eisenstein Series and Applications
Eisenstein series are an essential ingredient in the spectral theory of automorphic forms and an important tool in the theory of L-functions. They have also been exploited extensively by number theorists for many arithmetic purposes. Bringing together contributions from areas which do not usually interact with each other, this volume introduces diverse users of Eisenstein series to a variety of important applications. With this juxtaposition of perspectives, the reader obtains deeper insights into the arithmetic of Eisenstein series. The central theme of the exposition focuses on the common structural properties of Eisenstein series occurring in many related applications.
Automorphic Representations, L-Functions and Applications: Progress and Prospects
This volume is the proceedings of the conference on Automorphic Representations, L-functions and Applications: Progress and Prospects, held at the Department of Mathematics of The Ohio State University, March 27–30, 2003, in honor of the 60th birthday of Steve Rallis. The theory of automorphic representations, automorphic L-functions and their applications to arithmetic continues to be an area of vigorous and fruitful research. The contributed papers in this volume represent many of the most recent developments and directions, including Rankin–Selberg L-functions (Bump, Ginzburg–Jiang–Rallis, Lapid–Rallis) the relative trace formula (Jacquet, Mao–Rallis) automorphic representatio...
Proceedings Of The International Congress Of Mathematicians 2010 (Icm 2010) (In 4 Volumes) - Vol. I: Plenary Lectures And Ceremonies, Vols. Ii-iv: Invited Lectures
ICM 2010 proceedings comprises a four-volume set containing articles based on plenary lectures and invited section lectures, the Abel and Noether lectures, as well as contributions based on lectures delivered by the recipients of the Fields Medal, the Nevanlinna, and Chern Prizes. The first volume will also contain the speeches at the opening and closing ceremonies and other highlights of the Congress.
Categorical, Combinatorial and Geometric Representation Theory and Related Topics
This book is the third Proceedings of the Southeastern Lie Theory Workshop Series covering years 2015–21. During this time five workshops on different aspects of Lie theory were held at North Carolina State University in October 2015; University of Virginia in May 2016; University of Georgia in June 2018; Louisiana State University in May 2019; and College of Charleston in October 2021. Some of the articles by experts in the field describe recent developments while others include new results in categorical, combinatorial, and geometric representation theory of algebraic groups, Lie (super) algebras, and quantum groups, as well as on some related topics. The survey articles will be beneficial to junior researchers. This book will be useful to any researcher working in Lie theory and related areas.
Open Problems in Algebraic Combinatorics
In their preface, the editors describe algebraic combinatorics as the area of combinatorics concerned with exact, as opposed to approximate, results and which puts emphasis on interaction with other areas of mathematics, such as algebra, topology, geometry, and physics. It is a vibrant area, which saw several major developments in recent years. The goal of the 2022 conference Open Problems in Algebraic Combinatorics 2022 was to provide a forum for exchanging promising new directions and ideas. The current volume includes contributions coming from the talks at the conference, as well as a few other contributions written specifically for this volume. The articles cover the majority of topics in algebraic combinatorics with the aim of presenting recent important research results and also important open problems and conjectures encountered in this research. The editors hope that this book will facilitate the exchange of ideas in algebraic combinatorics.
String-Math 2022
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.
Integrability, Quantization, and Geometry: II. Quantum Theories and Algebraic Geometry
This book is a collection of articles written in memory of Boris Dubrovin (1950–2019). The authors express their admiration for his remarkable personality and for the contributions he made to mathematical physics. For many of the authors, Dubrovin was a friend, colleague, inspiring mentor, and teacher. The contributions to this collection of papers are split into two parts: “Integrable Systems” and “Quantum Theories and Algebraic Geometry”, reflecting the areas of main scientific interests of Dubrovin. Chronologically, these interests may be divided into several parts: integrable systems, integrable systems of hydrodynamic type, WDVV equations (Frobenius manifolds), isomonodromy equations (flat connections), and quantum cohomology. The articles included in the first part are more or less directly devoted to these areas (primarily with the first three listed above). The second part contains articles on quantum theories and algebraic geometry and is less directly connected with Dubrovin's early interests.
Frontiers in Geometry and Topology
This volume contains the proceedings of the summer school and research conference “Frontiers in Geometry and Topology”, celebrating the sixtieth birthday of Tomasz Mrowka, which was held from August 1–12, 2022, at the Abdus Salam International Centre for Theoretical Physics (ICTP). The summer school featured ten lecturers and the research conference featured twenty-three speakers covering a range of topics. A common thread, reflecting Mrowka's own work, was the rich interplay among the fields of analysis, geometry, and topology. Articles in this volume cover topics including knot theory; the topology of three and four-dimensional manifolds; instanton, monopole, and Heegaard Floer homologies; Khovanov homology; and pseudoholomorphic curve theory.
