Dimer Models and Calabi-Yau Algebras - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Dimer Models and Calabi-Yau Algebras write by Nathan Broomhead. This book was released on 2012-01-23. Dimer Models and Calabi-Yau Algebras available in PDF, EPUB and Kindle. In this article the author uses techniques from algebraic geometry and homological algebra, together with ideas from string theory to construct a class of 3-dimensional Calabi-Yau algebras. The Calabi-Yau property appears throughout geometry and string theory and is increasingly being studied in algebra. He further shows that the algebras constructed are examples of non-commutative crepant resolutions (NCCRs), in the sense of Van den Bergh, of Gorenstein affine toric threefolds. Dimer models, first studied in theoretical physics, give a way of writing down a class of non-commutative algebras, as the path algebra of a quiver with relations obtained from a `superpotential'. Some examples are Calabi-Yau and some are not. The author considers two types of `consistency' conditions on dimer models, and shows that a `geometrically consistent' dimer model is `algebraically consistent'. He proves that the algebras obtained from algebraically consistent dimer models are 3-dimensional Calabi-Yau algebras. This is the key step which allows him to prove that these algebras are NCCRs of the Gorenstein affine toric threefolds associated to the dimer models.
Representations of Algebras, Geometry and Physics
Representations of Algebras, Geometry and Physics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Representations of Algebras, Geometry and Physics write by Kiyoshi Igusa. This book was released on 2021-05-17. Representations of Algebras, Geometry and Physics available in PDF, EPUB and Kindle. This volume contains selected expository lectures delivered at the 2018 Maurice Auslander Distinguished Lectures and International Conference, held April 25–30, 2018, at the Woods Hole Oceanographic Institute, Woods Hole, MA. Reflecting recent developments in modern representation theory of algebras, the selected topics include an introduction to a new class of quiver algebras on surfaces, called “geodesic ghor algebras”, a detailed presentation of Feynman categories from a representation-theoretic viewpoint, connections between representations of quivers and the structure theory of Coxeter groups, powerful new applications of approximable triangulated categories, new results on the heart of a t t-structure, and an introduction to methods of constructive category theory.
Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes)
Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes) - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes) write by Boyan Sirakov. This book was released on 2019-02-27. Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes) available in PDF, EPUB and Kindle. 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.
Progress in Commutative Algebra 1
Progress in Commutative Algebra 1 - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Progress in Commutative Algebra 1 write by Christopher Francisco. This book was released on 2012-04-26. Progress in Commutative Algebra 1 available in PDF, EPUB and Kindle. This is the first of two volumes of a state-of-the-art survey article collection which originates from three commutative algebra sessions at the 2009 Fall Southeastern American Mathematical Society Meeting at Florida Atlantic University. The articles reach into diverse areas of commutative algebra and build a bridge between Noetherian and non-Noetherian commutative algebra. These volumes present current trends in two of the most active areas of commutative algebra: non-noetherian rings (factorization, ideal theory, integrality), and noetherian rings (the local theory, graded situation, and interactions with combinatorics and geometry). This volume contains combinatorial and homological surveys. The combinatorial papers document some of the increasing focus in commutative algebra recently on the interaction between algebra and combinatorics. Specifically, one can use combinatorial techniques to investigate resolutions and other algebraic structures as with the papers of Fløystad on Boij-Söderburg theory, of Geramita, Harbourne and Migliore, and of Cooper on Hilbert functions, of Clark on minimal poset resolutions and of Mermin on simplicial resolutions. One can also utilize algebraic invariants to understand combinatorial structures like graphs, hypergraphs, and simplicial complexes such as in the paper of Morey and Villarreal on edge ideals. Homological techniques have become indispensable tools for the study of noetherian rings. These ideas have yielded amazing levels of interaction with other fields like algebraic topology (via differential graded techniques as well as the foundations of homological algebra), analysis (via the study of D-modules), and combinatorics (as described in the previous paragraph). The homological articles the editors have included in this volume relate mostly to how homological techniques help us better understand rings and singularities both noetherian and non-noetherian such as in the papers by Roberts, Yao, Hummel and Leuschke.
Modern Trends in Algebra and Representation Theory
Modern Trends in Algebra and Representation Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Modern Trends in Algebra and Representation Theory write by David Jordan. This book was released on 2023-08-17. Modern Trends in Algebra and Representation Theory available in PDF, EPUB and Kindle. Expanding upon the material delivered during the LMS Autumn Algebra School 2020, this volume reflects the fruitful connections between different aspects of representation theory. Each survey article addresses a specific subject from a modern angle, beginning with an exploration of the representation theory of associative algebras, followed by the coverage of important developments in Lie theory in the past two decades, before the final sections introduce the reader to three strikingly different aspects of group theory. Written at a level suitable for graduate students and researchers in related fields, this book provides pure mathematicians with a springboard into the vast and growing literature in each area.
