Difference sets belong both to group theory and to combinatorics. Studying them requires tools from geometry, number theory, and representation theory. This book lays a foundation for these topics, including a primer on representations and characters of finite groups. It makes the research literatur
Connections Between Algebra, Combinatorics, and Geometry
β Scribed by Susan M. Cooper, Sean Sather-Wagstaff (eds.)
- Publisher
- Springer-Verlag New York
- Year
- 2014
- Tongue
- English
- Leaves
- 328
- Series
- Springer Proceedings in Mathematics & Statistics 76
- Edition
- 1
- Category
- Library
No coin nor oath required. For personal study only.
β¦ Synopsis
Commutative algebra, combinatorics, and algebraic geometry are thriving areas of mathematical research with a rich history of interaction. Connections Between Algebra and Geometry contains lecture notes, along with exercises and solutions, from the Workshop on Connections Between Algebra and Geometry held at the University of Regina from May 29-June 1, 2012. It also contains research and survey papers from academics invited to participate in the companion Special Session on Interactions Between Algebraic Geometry and Commutative Algebra, which was part of the CMS Summer Meeting at the University of Regina held June 2β3, 2012, and the meeting Further Connections Between Algebra and Geometry, which was held at the North Dakota State University February 23, 2013. This volume highlights three mini-courses in the areas of commutative algebra and algebraic geometry: differential graded commutative algebra, secant varieties, and fat points and symbolic powers. It will serve as a useful resource for graduate students and researchers who wish to expand their knowledge of commutative algebra, algebraic geometry, combinatorics, and the intricacies of their intersection.
β¦ Table of Contents
Front Matter....Pages i-xvi
Front Matter....Pages 1-1
A Somewhat Gentle Introduction to Differential Graded Commutative Algebra....Pages 3-99
Four Lectures on Secant Varieties....Pages 101-146
Regina Lectures on Fat Points....Pages 147-187
Front Matter....Pages 189-189
A Good Leaf Order on Simplicial Trees....Pages 191-207
A Survey of StanleyβReisner Theory....Pages 209-234
Numerical Computation of the Hilbert Function and Regularity of a Zero Dimensional Scheme....Pages 235-250
Regularity of Squarefree Monomial Ideals....Pages 251-276
Planar Graphs and the Koszul Algebra Structure for Trivariate Monomial Ideals....Pages 277-297
Non-Gorenstein Isolated Singularities of Graded Countable CohenβMacaulay Type....Pages 299-317
β¦ Subjects
Commutative Rings and Algebras; Algebraic Geometry
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