How can the behavior of elementary particles and the structure of the entire universe be described using the same mathematical concepts? This question is at the heart of the recent work by ...

This introductory textbook for a graduate course in pure mathematics provides a gateway into the two difficult fields of algebraic geometry and commutative algebra. Algebraic geometry, supported ...

This is a topics course in continuation of MAT4215 – Algebraic Geometry II. The content varies between different current fields of research and covers both advanced methods and topics. Examples of ...

This is a graduate-level text on algebraic geometry that provides a quick and fully self-contained development of the fundamentals, including all commutative algebra which is used. A taste of the ...

Algebraic geometry is a classical subject with a modern face that studies geometric objects defined by polynomial equations in several variables. The course introduces the basic objects in algebraic ...

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“THIS volume is the first part of a work designed it provide a convenient account of the foundations and methods of modem algebraic geometry.” These words from the authors' preface explain the scope ...

Columbia professor Johan de Jong has spent the last 15 years gathering the foundational theorems of algebraic geometry in one place. His creation, the Stacks Project, offers a new model for organizing ...

Abstract:-Basic theorems of algebraic geometry are applied to prove some pole-placement theorems, including an improved version of pole placement with output feedback. Examples are given which show ...

…and here’s a proof. They are, of course, very useful in algebraic geometry (as is the equals sign). Also, human beings discovered them while developing algebraic geometry, which is why many of them ...

Matroid theory is a way mathematicians describe the property of independence in a space, with uses across mathematics, physics, computer science and more. Carnegie Mellon University Mathematician ...