Combinatorial Commutative Algebra

Three Topics in Combinatorial Commutative Algebra
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About Us. General Scientific Activity. Centre for Mathematical Medicine. The second set of questions concern the toric Hilbert scheme, a parameter space for all polynomial ideals with the same multi-graded Hilbert function as a given toric ideal.

A central open question about these schemes is whether they are connected. The proposer will work with Diane Maclagan on this connectivity question, building on their recent construction of a graph on the monomial ideals of the scheme which is connected if and only if the scheme is connected.

Over the past decade, the proposer has contributed to the development of several new theories in discrete optimization using algebraic techniques and has worked on the application of the resulting, non-traditional algorithms to practical problems. The research that has contributed to these theories brings tools from algebra, combinatorics, optimization and discrete geometry to bear on problems from all of these fields. The application of algebraic techniques has led to new understanding in the field of integer programming, a branch of discrete optimization, but tools and ideas from optimization have also led to new results in algebra.

This interplay of ideas and techniques has shed light on questions from each of these areas and promises to lead to greater insight and advancement. The proposer works with students on some of the computational aspects of the research and plans to involve students in the development of software that implements these algorithms. The proposer is also interested in curriculum development in subject areas related to this research at the University of Washington.


Thomas and Edwin O'Shea. Categories of Symmetries and Infinite-Dimensional Groups. Octonions, Jordan Algebras and Exceptional Groups. Tonny A.


Essays in Group Theory. Introduction to Algebra. Peter J. Your review has been submitted successfully.

Combinatorial commutative algebra

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