Ordinary and Symbolic Powers of Ideals (17w5027)


(Oklahoma State University)

(Tulane University)

(McMaster University)


The Casa Matemática Oaxaca (CMO) will host the "Ordinary and Symbolic Powers of Ideals" workshop from May 14th to May 19th, 2017.

Commutative algebra, combinatorics, and algebraic geometry are three areas of mathematics that often study similar problems with different techniques. Commutative algebraists are often interested in studying relationships among polynomials. Combinatorial mathematicians study discrete structures, like graphs, which model networks. Algebraic geometers study solutions to polynomial equations from both an algebraic and geometric perspective. Researchers in all three fields have been interested in powers of algebraic structures called ideals in recent years, and the questions that have arisen have significant implications in mathematics, including applied areas like combinatorial optimization. Because there are questions common to the different areas, there is great opportunity for useful collaboration. For example, researchers in graph theory, a branch of combinatorics, recently helped disprove a widely-believed conjecture in algebra after algebraists translated the question into problems about graphs. The goal of this workshop is to facilitate communication among mathematicians in the three areas in order to combine the different approaches in the best way possible.

The Casa Matemática Oaxaca (CMO) in Mexico, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, are collaborative Canada-US-Mexico ventures that provide an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry.

The research station in Banff is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT). The research station in Oaxaca is funded by CONACYT.