A basic introduction to toric ideals, which are of fundamental importance in computational algebra and algebraic statistics. In this introduction to toric ideals, we will cover equivalent definitions, basic properties, and examples of toric ideals. This will be the first in a series of 3 lectures.

Polynomial systems occur in many fields of science and engineering. Polynomial homotopy continuation methods apply symbolic-numeric algorithms to solve polynomial systems. We describe the design and implementation of our web interface and reflect on the application of polynomial homotopy continuation methods to solve polynomial systems in the cloud. Via the graph isomorphism problem we organize and classify the polynomial systems we solved. The classification with the canonical form of a graph identifies newly submitted systems with systems that have already been solved. This is joint work with Nathan Bliss, Jeff Sommars, and Xiangcheng Yu.

An introduction to Markov bases: definitions, properties and examples. I will also make connections to my previous talk on toric ideals.

Wilburne will discuss Markov bases for multinomial logistic regression models and present partial progress toward obtaining sharp upper bounds for the elements in the basis. Wilburne will also explore the connection between these models and primitive partition identities (ppi).