Seminar

Abstract:

Toric ideals are a class of binomial ideals with many applications including to integer programming and algebraic statistics. One can associate a toric ideal to a finite simple graph by taking the kernel of the monomial map which sends the edges of the graph to the product of their endpoints. In this talk I will discuss some algebraic properties of toric ideals of graphs, focusing particularly on the Castelnuovo-Mumford regularity which is an invariant which measures the complexity of the relations among the generators of the ideal.
 

Abstract:

Matrix factorization features in many high dimensional data analysis problems. Typically, factorization methods are used to reduce the dimensionality of data and to visualize its structure. Factorization methods can also be viewed as models for whatever process is actually generating the data represented by the matrix. However, unlike for dimensionality reduction or visualization, success at this third goal is highly dependent on the specific factorization technique used.

Looking for career advice? Join Emily Bennett, Pitt's STEM Career Consultant as she discusses how to best utilize the university's resources, creating a network, preparing for the Fall Career Fair and more! Please come prepared with some questions and if you'd like to have your resume reviewed before the Fair, you can leave it with her after the discussion.