Seminar

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.

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This introduction will be hosted by the organizers of this seminar. We will discuss certain events we do at Pitt and we can answer any questions you may have for us. It is a laid back environment meant for undergraduates who want to pursue higher knowledge mathematics, though most of the talks given do not require any higher knowledge than Linear Algebra or even introductory Calculus.

Abstract:

For incompressible flow models, the pressure term serves as a Lagrange multiplier to ensure that the incompressibility constraint is satisfied. In engineering applications, the pressure term is necessary for calculating important quantities based on stresses like the lift and drag. For reduced order models (ROMs) generated via a Proper Orthogonal Decomposition (POD), it is common for the pressure to drop out of the equations and produce a velocity-only ROM.

Abstract:

I will outline a proof (joint with Christian Sattler) of Voevodsky's Homotopy Canonicity Conjecture.