Complex coupled systems arise in medicine, science and engineering. Mathematically, these can be nonlinear coupled systems of PDEs or the nonconvex minimization problems found in deep learning. In this talk, we show how multi-scale approaches give a mathematical technique for accurate and efficient simulation of complex systems. Rolf Krause holds a chair of advanced scientific computing in the Fa...

An expander graph may be defined in any of several ways: in terms of boundaries of vertex sets, or in terms of eigenvalues of the graph Laplacian, or by random walks... Expander graphs have become a central object of study in discrete mathematics. Helfgott will discuss a graph that encodes the divisibility properties of integers by primes. Harald Helfgott is a Humboldt Professor at the University...

We have three more MATH+ Friday Talks coming up in the current winter semester:  15 January: Harald Helfgott (Göttingen) 22 January: Rolf Krause (Lugano) 05 February: Sylvia Serfaty (Courant Institute, NYU)

Multilevel Strategies for Non-Linear Problems and Machine Learning: On Non-Linear Preconditioning, Multilevel Optimization, and Multilevel Training

In classical mechanics, symmetry occurs for a reason: there is a conserved quantity such as angular momentum. This is Noether’s theorem, and it points to a broader theme in dynamics that symmetry is rare and meaningful. Wilkinson will discuss, in the contexts of modern dynamics and geometry, how this theme recurs in beautiful ways. Amie Wilkinson is a professor at the University of Chicago.

This talk addresses recent research on the modeling and analysis of diffuse-interface tumor growth problems. Elisabetta Rocca is professor at the University of Pavia. From 2013-2016 she had her own research group at WIAS.