Carnegie Mellon University

Working Group Seminars

Working Group, Fall 2020

Nonlocal PDE and variational problems for data

Organizers: Dejan Slepcev and Raghav Venkatraman

In the first few weeks we will discuss variational problems on random graphs and their consistency. In particular the recent results on graph Laplacian. The second part of the semester will be devoted to Stein Variational Descent and the relevant related geometries. In particular the novel transportation based geometries with nonlocal norms on the velocity and nonlocal continuity equation. Other topics may be discussed depending on the interests of participants.


Working Group, Fall 2019

Progress in nonlinear optimization and gradient descent

Organizers: Bob Pego, Hayden Schaeffer and Noel Walkington

Participants in this working group will discuss recent works that concern novel and interesting methods for determining optimizers and understanding gradient-like dynamics in nonlinear systems. Topics of interest include, e.g.: relaxed variational principles, acceleration techniques, stochastic approaches to minimization and approximation, and use of analytic structure.

Working Group, Spring 2019

Calculus of Variations

Organizers: Irene Fonseca and Giovanni Leoni

Topics to be Addressed: Rigidity estimates; Minimizing movements; BV spaces, fracture, crystal defects; Convex integration. If time remains: Free boundary problems; Topological methods.

Fenics Study Group, Fall 2018

Author: Noel Walkington
This study group will meet weekly learn about the FEniCS finite element software package and related issues. This will include an introduction the Python programing language which is required to utilize this software.

Syllabus: Python Basics (I); Python Basics (II); Fenics and Paraview demonstration (Neilan); Fenics Basics; Introcution to numpy (Weber); FireDrake vs Fenics; Discontinuous Spaces - Convection Problem; DG Schemes - Convection Diffusion Problem; Nonlinear Problems.