1. Approximation of nonvariational problems
Abner SALGADO — University of Tennessee, USA
Description
Elliptic problems in nondivergence form appear in weather and climate modelling, stochastic optimal control, and geometric analysis. This course surveys recent developments regarding finite element approximations of nonvariational problems.
2. Calculus of Variations in Geometric Analysis & Elasticity
Marta LEWICKA — University of Pittsburgh, USA
Description
Focuses on analytical and geometrical questions emerging from thin elastic films exhibiting residual stress at free equilibria, including Monge-Ampère systems and convex integration.
3. Integro-Differential and Nonlocal Equations
Qiang DU — Columbia University, USA
Description
Introduces nonlocal equations describing systems where behavior at a point is influenced by extended domains, covering anomalous diffusion, peridynamics, and fractional Laplacians.
4. PDEs in Mathematical Biology: Dynamics and Patterns
Abba GUMEL — University of Maryland, USA
Description
Explores animal movement models, spatial disease spread, tumor growth, and bifurcation theory leading to pattern formation (Turing patterns).
5. Variational Theory of PDEs: Analysis and Numerical Methods
Lars DIENING — University of Bielefeld, Germany
Description
Covers Sobolev spaces, weak solutions, Lax-Milgram theory, and Galerkin/finite element methods for Laplace, heat, and wave equations.
6. PDEs and Machine Learning: A Data-Driven Connection
Xiaochuan TIAN — University of California San Diego, USA
Description
Examines two-way PDE/data-science connections: PDE models in image processing/optimal transport and machine learning methods to solve complex nonlinear PDEs.