In this series of lectures I will present a set of tools that have proved useful in computing limits of quadratic quantities involving sequences that are weakly converging in an L^2 space, an issue that is of particular importance in the Calculus of Variations and the analysis of non-linear PDE. Topics to be discussed will tentatively include: 1. Defect measures (in physical and Fourier space) and applications; 2. Phase-space defect measures: semiclassical measures and Pseudo-Differential Operators; 3. Passing to the limit in a product of bounded sequences in L^2. Applications to generalized Compensated-Compactness theorems 4. Applications to Quantum Dynamics: the semiclassical limit and scarring of eigenstates of quantum Hamiltonians.

In this series of lectures I will present a set of tools that have proved useful in computing limits of quadratic quantities involving sequences that are weakly converging in an L^2 space, an issue that is of particular importance in the Calculus of Variations and the analysis of non-linear PDE. Topics to be discussed will tentatively include: 1. Defect measures (in physical and Fourier space) and applications; 2. Phase-space defect measures: semiclassical measures and Pseudo-Differential Operators; 3. Passing to the limit in a product of bounded sequences in L^2. Applications to generalized Compensated-Compactness theorems 4. Applications to Quantum Dynamics: the semiclassical limit and scarring of eigenstates of quantum Hamiltonians.

In this series of lectures I will present a set of tools that have proved useful in computing limits of quadratic quantities involving sequences that are weakly converging in an L^2 space, an issue that is of particular importance in the Calculus of Variations and the analysis of non-linear PDE. Topics to be discussed will tentatively include: 1. Defect measures (in physical and Fourier space) and applications; 2. Phase-space defect measures: semiclassical measures and Pseudo-Differential Operators; 3. Passing to the limit in a product of bounded sequences in L^2. Applications to generalized Compensated-Compactness theorems 4. Applications to Quantum Dynamics: the semiclassical limit and scarring of eigenstates of quantum Hamiltonians.

In this series of lectures I will present a set of tools that have proved useful in computing limits of quadratic quantities involving sequences that are weakly converging in an L^2 space, an issue that is of particular importance in the Calculus of Variations and the analysis of non-linear PDE. Topics to be discussed will tentatively include: 1. Defect measures (in physical and Fourier space) and applications; 2. Phase-space defect measures: semiclassical measures and Pseudo-Differential Operators; 3. Passing to the limit in a product of bounded sequences in L^2. Applications to generalized Compensated-Compactness theorems 4. Applications to Quantum Dynamics: the semiclassical limit and scarring of eigenstates of quantum Hamiltonians.