Chapter 1: Condensate growth term: existence, uniqueness, propagations of moments *(Joint work with Ricardo Alonso and Irene M. Gamba)*

Chapter 2: Uniform in time lower bound for solutions to a quantum Boltzmann equation of bosons *(Joint work with Toan Nguyen)*

Chapter 3: What else besides the condensate growth term? *(Joint work with Avy Soffer)*

Chapter 4: Convergence to equilibrium of a linearized quantum Boltzmann equation for bosons at very low temperature *(Joint work with Miguel Escobedo)*

Chapter 5: A toric dynamical system approach to the convergence to equilibrium of quantum Boltzmann equations for Bose gases *(Joint work with Gheorghe Craciun)*

Chapter 6: Derivation of quantum kinetic equations *(Joint work with Linda Reichl)*

Chapter 7: Coupling kinetic and Schrodinger equations – A simplified model by Soffer and Tran *(Joint work with Avy Soffer)*

Chapter 8: Quantum hydrodynamic approximations to finite temperature trapped Bose gases *(Joint work with Shi Jin)*

Chapter 9: Wave turbulence theory for capillary water waves *(Joint work with Toan Nguyen)*

Chapter 10: On the wave turbulence theory for stratified flows in the ocean *(Joint work with Irene M. Gamba and Leslie M. Smith)*

Chapter 11: Optimal local well-posedness theory for the kinetic wave equation. *(Joint work with Pierre Germain and Alexandru D. Ionescu)*

Chapter 12: On the energy cascade of acoustic wave turbulence: Beyond Kolmogorov-Zakharov solutions *(Joint work with Avy Soffer)*

**EXTRA CHAPTERS: SCIENTIFIC COMPUTING-COMPUTATIONAL SCIENCES and UNCERTAINTY QUANTIFICATION-SENSITIVITY ANALYSIS**

Extra Chapter 1: iHDG – Iterative Hybridized Discontinuous Galerkin method *(Joint work with Tan Bui-Thanh and Sriramkrishnan Muralikrishnan)*

Extra Chapter 2: iHDG – Iterative Hybridized Discontinuous Galerkin method (Part 2) *(Joint work with Tan Bui-Thanh and Sriramkrishnan Muralikrishnan)*