Title: Cluster Algebras and Quiver Grassmannians Abstract: Since their conception, cluster algebras have made appearances in different fields such as algebra, combinatorics, geometry, and topology. For example, a class of objects from representation theory called quiver Grassmannians have been useful in describing the generators of cluster algebras using the Euler characteristic. This has motivated the
Title: Stability of Nonlinear Waves in Hamiltonian PDE Abstract: Nonlinear dispersive wave equations arise as reduced mathematical models from governing equations of mathematical physics, such as the Navier-Stokes and Maxwell equations. These reduced models combine the leading-order balance between nonlinear and dispersive effects present in wave propagation. The existence and stability of coherent structures such