In this thesis we study the $L^p$ Dirichlet problem for second order divergence-form operators having a BMO antisymmetric part. To be precise, for the divergence-form …
We define a category of smooth 1-motives with torsion over a locally noetherian base scheme and prove its Cartier duality. More precisely, we prove that …
The Teichmüller space of a surface that admits a hyperbolic structure can be equipped with the Weil-Petersson metric. The Weil-Persson Ending Lamination is a candidate …
This dissertation is devoted to the study of inverse spectral problem of Hankel operators. It is well-known that spectral characteristics of a Hankel operator does …
Polygon iterations, which can be thought of as discrete dynamical systems on the space of polygons, provide an abundance of interesting discrete dynamical systems in …
Harmonic analysis is an artform of understanding how mathematical objects behave. In this thesis, we develop a framework for understanding Calder\'on-Zygmund Singular Integral Operators (CZOs), …
Call a diagram D of spaces ``absolute'' if, for all enriched homotopy functors F, the induced map F(holim(D)) -> holim(FD) is an equivalence of spaces. …
This thesis consists of four chapters on the author's research in algebraic dynamics. The first chapter introduces the main results. The second chapter is an …
In the field of arithmetic dynamics, we study number theoretic aspects of discrete dynamical systems induced by rational maps on projective spaces. Among the rational …
We introduce spaces which generically parametrize con?gurations of n points on a degree d rational normal curve. The quotients of these spaces by SL(d+1) are …
We consider the one-dimensional nonlinear Schroedinger equation (NLS) with focusing point nonlinearity, which replaces the pure power nonlinearity in the standard NLS by inserting a …
The work in this thesis concerns three projects at the interface of statistical mechanics and cluster integrable systems. We describe each of these in the …
We provide complete proofs for some statements made by David Wigner and Lawrence Brown and introduce a “Grothendieck topologies” approach to working with the cohomology …
In this thesis, we study three families of moduli spaces: those of tropical curves, relative stable maps to the Riemann sphere, and weighted stable curves. …
This thesis exhibits two of the author's works: the first is about interpreting the derived equivalences of K3 surfaces through Cremona transformations, where we construct …