We analyze the cutting sequences associated to geodesic flow on a large class of translation surfaces, including Bouw-Möller surfaces and certain rectilinear surfaces. We give …
The theory of Mirkovic-Vilonen (MV) cycles and polytopes associated to a complex reductive group G has proven to be a rich source of structures related …
In this disseration, we generalize the classical result relating special values of the real analytic GL2 Eisenstein series to the product of the Riemann zeta …
In this work, we develop new harmonic analytic tools to study local and global well-posedness of nonlinear Schrödinger equations perturbed by a general class of …
The first part of this thesis concerns the growth of the Shafarevich-Tate group in cyclotomic Z_p-extensions, where we give a formula for its p-primary part …
In this work we provide a meromorphic continuation in three complex variables of two types of triple shifted convolution sums of Fourier coefficients of holomorphic …