One of the most challenging problems in dynamic concurrent multiscale simulations is the reflectionless transfer of physical quantities between the different scales. In particular, when coupling molecular dynamics and ......

We give tight upper and lower bounds of the cardinality of the index sets of certain hyperbolic crosses which reflect mixed Sobolev-Korobov-type smoothness and mixed Sobolev-analytic-type smoothness in the infinite-dimensional ......

We study the sup-norm of Hecke-Maaß cusp forms on certain locally symmetric spaces of SL_n(ℝ). The latter correspond either to cocompact lattices defined by orders in division algebras, or to the Hecke ...

This thesis concerns modularity properties of Nahm sums, a family of q-hypergeometric series, and applications. They appear, for example, as characters of VOAs, knot invariants, and generating functions for classes of ......

Global equivariant homotopy theory is often motivated as the study of compatible collections of equivariant objects for some family of compact Lie groups. In this thesis we make this heuristic precise, by exhibiting the ...

In this thesis I study geometric problems which commonly arise in material science. The goal of these models is to derive structural properties of the material by describing the time evolution of defects inside the material, ......

The Hodge conjecture predicts a deep connection between topology, complex geometry, and algebraic geometry. It asserts that any Hodge class on a smooth complex projective variety is algebraic, meaning it is a linear ......

We consider the L²-norm of Siegel modular forms when restricted to the imaginary axis in an average sense. We establish an asymptotic formula with a power-saving error for cusp forms of degrees 1 and 2 in the ...

In this thesis, we study the degenerations of complex projective structures on an orientable surface S of genus at least two, aiming to describe a compactification of their moduli space and provide a geometric interpretation ...