The category of Segal spaces was proposed by Charles Rezk in 2000 as a suitable candidate for a model category for homotopy theories. We show that Quillen functors induce morphisms in this category and that the morphisms ...

Lithium-ion battery is a family of rechargeable batteries with increasing importance that is closely related to everyone's daily life. However, despite its enormously wide applications in numerous areas, the mechanism of ...

In this thesis, we study the mating of trees approach to Liouville quantum gravity decorated with SLE curves and its application to the scaling limit theory of decorated random planar maps. We focus on the less investigated ...

This doctoral dissertation is on the theory of Minimal Surfaces and of singularities in Mean Curvature Flow, for smooth submanifolds Y" in an ambient Riemannian (n+ 1)-manifold Nn+1, including: (1) New asymptotically conical ...

We present new techniques for generation of unstructured meshes for geometries specified by implicit functions. An initial mesh is iteratively improved by solving for a force equilibrium in the element edges, and the ...

Let G be a split, semisimple p-adic group. We construct a derived localization functor Loc : ... from the compactified category of [BK2] associated to G to the category of equivariant sheaves on the Bruhat-Tits building ...

Solar activity, as indexed by sunspots, has a cycle of length varying from about 9 to 13 years. Statisticians have fitted several models to predict sunspot numbers one year ahead. We instead focus on predicting the magnitudes ...