This dissertation deals with the combination of two key problems that arise in the physical design of computer chips: global routing and buffering.
The task of buffering is the insertion of buffers and inverters into ...

This thesis adds some details to the seminal approach to logarithmic formality and interpolation formality by Alekseev, Rossi, Torossian and Willwacher: We prove that the interpolation family of Kontsevich formality maps ......

In recent years, several major breakthroughs in the field of geometry have been closely linked to the investigation of two pivotal topics: curvature and singularities. The objective of this thesis is to explore the geometric ...

We study several geometric problems arising from partial differential equations: (1) the geometry of Laplacian Eigenfunctions on smooth, compact manifolds without boundary (2) the energy landscape of the conservation laws ...

The notion of order in triangulated categories, as introduced by Schwede, is investigated in the case of the stable category of kG-modules, where k is a field of characteristic p and G is a ...

This thesis examines numerical methods for approximating various nonlinear bending models for elastic plates and shells. The numerical treatment of these models is challenging because they involve fourth-order partial ...

In this thesis we study modular compactifications of Jacobian varieties attached to nodal curves.
Unlike the case of smooth curves, where the Jacobians are canonical, modular compact objects, these compactifications ...

In this thesis we develop highly accurate simulation tools for variably saturated flow through porous media able to take advantage of the latest supercomputing resources. Hence, we aim for parallel scalability to very large ...

We study two equations of KP-II type: the Kadomtsev-Petviashvili II equation and its cubical generalization (gKP-II)$_{3}$.
In Chapter 3, we discuss the qualitative properties of the Kadomtsev-Petviashvili II equation ...

This thesis concerns relative determinants for Laplacians on surfaces with asymptotically cusps ends and the inverse spectral problem on surfaces with cusps. We consider $(M,g)$, a surface with cusps, and a metric on the ...