Categorical Foundations for K-theory

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Hochschild homology has proved to be an important invariant in algebra and homotopy theory, in particular due to its relevance in algebraic K-theory and fixed point theory, leading to the development of numerous variants of the original construction. Ponto ...

The Birman-Williams theorem gives a connection between the collection of unstable periodic orbits (UPOs) contained within a chaotic attractor and the topology of that attractor, for three-dimensional systems. In certain cases, the fractal dimension of a ch ...

In this thesis, we apply cochain complexes as an algebraic model of space in a diverse range of mathematical and scientific settings. We begin with an algebraic-discrete Morse theory model of auto-encoding cochain data, connecting the homotopy theory of d ...

Let K be an algebraically closed field of characteristic zero, and let G be a connected reductive algebraic group over K. We address the problem of classifying triples (G, H, V ), where H is a proper connected subgroup of G, and V is a finitedimensional ir ...

In this thesis we study stability from several viewpoints. After covering the practical importance, the rich history and the ever-growing list of manifestations of stability, we study the following. (i) (Statistical identification of stable dynamical syste ...

We define p-adic BPS or pBPS invariants for moduli spaces M-beta,M-chi of one-dimensional sheaves on del Pezzo and K3 surfaces by means of integration over a non-archimedean local field F. Our definition relies on a canonical measure mu can on the F-analyt ...

Because building-integrated photovoltaic (BIPV) modules are fully integrated into a building envelope, the back of the module can be exposed to little or no ventilation, resulting in increased operating temperatures. As the temperature increases, the perfo ...

Kontsevich and Soibelman reformulated and slightly generalised the topological recursion of [43], seeing it as a quantisation of certain quadratic Lagrangians in T*V for some vector space V. KS topological recursion is a procedure which takes as initial da ...

We introduce an algorithm to reconstruct a mesh from discrete samples of a shape's Signed Distance Function (SDF). A simple geometric reinterpretation of the SDF lets us formulate the problem through a point cloud, from which a surface can be extracted wit ...

Topological Weyl semimetals represent a novel class of nontrivial materials, where band crossings with linear dispersions take place at generic momenta across reciprocal space. These crossings give rise to low -energy properties akin to those of Weyl fermi ...

Modular robotics link the reliability of a centralised system with the adaptivity of a decentralised system. It is difficult for a robot with a fixed shape to be able to perform many different types of tasks. As the task space grows, the number of functi ...

This Ph.D. thesis unveils the unique topological phenomena occurring in such networks, focusing on the intricate interplay between their Floquet topology, the presence of disorder, and their unitary scattering at microscopic and macroscopic scales. Using t ...

In algorithms for solving optimization problems constrained to a smooth manifold, retractions are a well-established tool to ensure that the iterates stay on the manifold. More recently, it has been demonstrated that retractions are a useful concept for ot ...

Motion forecasting is crucial in enabling autonomous vehicles to anticipate the future trajectories of surrounding agents. To do so, it requires solving mapping, detection, tracking, and then forecasting problems, in a multi-step pipeline. In this complex ...

We introduce robust principal component analysis from a data matrix in which the entries of its columns have been corrupted by permutations, termed Unlabeled Principal Component Analysis (UPCA). Using algebraic geometry, we establish that UPCA is a well-de ...

This study explores the differences in performance and results by various versions of the ISORROPIA thermodynamic module implemented within the ECHAM/MESSy Atmospheric Chemistry (EMAC) model. Three different versions of the module were used, ISORROPIA II v ...

Solar photovoltaics (PV) is one of the most competitive renewable energy technologies in order to meet the increasing global energy demand and decrease CO2 emissions by competing effectively with fossil fuels. One of the important applications of PV energy ...

We develop a very general version of the hyperbola method which extends the known method by Blomer and Brudern for products of projective spaces to complete smooth split toric varieties. We use it to count Campana points of bounded log-anticanonical height ...

Hyperbolic lattices are a new type of synthetic materials based on regular tessellations in non-Euclidean spaces with constant negative curvature. While so far, there has been several theoretical investigations of hyperbolic topological media, experimental ...

We determine the bounded cohomology of the group of homeomorphisms of certain low-dimensional manifolds. In particular, for the group of orientation-preserving homeomorphisms of the circle and of the closed 2-disc, it is isomorphic to the polynomial ring g ...

Categorical Foundations for K-theory

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Shadows are bicategorical traces

The topology of a chaotic attractor in the Kuramoto-Sivashinsky equation

Cochains are all you need

Multiplicity-free Representations of Algebraic Groups

Stability: a search for structure

BPS invariants from p-adic integrals

Correlating long-term performance and aging behaviour of building integrated PV modules

The ABCD of topological recursion

Reach For the Arcs: Reconstructing Surfaces from SDFs via Tangent Points

High-throughput screening of Weyl semimetals

Memento Mori: Reliable robustness in self-reconfigurable modular robots

Topological photonic transport in disordered scattering networks

From low-rank retractions to dynamical low-rank approximation and back

Towards Motion Forecasting with Real-World Perception Inputs: Are End-to-End Approaches Competitive?

Unlabeled Principal Component Analysis and Matrix Completion

Implementation of the ISORROPIA-lite aerosol thermodynamics model into the EMAC chemistry climate model (based on MESSy v2.55): implications for aerosol composition and acidity

Reliability and Long-term Performance of Building Integrated Photovoltaic (BIPV) Modules

HYPERBOLA METHOD ON TORIC VARIETIES

Anomalous and Chern topological waves in hyperbolic networks

Bounded and unbounded cohomology of homeomorphism and diffeomorphism groups