We will discuss the solution of eigenvalue problems associated with partial differential equations (PDE)s that can be written in the generalised form Ax = λMx, where the matrices A and/or M may depend on a scalar parameter. Parameter dependent matrices occur frequently when stabilised formulations are used for the numerical approximation of PDEs. With the help of classical numerical examples we will show that the presence of one (or both) parameters can produce unexpected results.

Hessian-dependent functionals play a pivotal role in a wide latitude of problems in mathematics. Arising in the context of differential geometry and probability theory, this class of problems find applications in the mechanics of deformable media (mostly in elasticity theory) and the modelling of slow viscous fluids. We study such functionals from three distinct perspectives.

We present a theoretical analysis of the Weak Adversarial Networks (WAN) method, recently proposed in [1, 2], as a method for approximating the solution of partial differential equations in high dimensions and tested in the framework of inverse problems. In a very general abstract framework.

Analogies between financial markets and critical phenomena have long been observed empirically. So far, no convincing theory has emerged that can explain these empirical observations. Here, we take a step towards such a theory by modeling financial markets as a lattice gas.

Wave propagation and scattering problems are of huge importance in many applications in science and engineering - e.g., in seismic and medical imaging and more generally in acoustics and electromagnetics.

In this short course, we will introduce some elements in deriving the hp a posteriori error estimate for a high-order unfitted finite element method for elliptic interface problems. The key ingredient is an hp domain inverse estimate, which allows us to prove a sharp lower bound of the hp a posteriori error estimator.

We develop a derivative-free global minimization algorithm that is based on a gradient flow of a relaxed functional. We combine relaxation ideas, Monte Carlo methods, and resampling techniques with advanced error estimates. Compared with well-established algorithms, the proposed algorithm has a high success rate in a broad class of functions, including convex, non-convex, and non-smooth functions, while keeping the number of evaluations of the objective function small.

It is difficult to predict the future, but ultimately, what matters is creating the future we want to live in. Our past and present are the product of our previous decisions. The decisions we make today will pave the way for the future. It is important that the right decision is made at the right time leading to the right outcome, paving the way towards the desired future.

Tilt-series cryo-electron tomography (cryo-ET) is an established imaging tech- nique used in several fields like biology and material science. Despite its success, cryo-ET remains an arduous task. The missing-wedge acquisition, the motion, and the high level noise are the main challenges existing in this field. In this dissertation, we tackle these challenges through the exploration of three distinct approaches: plug and play approach, adaptive differentiable density grids and adaptive tensorial density fields representation.

This talk covers a selection of previous and current work presenting a broad spectrum of research highlights ranging from simulating stiff phenomena such as the dynamics of fibers and textiles, over liquids containing magnetic particles, to the development of complex ecosystems and weather phenomena. Moreover, connection points to the growing field of machine learning are addressed and an outlook is provided with respect to selected technology transfer activities.

UAVs, or drones, are a dual-use technology that is gaining momentum, with applications spanning from agriculture to warfare. In this talk we will survey some of the threats posed by drones, and will discuss some scientific contributions to the field aimed at providing a way to reduce the risk posed by a rogue use of this technology. We will also highlight some related research directions.

Recent advancements in inverse rendering have exhibited promising results for 3D representation, novel view synthesis, scene parameter reconstruction, and direct graphical asset generation and editing.

The growth of digital cameras and data communication has led to an exponential increase in video production and dissemination. As a result, automatic video analysis and understanding has become a crucial research topic in the computer vision community. However, the localization problem, which involves identifying a specific event in a large volume of data, particularly in long-form videos, remains a significant challenge.

Conversational AI and Question-Answering systems (QASs) for knowledge graphs (KGs) are both emerging research areas: they empower users with natural language interfaces for extracting information efficiently and effectively. While Conversational AI simulates human-like conversations, its effectiveness is limited by the available training data. However, QASs retrieve the most up-to-date information from KGs by translating natural language queries into formal queries that the database engine can process. In this talk, we examine the characteristics of existing approaches for combining Conversational AI and QASs to create novel KG chatbots. We also introduce KGQAn, a universal QA system that can be applied to any KG without the need for customization.

Generative Adversarial Networks (GANs) are a very successful method for high-quality image synthesis and are a powerful tool to generate realistic images by learning their visual properties from a dataset of exemplars. However, the controllability of the generator output still poses many challenges. In this thesis, we propose several methods for achieving larger and/or higher visual quality in GAN outputs by combining latent space manipulations with image compositing operations

This talk introduces serverless computing, a programming model that has flourished in the last few years, mainly because it allows developers to concentrate on the application logic and not worry about scalability and resource management. Current serverless offerings give users limited flexibility for configuring the resources allocated to their function invocations. We take a principled approach to the problem of resource allocation for serverless functions, analyzing the effects of automating this choice in a way that leads to the best combination of performance and cost.

In this seminar I will present how to create 3D computer graphics and visualization systems for the web, using WebAssmbly and WebGPU language specifications, which are new, bleeding-edge technologies. Previously, accelerated graphics on the web was based on JavaScript libraries, which is still very popular, but they do not offer detailed memory management and code optimization, necessary for systems requiring high memory load and high computational demands. WebAssembly and WebGPU can be compiled from the C++ or Rust code, which also allows the deployment of the same codebase either for web or for the desktop-based applications.

I will discuss the limitations of the current state of the art, and present a proposal for an integrated pipeline, considering data acquisition, meshing, basis design, and numerical optimization as a single challenge, where tradeoffs can be made between different phases to increase automation and efficiency. I will demonstrate that this integrated approach offers many advantages, while opening exciting new geometry processing challenges, and that a fully opaque meshing and analysis solution is already possible for heat transfer and elasticity problems with contact. I will present a set of applications enabled by this approach in reinforcement learning for robotics, force measurements in biology, shape design in mechanical engineering, stress estimation in biomechanics, and simulation of deformable objects in graphics.

Many tasks in the analysis and synthesis of (collections of) 3D shapes boils down to computing a map between two surfaces. Such inter-surface maps can be used to establish correspondences, to transfer information or annotation from one object to another, or to plausibly deform one shape into another. If the two shapes are represented as polygon meshes, a continuous inter-surface map does not only assign the vertices of the source mesh to the target mesh but also maps the interior of the triangles which adds to the complexity of the task.

We will discuss several settings in which smooth developable strips are attached to each other or assembled in some other way to obtain surfaces with interesting geometric properties. Driven by the view towards applications we will investigate collections of strips which lie orthogonal or tangential to a reference surface and assume particular shapes. Such strips can serve as support structures or cladding panels of free-form shapes in architectural contexts. Our focus will lie on surfaces with a constant ratio of principal curvatures, cone nets, geodesic grid shells, and others.

In this talk I will discuss the shift towards hardware acceleration and show with several examples from industry and from research the large role that FPGAs are playing. I will hypothesize that we are in a new era where most of the established assumptions, rules of thumb, and accumulated wisdom about many aspects of computation in general and of data processing in particular no longer hold and need to be revisited.

We present a topological analysis of the vorticity formulation in describing fluid dynamics.  Despite its widespread use in fluid mechanics, this formulation is insufficient at describing fluid dynamics on a non-simply-connected domain.  What is missing is an equation of motion for fluid's cohomology component, which exhibits fascinating dynamics previously under explored.  Using geometric language, we derive the new equation of motion and establish new conservation laws, as Casimir invariants in Hamiltonian mechanics, for fluids on domains with general topology.  Significantly, we present the first physically correct vortex method on curved surfaces with genus and boundaries.

Being able to accurately solve PDEs on arbitrary polygonal/polyhedral meshes is a central goal and has been considered for various differential operators over the last years. In this talk I will present a simple approach for computing (piecewise) linear and quadratic basis functions for general polygons and polyhedra, from which discrete operators for gradient, divergence and Laplacian can be derived.

In this talk, I will discuss our recent advances in approximation of free-form surfaces by motions of curvature varying tools in the context of 5-axis flank CNC machining. In particular, I will discuss path-planning strategies using fixed tools, or custom-shaped ones, and on an example of spiral bevel gears will demonstrate even more efficient variant of flank machining, called double-flank.