Vorträge

Robots have the potential to disrupt many aspects of our lives, from healthcare to manufacturing. To realize this potential, a key challenge is real-time robot manipulation. Given a task, how can a robot quickly generate a motion plan to successfully complete it? How can the robot react in real-time to potential uncertainties in the real-world as it executes its plan? In this talk, we will overview recent developments at the University of Leeds, to realize real-time robot manipulation. These will include parallel-in-time integration methods that leverage parallel computing to significantly speed-up physics predictions for various robot manipulation tasks. It will also include learning-based and optimal control-based methods for robots to handle real-world uncertainties in object pose estimation and model parameters. We hope these recent advances will help accelerate the next generation of intelligent robots.

Zoomlink: https://tuhh.zoom.us/j/85353626407?pwd=MEIzeTEvY3dRTmtYZjFWUHJaVll4UT09

Meeting ID: 853 5362 6407
Passcode: 045209

The Norros-Reittu model is an inhomogeneous random multigraph that exhibits the so-called scale-free or power-law behaviour, which is observed in real-world complex networks. We study the component sizes of the Norros-Reittu model in the subcritical regime, i.e. in the abscence of a giant component, and show convergence of the point process of the component sizes to a Poisson process. It is planned to derive similar results for other models such as the random connection model.

The thesis deals with boundary layer enrichment of convection dominated flow problems using the Hybrid Discontinuous Galerkin Method. It aims to introduce an appropriate and computationally efficient Hybrid Discontinuous Galerkin formulation for the most important model problems of incompressible fluid flow, namely the convection-diffusion equation.The main contribution is the derivation, discussion and analysis of the Enriched Finite elementSpace using non-polynomial spaces (specifically boundary layer functions) for both the Discontinuous Galerkin Methods and the Hybrid Discontinuous Galerkin Method. We evaluate the robustness (i.e linear stability as well as reasonable linear systems) and accuracy of this method using various analytical and realistic problems and compare the results to those obtained using the standard (H)DG method. Numerical results are provided to contrast the Enriched (H)DG methods with standard (H)DG approaches.

In the early 1980s, Erd\H{o}s and S\'os initiated the study of the classical Tur\'an problem with a uniformity condition: the uniform Tur\'an density of a hypergraph $H$ is the infimum over all $d$ for which any sufficiently large hypergraph with the property that all its linear-size subhyperghraphs have density at least $d$ contains $H$. In particular, they raise the questions of determining the uniform Tur\'an densities of $K_4^{(3)-}$ and $K_4^{(3)}$. The former question was solved only recently in [Israel J. Math. 211 (2016), 349--366] and [J. Eur. Math. Soc. 20 (2018), 1139--1159], while the latter still remains open for almost 40 years.
In addition to $K_4^{(3)-}$, the only $3$-uniform hypergraphs whose uniform Tur\'an density is known are those with zero uniform Tur\'an density classified by Reiher, R\"odl and Schacht~[J. London Math. Soc. 97 (2018), 77--97] and a specific family with uniform Tur\'an density equal to $1/27$.

In this talk, we give an introduction to the concept of uniform Tur\'an densities, present a way to obtain lower bounds using color schemes, and give a glimpse of the proof for determining the uniform Turán density of the tight $3$-uniform cycle $C_\ell^{(3)}$, $\ell\ge 5$.