Related papers: Extrinsic curvature flows and applications
In stochastic analysis, the flow of information through time is typically modelled using a filtration. We introduce some of the basic ideas involving enlargements of filtration. Here, we focus mainly on initial enlargements, where a given…
Thanks to recent advancements in the technology, eXtended Reality (XR) applications are gaining a lot of momentum, and they will surely become increasingly popular in the next decade. These new applications, however, require a step forward…
I give a pedagogical introduction to the concepts and the tools that are necessary to study particle physics models in higher dimensions. I then give a more detailed presentation of warped compactifications and discuss their possible…
It is a working version of a lecture on the theory of enlargement of filtration, given at the African Mathematic School in Marrakech, October 19-23, 2015.
Extra dimensions provide a new window on a number of problems faced by the Standard Model. The following provides an introduction to this very broad subject aimed at experimental graduate students and post-docs based on a lecture given at…
Bounds of total curvature and entropy are two common conditions placed on mean curvature flows. We show that these two hypotheses are equivalent for the class of ancient complete embedded smooth planar curve shortening flows, which are…
This is a collection of notes for part of a short course on modal methods in fluid mechanics held at DAMTP, University of Cambridge, in the summer of 2019. These notes introduce the reader to resolvent analysis as it is currently used in…
These are the lecture notes that accompanied the course of the same name that I taught at the Eindhoven University of Technology from 2021 to 2023. The course is intended as an introduction to neural networks for mathematics students at the…
The theory of classical types of curves in normed planes is not strongly developed. In particular, the knowledge on existing concepts of curvatures of planar curves is widespread and not systematized in the literature. Giving a…
This text is a support for different courses of the master of Mechanics of the University Paris-Saclay. The content of this text is an introduction, for graduate students, to tensor algebra and analysis. Far from being exhaustive, the text…
Over the last several years, the field of natural language processing has been propelled forward by an explosion in the use of deep learning models. This survey provides a brief introduction to the field and a quick overview of deep…
These lecture notes give a very short introduction to coarsening phenomena and summarize some recent results in the field. They focus on three aspects: the super-universality hypothesis, the geometry of growing structures, and coarsening in…
We discuss some open problems and recent progress related to the 4th order Paneitz operator and Q curvature in dimensions other than 4.
This extended abstract is based on a talk given at the workshop and summer school ``Direct and Inverse Problems with Applications" in Ghent Analysis and PDE Centre in August 2024. It focuses on nonlinear diffusion equations of slow and fast…
In the last 15 years, White and Huisken-Sinestrari developed a far-reaching structure theory for the mean curvature flow of mean convex hypersurfaces. Their papers provide a package of estimates and structural results that yield a precise…
We revisit the well-known Curve Shortening Flow for immersed curves in the $d$-dimensional Euclidean space. We exploit a fundamental structure of the problem to derive a new global construction of a solution, that is, a construction that is…
We introduce one-way flows in near algebras and two-way flows in double near algebras with two interrelated multiplications. We establish parametric representations of the one-way and two-way flows in terms of a single element of the…
We introduce Forman-Ricci curvature and its corresponding flow as characteristics for complex networks attempting to extend the common approach of node-based network analysis by edge-based characteristics. Following a theoretical…
In this paper we introduce the branched $\alpha$-flows on closed surfaces with Euler characteristic \(\chi \leq 0\). Based on the strict convexity of the branched $\alpha$-potentials, we establish the long time existence and convergence of…
In this sequence of two papers, we introduce a curvature flow on (mixed) weighted graphs which is based on the Bakry-\'Emery calculus. The flow is described via a time-continuous evolution through the weighting schemes. By adapting this…