About Me

I'm a mathematician working with Maria G. Westdickenberg at the Lehrstuhl I für Mathematik at RWTH Aachen University. My research focusses on geometric knot theory, discrete differential geometry, calculus of variations and the analysis of partial differential equations.

Contact Details

Lehrstuhl I für Mathematik
RWTH Aachen
Pontdriesch 14-16
Room 215
52056 Aachen, GERMANY
+49 (0)241 80 94620
scholtes (at) math1.rwth-aachen.de

Publications

Metastability of the Cahn-Hilliard equation in one space dimension

arXiv:1705.10985 (2017). Sebastian Scholtes und Maria G. Westdickenberg

Discrete knot energies

arXiv:1603.02464 (2016). To appear in New Directions in Geometric and Applied Knot Theory, OA Measure Theory.

Comparing maximal mean values on different scales

arXiv:1501.06391 (2015). Thomas Havenith and Sebastian Scholtes

Geometric Curvature Energies

Dissertation, RWTH Aachen University (2014).

Discrete Möbius energy

J. Knot Theory Ramifications 23 (2014), 1450045, 16.

Discrete thickness

Mol. Based Math. Biol. 2 (2014), 73-85.

Convergence of Discrete Elastica

Oberwolfach Reports, 9 (2012) no.3, 2108-2110. Henrik Schumacher, Sebastian Scholtes and Max Wardetzky

Elastic catenoids

Analysis (Munich) 31 (2011), 125-143.

Kinematic improvements in sliver laying using simulation tools

In: Proceedings of the 3rd Aachen-Dresden International Textile Conference, Aachen, B. Küppers (ed.), 2009. Bayram Aslan, Sebastian Scholtes, Christopher Lenz and Thomas Gries

Elastische Katenoide

Diplomarbeit, RWTH Aachen University (2009).

Research

Calculus of Variations and PDE

In a current project with Maria G. Westdickenberg and Felix Otto we investigate metastability of the one-dimensional Cahn-Hilliard equation for initial data that is order-one away from the so-called slow manifold.

Geometric Knot Theory and Discrete Geometry

Geometric knot theory is concerned with analytic properties of knots such as the existence and regularity of minimizers of knot energies. The most prominent of these knot energies are the thickness, integral Menger curvature, and the Möbius energy. Discrete differential geometry adapts notions from classic differential geometry to discrete objects like polygons and meshes. Besides questions that belong to one of these fields, my research lies at the intersection of these two exciting areas: I'm interested in developing discrete counterparts for knot energies that have some of the same features as the original energies and are designed to provide a geometrically pleasing and consistent discrete theory. Moreover, the discrete energies should approximate the smooth energies as their underlying objects refine. Now, we want to take theorems that can be proven for the discrete energies to the limit to learn something new about the initial energies.

Applied and Industrial Mathematics

Coming from an engineering school, I'm always very interested in using a broad variety of mathematical tools in real world applications. I have worked together with engineers from different fields from both academia as well as the industry. For example, I helped the textile engineers from ITA RWTH Aachen to improve a pattern for sliver laying in cans and together with the German railway company DB we investigated data inconsistencies.

Teaching

If you are a student, scientist or company interested in working with me or writing a thesis, please don't hesitate to contact me.