About Me

I'm a professor of applied mathematics at Augsburg University of Applied Sciences. I regularly teach mathematics courses for computer engineering (technische Informatik) and international industrial engineering (internationales Wirtschaftsingenieurwesen) students as well as an introduction to computer science for data scientists.

Before I became a professor, I did my PhD with Heiko von der Mosel, a postdoc with Maria G. Westdickenberg both at RWTH Aachen University and worked for TN CURA.

Teaching

Research

Applied and Industrial Mathematics

Coming from an engineering school, I'm 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.

Calculus of Variations and PDE

During my postdoc I investigated the metastability of the one-dimensional Cahn-Hilliard equation for initial data that is order-one away from the so-called slow manifold. In other projects we derived optimal relaxation rates for this equation and explore the energy landscape of the Cahn-Hilliard energy.

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.

I'm especially interested in topics at the intersection of these two fields: For example in developing discrete counterparts for knot energies that have similar features as the original energies and that 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.

Publications

Corrigendum to "Metastability of the Cahn-Hilliard equation in one space dimension" [J. Differ. Equ. 265 (4) (2018) 1528–1575]

Sebastian Scholtes and Maria G. Westdickenberg, J. Differential Equations, 362 (2023), 576-580.

Numerics and analysis of Cahn-Hilliard critical points

arXiv:2104.03689 (2021). Tobias Grafke, Sebastian Scholtes, Alfred Wagner, Maria G. Westdickenberg

Variational Convergence of Discrete Elasticae

Sebastian Scholtes, Henrik Schumacher and Max Wardetzky, IMA J. Numer. Anal., draa084 (2020).

Optimal L¹-type relaxation rates for the Cahn-Hilliard equation on the line

Felix Otto, Sebastian Scholtes and Maria G. Westdickenberg, SIAM J. Math. Anal., 51 (2019), 4645–4682.

Metastability of the Cahn-Hilliard equation in one space dimension

Sebastian Scholtes and Maria G. Westdickenberg, J. Differential Equations, 265 (2018), 1528-1575.

Discrete knot energies

In: New Directions in Geometric and Applied Knot Theory, Sciendo, 2017, 109-124.

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).

If you are a student that is looking for a supervisor for their thesis, a company or scientist interested in working with me, ... please don't hesitate to contact me.