Algebra, Geometry and Computer Algebra Group

Humboldt-Fellow works on singularities


Delphine Pol is working on such "free divisors", a special kind of singularities. Picture: CC BY-NC-SA-3.0 (https://imaginary.org/gallery/free-surfaces)

Dr. Delphine Pol. Picture: Koziel/TUK

The French mathematician Dr. Delphine Pol has received a scholarship from the Alexander von Humboldt Foundation. As such, she is a guest at the Technical University of Kaiserslautern (TUK) for two years. She leads research in the Department of Mathematics under the supervision of Professor Dr. Mathias Schulze in the fields of algebra, geometry and computer algebra. Pol investigates singularities of geometric objects using algebraic and combinatorial methods.

Pol studied mathematics at the University of Angers, in the west of France, and graduated in 2016 with a doctorate in singularity theory. During this time, a close contact with the research team led by Professor Schulze was developed. She then spent one year as a post-doctoral fellow in Japan at Hokkaido University in Sapporo. Since October 2018 she is working as a Humboldt Fellow at the TUK.

 Pol's research is at the interface between geometry, algebra and combinatorics. More specifically, she deals with sets of solutions of (non-linear) equations. These sets can be considered as geometric objects. As such, they are "smooth" in many places, but they also occasionally have "corners and edges". These so-called singularities have a great influence on the structure of the solution set and are at the center of their own field of research, the singularity theory. Pol uses various methods of algebra, algebraic analysis, and combinatorics to explore the structure of certain types of singularities.

In the research group of Professor Schulze she works on a joint project with their research colleagues Uli Walther (Purdue University, USA) and Graham Denham (Western University, Kanda) on the so-called configuration polynomials. These arise, for example, from Feynman graphs, which describe the interactions of elementary particles in physics.

 Every year, the Alexander von Humboldt Foundation grants scholarships and prizes to researchers from all over the world. A scholarship of the foundation is a particularly high honor for the scholarship holder as well as for the host institution. Post-doctoral fellows receive it because of their extraordinary research achievements.

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