# Phirotopes for beginners

## Katharina Schaar speaks "KlarText"

17 October 2018

Chirotopes and phirotopes very well explained. Dr. med. Katharina Schaar has been awarded the KlarText Prize of the Klaus Tschira Foundation for Science Communication. It's all about friends and cappuccino.

"What are you working on?" is sometimes a difficult question, as many scientists know. But that is especially true in the case of mathematicians, as mathematics is often too complex for a general public. In her article "Die reine Mathematik" (The Pure Mathematics) Dr. Katharina Schaar explains mathematical structures in an understandable way, and shows her enthusiasm for mathematics at the same time.

### Properties of Phirotopes - the short mathematical version

"Fundamental Properties of Phirotopes - Duality, Chirotopality, Realisability, Euclideaness" is the title of the dissertation submitted by Katharina Schaar in 2017. For non-mathematicians, the regular synopsis is fairly hard to understand:

"In this thesis, fundamental concepts of complex oriented matroids (phirotopes) are presented. The existing theory of duality, chirotopality and realisability is generalised to non-uniform phirotopes of arbitrary rank. Furthermore, the relationship of phirotopes and Euclidean geometry is examined and Euclidean theorems are proven with the help of phirotopes. Finally, it is proven that certain incidence theorems always hold true for non-chirotopal phirotopes, regardless of the realizability of the phirotopes."

### Masked balls, unruly chirotopes and a cup of cappuccino

To put it more simply, Schaar's dissertation deals with the mathematical description of chirotopes and phirotopes. These are abstractions of relative location information - and not very easy to explain. "Imagine we meet with friends for a cup of cappuccino", Schaar begins her prize-winning contribution "Die reine Mathematik", to which a video was filmed at the Department of Mathematics:

"I like trying to convey that it's just amazing to do math for its own sake, because it's so pretty," says Schaar in the video.

When asked why she applied for the KlarText Prize, she replies, "It's always been a great interest of mine to bring math and its research to a wider audience. That's why I like teaching mathematics. So writing an article about my work, which is commonly understandable for all was so much fun!"

### KlarText Prize for Science Communication 2018

Dr. Katharina Schaar was a teacher and student advisor for undergraduate students at the Department of Mathematics from 2013 to 2017. She attained her PhD under the supervision of Jürgen Richter-Gebert, Professor of Geometry and Visualization, and currently works at the Helmholtz Zentrum München at the IBMI (Institute of Biological and Medical Imaging).

She is one of 6 researchers selected by the jury of scientists and journalists from 161 applicants. And what is she going to do with the 5,000 € prize money? "I don't know yet, but first of all I'll invite the people who helped me with the video shoot to dinner."