# Yuanyuan’s research can be applied to things we don’t even know exist

Yuanyuan Chen has just a few colleagues around the world in the field that she has done research for her dissertation in mathematics. Her work concerns general functions and can be applied to extreme physical objects like black holes – or even objects that mankind has not yet discovered.

After four years of research in mathematics, Yuanyuan Chen has presented her doctoral thesis entitled "Continuity and compositions of operators with kernels in ultra-test function and ultra-distribution spaces". Her research has focused on generalized functions, as well as on operator theory, Fourier analysis and time-frequency analysis.

– Sometimes we need frameworks to model reality, said Yuanyuan, and that is what my research on generalized functions has targeted to a large extent.

To get some idea of what it's all about, let's take a practical example. When we talk of electric current we think that "it is electrons that migrate". We can plug in a gauge and measure the current. But this provides no absolute representation of the current – there may be other characteristics of the current that one would need other types of instruments to detect.

This is the idea behind generalized functions: you have an object and create various gauges which can then investigate its properties. These gauges are abstract and mathematical, and called test functions. The applications can also be within the world of physics.

Yuanyuan studied electronics and information engineering in China. She came to Växjö and Linnaeus University in 2010 to study electrical engineering, because she wanted more than just a bachelor's degree. Then she started to do research in mathematics in 2013.

– I became interested in research because it was totally new to me and I like challenges. Also, of course, I think mathematics is fun. The most exciting about doing research is when, after hard work, you finally get the result you wanted.

Yuanyuan has looked at general functions of really extreme kinds. In practice, these can be applied to extreme physical objects, such as black holes or things we do not even know exist yet, says her supervisor Professor Joachim Toft, who looks to the future with great curiosity.

– Mathematics is something we humans have made up, like a collection of languages. The mathematician Gauss got a mission to find a model to calculate the surface area of France in the 1800s. This created a whole new research field, differential geometry, with an entirely new mathematical language. When Einstein much later formulated his general theory of relativity, he found that mathematical language, which was just what he needed. Otherwise, perhaps we had not had any general theory of relativity at that time.

– The area Yuanyuan started to do research in is quite unique in the academic world. Many people download the articles that she and we, her colleagues, have written. So the field seems to have a future – who knows what Yuanyuan's dissertation can form the basis for in ten or fifty years? speculates Joachim Toft.

### More information

Yuanyuan Chen, PhD at the Department of Mathematics, Linnaeus University, +46 (0)70-544 52 73, yuanyuan.chen@lnu.se

Annika Sand, Press Officer, +46 (0)76-830 01 05

The doctoral thesis: http://lnu.diva-portal.org/smash/record.jsf?pid=diva2%3A1045986&dswid=-3756