Illia Donhauzer

Where are you in your career?

I completed my PhD in 2022 and started a new role as a research officer at La Trobe University.

Why do you want to attend the HLF?

I wanted to broaden my professional connections and learn new ideas and concepts from other participants and laureates. Recently, I got interested in a new developing theory that combines algebraic and differential topology and the theory of random fields. The theory uses the notions of expected Euler characteristics of excursions sets of random fields, persistent homologies, and others to study distributions of random fields. In my opinion, it is fascinating that so far mathematical theories are finding connections with each other. Last year, there were many participants at HLF specialising in topology, algebra, and geometry. I would be happy to discuss with them this arising theory and hear their comments on it.

Tell us about your research?

The topic of my research at La Trobe University is the analysis of various types of random fields such as weak and long-range dependent fields, fields defined on discrete and continuous domains, Gaussian and non-Gaussian fields. I study functionals of fields that have a wide range of applications in statistics. The obtained results allow the statistical analysis of data defined on various domains.

I also study methods to model a specific type of fields which is called multifractal fields. Contrary to fractals, multifractal systems possess many scaling rules and cannot be described by a single fractal dimension. This type of fields has been observed in various areas such as communication systems, precipitation fields, ore deposits.

If you could meet any Fields Medalist or Abel Prize winner which would it be and why?

I would like to talk to Maryna Viazovska, a distinguished expert in the fields of geometry and topology. I am particularly interested in the theories that emerge at the intersection of geometry and probability. As a probabilist, I believe that delving into the realms of geometry can help me to obtain new results in the theory of random fields. By exploring the geometric aspects of probability, I can gaini a deeper understanding of the underlying structures and patterns that govern random geometric events.

 

 

9th Heidelberg Laureate Forum Report

 

The 9th Heidelberg Laureate Forum (HLF) took place in Heidelberg, Germany, from 18 to 28 September 2022. It was a remarkable gathering where 200 young researchers from around the world had the extraordinary opportunity to engage with and learn from some of the most influential mathematicians and computer scientists who have reached the pinnacle of their fields.

Thanks to the generous support of La Trobe University and AMSI/AustMS, I was fortunate enough to attend the Forum. Each day commenced with an insightful introductory lecture that set the stage for the enriching discussions that followed. The panel discussions among the laureates were extensive and inclusive, covering a broad range of multidisciplinary topics. The discussions explored future challenges in mathematics and computer science, effective science communication with the public, the profound impact of these disciplines on society, and much more.

One lecture that particularly resonated with me was ”A 40-year Journey” by Reinhard Genzel, the 2020 Nobel Prize winner in Physics. His talk delved into the extensive research conducted by Prof. Genzel and his colleagues to study the mass distribution in the center of our Milky Way through precise observations of the motions of gas and stars as test particles of spacetime. The remarkable results revealed the existence of a four million solar mass object, conclusively identifying it as a massive black hole. This lecture not only showcased groundbreaking research but also provided valuable insights into the perseverance and dedication required for long-term scientific investigations.

I must also commend the organisers of the HLF for their outstanding work in arranging various communication events for young researchers. One of the most engaging events was Speed Networking, where participants had the opportunity to meet and exchange brief introductions, fostering connections and knowledge sharing in a dynamic environment. Additionally, cultural events such as the Bavarian Evening, featuring traditional dances and songs, and the Heidelberg Castle Tour, offering a glimpse into the history of the German southern lands, added a delightful touch to the overall experience.

As someone with experience in organising student conferences, I can confidently say that the HLF stood out as an exceptionally well-organised event in every aspect. The atmosphere was conducive to fostering connections among young researchers from diverse backgrounds and providing them with direct access to the laureates. It was inspiring to witness the participants approach the laureates, ask questions, and seek advice for their future careers. I also was happy to discuss my research with three laureates and many young researchers.

Attending the 9th Heidelberg Laureate Forum was an extraordinary journey that profoundly enriched my understanding of the field and provided invaluable networking opportunities with esteemed researchers and fellow peers from across the globe. I left the Forum inspired, with a renewed sense of purpose, and a deep commitment to contribute to the advancement of mathematics in ways that positively impact society.