# Interviews

## Erika Hausenblas

Erika Hausenblas works in the field of stochastic partial differential equations and their applications. She studied Mathematics and received her PhD degree at Paris Lodron University of Salzburg, being employed at Siemens-Munich several times before and after her graduate studies. She has obtained quite a number of thirdparty projects during her career, such as the APART-fellowship of the Austrian Academy of Sciences, and several projects from the Austrian Science Fund, such that she could finance herself. After being a fellow of the Newton Institute for Mathematical Science (Cambridge) for several months in 2010, she started her professorship in Applied Mathematics at University of Leoben.

Your research concerns quite a modern field of mathematics, namely stochastic partial differential equations and their applications. Can you elaborate on your current research interests and on the motivation for it?

I got acquainted with the topic at a summer school in Edinburgh. However, I started with stochastic analysis even earlier, by studying the books of Karatzas and Shreve (Brownian motion and Stochastic Calculus), Revuz and Yor (Continuous Martingales and Brownian motion) and Roger and Williams (Diffusion, Markov Processes, and Martingales I and II). I liked the topic and, in particular, that there were still many open questions.

Both during and several months after your studies of mathematics at the University Salzburg, you worked at Siemens-Munich in Germany. What motivated you to return to academia to pursue a PhD in Mathematics and a scientific career? Do you still have any collaborations with industry partners?

I was interested in Mathematics and planned to make a PhD, but also to study Spanish and Mathematics for teaching. However, since I was working for Siemens Vienna during my doctoral studies, not so much changed – I was still working for the industry while writing the PhD.

With (at least) eleven approved grants so far, you have been very successful when applying for third party funding. How important was in particular the APARTfellowship of the Austrian Academy of Science that supports excellent young scholars in their early PostDoc careers for you? In your opinion, what are the main factors to take into consideration when submitting a grant proposal?

The only University position I could qualify for after my PhD in Mathematics was an administrative position at the Department of Psychology in Salzburg. So, getting the APART-fellowship (and then my first two FWF grants, which were only written by me, without any help) was essential for my career – with these three grants, I succeeded in getting a chair or professorship. I guess, without these grants, it would not have been possible to get a tenure-track position. Most of the positions are distributed due to your supervisor or some network. It is like most of the prizes or awards: One needs to be nominated by someone. If nobody takes the nomination responsibility for you or you do not belong to a good network, it is quite difficult. However, to get a grant, the most important part is the proposal.

So, for me it is important to have an institution next to the universities like the Austrian Science Fund or the Academy of Science supporting researchers – the proposals are evaluated by independent referees, objective criteria are assessed. For me, the universities are too old-fashioned.

How to write a grant: One has to be self-critical, and one needs to have ideas, and to take it seriously.

You are a very internationally oriented researcher and you have supervised PhD students from many different nations. What strategies did you pursue to create your scientific network? Can you share with us some of your experience with working with people of rather diverse background?

Firstly, since the Montanuniversität is a small university, people from Austria or Germany are not really interested in coming to that place. Secondly, one cannot study mathematics in Leoben. However, outside Austria or Europe there are also excellent researchers. For instance, now I have an excellent PostDoc from Cameroon, and I enjoy working with him.

You are one of the two women professors out of forty-four professors at Leoben University. How do you feel this imbalance, how does it affect your work?

I am usually addressed by: “Liebe Erika, liebe Kollegen”. Apart from that, it is difficult to say. In the industry, I was usually the woman in the office (excepting the secretaries). In Salzburg, at the Department of Mathematics (also at the Department of Computer Science), the number of women was not really high. At my time, there was no globally financed woman apart from the secretary.

I guess there are some situations one will never experience if there are more female professors. E.g. to be asked in the own office, if I can give some information where one can find “Herr Professor Hausenblas” or “the Professor”. Another situation: At a meeting with people from the industry, someone hands me his coat to hang up, assuming each woman at the meeting is a secretary. This is a proof that the male form “Professor” does not include women at all, a claim made by many germanists.

How do you see the role of our network of women in math in Austria? What could be done via this network?

Since I had children and was a single mother, I was never engaged in such networks. In order to build a successful network, one needs many people. In my opinion, one big problem is that the critical mass of female professors in Austria is too small, and Austria is too small. Maybe one should include men, to increase the network. Also, it would be good for women to have good contacts to male mathematicians. I have seen that for a woman it takes much longer to change from “Sie” to “Du”, and to build up a more personal relationship to e.g. the advisor or to other male researchers.

## Sandra Müller

Sandra Müller studied Computer Science and Mathematics at the University of Münster, where she obtained a PhD in Mathematics in 2016. Afterwards she was a Postdoc and later a University Assistant at the University of Vienna, where she received a fellowship sponsored by L’Oreal Austria, the Austrian UNESCO ( ÖUK) and the Austrian Academy of Sciences (ÖAW). In 2020, during maternity leave, she received an Elise Richter Fellowship of the Austrian Science Fund FWF. In 2021 she moved to TU Wien, where she was awarded an FWF START Prize and the Forderungspreis of the Austrian Mathematical Society in 2022. In the same year she was elected as a member of the Young Academy of the ÖAW. Since March 2023 she is an assistant professor at TU Wien. She serves as the editor for thesis abstracts for the Bulletin of Symbolic Logic and is a member of the Council of the Association for Symbolic Logic. Her research focuses on inner model theory, determinacy axioms and descriptive set theory, as well as their relationships and connections to other areas of logic and mathematics.

Was mathematics love at first sight for you or did you realize at a later stage that a career in mathematics is your calling?

As a teenager I was more interested in computer science, programming and physics. So, I started taking university lectures in computer science during my last years of school. In fact, I thought lectures in mathematics would be too hard. But then I realized that I really want to understand the foundations and theory behind everything. Mathematics fascinated me because apparently simple statements, for example, whether there is a set of size strictly between the size of the natural numbers and the size of the real numbers, turn out to have a very complicated answer or even no answer at all in our current mathematical framework. This was a shock for me, so I wanted to learn all I could about these problems.

You work in the field of set theory. Could you describe your scientific focus, most important results and possible applications?

My research is driven by questions that cannot be answered in the standard framework for mathematics, called the Zermelo-Fraenkel-Axioms. We aim to understand and connect possible extensions of these standard axioms to get a clearer picture of the mathematical universe. I recently extended the connection between so-called mice with large cardinals and winning strategies in certain infinite games by proving an approximately 10-year-old conjecture of Sargsyan. The subarea of set theory I am working in is called inner model theory. While the work itself is technical and theoretical, it is highly influenced by and connected with philosophical believes. The starting point is Kurt Gödel’s work. He showed in the 1930’s in Vienna that the foundations of mathematics are incomplete: There are statements that can neither be proven nor disproven in the standard axioms. While his statement was very abstract, we nowadays know several natural examples for such statements from various areas of mathematics, including group theory, analysis, measure theory, and C*-algebras. Therefore, our study of extensions of the standard axioms can ultimately be applied to these areas and is likely to yield answers to questions there that do not have an answer otherwise.

Your CV includes an impressive list of awards and distinguished grants, such as the FWF START prize, the Austrian Mathematical Society prize, the FWF Elise Richter fellowship and the L’Oreal Austria fellowship. How do you get interesting ideas for grant proposals? Could you share some advice on how to write successful proposals?

I believe finding the time to write a good proposal is sometimes more difficult than getting ideas. It takes time to write a good proposal and I always started drafting a proposal long before the deadline. My research has a clear overarching goal and every day I am confronted with many interesting questions I would like to work on. One advice I got a few years ago that I found particularly helpful was that to write a successful proposal you need to own the problem. If you have a question you really want to solve and you make it “your question”, it is much easier to convince others that this question needs to be solved and you are the person to do that. One thing I would add to that is think big and believe in yourself! If you are not convinced that you can do it, why should others be? But if you managed to convince yourself, you already know what to write into the proposal.

It is known that scientific networking is essential for scientific success. How did you manage to engage with such an extensive group of collaborators?

I enjoy travelling to conferences and giving talks, so I have done this extensively in the past years. Meeting friends and collaborators during the coffee breaks and listening to their recent work is always a source of inspiration for me and I sometimes get ideas how to attack a difficult mathematical problem even after a long day of talks in the evening when I am back in my hotel. Of course, writing papers and grant proposals is more productive in the office, but this is only half of the job as a mathematician. The most difficult thing here is to find the right balance.

Have you faced difficult moments in your career? If yes, how did you cope with them?

I feel very comfortable in the inner model theoretic community, but I am often worried about the fact that I am worldwide the only woman in the research area. In several conferences in the past years I was, for example, the only female speaker. I aim to change this by supporting and mentoring strong female students and join forces with other women in set theory and, more generally, in mathematics. When I started my position at TU Wien, I initiated a network of women in mathematics across the three math institutes at TU Wien. I believe that it needs a structural change to substantially improve the gender balance in mathematics, so I do whatever I can to support this. Keep in mind that approximately 50% of the world’s population is female. So currently we are missing ideas and inspiration from a large unexplored source of talent.

You have been involved in quite a number of outreach activities, including some podcasts. What is your motivation for that? Which activities have proven to be the most efficient, in your opinion?

It is often claimed that mathematics is difficult, abstract and hard to follow for nonexperts. I completely disagree with this. Of course, to fully understand the heart of a technical argument one might need months or even years of preparation. But to get a feeling for the main ideas and the driving force behind my work one only needs an open mind and a few minutes of time. I am very passionate about my research, so I enjoy explaining to others why I am fascinated by the questions that I work on every day (and sometimes night).

What is your approach toward achieving work-life balance? Have you received assistance from your personal and job surroundings?

I find it hard to distinguish between work and life. I feel very privileged that I am able to work on the problems I like and there are very few moments in my life where I do not think about some mathematical question, at least in the back of my head. Concerning practical things in work and life, for example, taking care of a 2-year-old while at the same time leading a group of 6 researchers, it requires some flexibility and spontaneity on every side. But sometimes this even helps to focus on the important things!

## Karin Schnass

Karin Schnass studied mathematics at the University of Vienna. After an internship at Philips in Eindhoven, she pursued a PhD in Computer, Communication and Information Sciences at EPFL. Following two maternity leaves and a Postdoc stay at RICAM Linz she was a Schroedinger fellow at the University of Sassari. In 2014 she was awarded an FWF-START project and in 2015 joined the Institute of Mathematics at the University of Innsbruck first as postdoc, later assistant professor and since 2020 as full professor. Her main research interests are sparse approximation and dictionary learning as well as their applications in signal processing.

You hold a Master degree in Mathematics and a PhD in Computer, Communication and Information Sciences. Were you attracted to formal sciences early on in your childhood or much later? What sparked your interest?

I have always liked math, because first of all I had great teachers, so thanks to Margit Pell and to Helmut Lerperger, who was especially encouraging. Second, you just had to understand math and then it was not a lot of effort. So I watched a lot of Pinky & the Brain, while doing the math homework, while German and English was relegated to the night before the deadline. Of course that did not work anymore at a university level, where I guess the first year is a trauma for most people. What helped to get over the weirdness of math in the first year (apart from Johanna Gaier, who needs to be credited for patiently explaining to me Analysis 1+2) was that I also did biology, which is much less weird and more like in school. If you ask what sparked the interest in biology – well that is probably one part family obsession – a lizard in the garden meant the whole family had to gather and one part also great biology teachers, thanks to Reinhard Judt and Susanne Tunner. I assume it is a bit obvious that I am using the question to say thanks to a lot of people. Come to think of it, I should say thanks to my parents – not many children get fatherly instructions to make Mobius-strips or books with Escher’s Kaleidocycles, and not many mothers have such fond high-school memories of groups, rings and fields.

Did you ever have second thoughts about pursuing an academic career as a mathematician?

Every time a PhD student from the institute get’s a ‘real’ job!!

“Sparse dictionary learning” seems to be an important keyword in your work. Can you describe your research?

A dictionary is a set of vectors in vector space, called atoms, that can be used to build other vectors as linear combination of the atoms. Such a vector is then called sparse if only a small number of atoms, small compared to the dimension, is needed to represent the vector. The goal of dictionary learning is to find such dictionaries for a (huge) set of vectors. In my research I assume that the set of vectors is sparsely generated from some ground truth dictionary and try to find out if an algorithm can recover this ground truth dictionary.

Being a full professor at an Austrian university typically means working considerably more than 40 hours per week. Are you satisfied with your current time management and do you manage to reach a balance between research, teaching, administration and other commitments?

That’s definitely twice no. I’m quite bad with time management and balance, especially in the last two years, where on top of the usual duties I was also associate dean of studies for the math institute and/or home school teacher for the kids. So I sort by importance and then there is not as much time and brain left for research as I would like.

You were awarded prestigious FWF grants such as the START prize and the Schrödinger fellowship. Can you share with us some advice for submitting a successful grant proposal?

Be lucky! Give your best and be persistent! There is a rumour that Agata Ciabattoni got the START prize in her 3rd and last attempt. She is my hero!! There are other things that help, like a cute idea, colleagues, who let you read their proposals, a good friend, who reads your proposals with the eyes of Tom Henzinger, a mentor, who tells you how to explain your 6-year proposal in 10 min (only pictures!!!), but really being lucky is the most important aspect. (Also thank you Holger & Peter, Maria and Massimo!).

Do you have any special career advice for (women) mathematicians at the beginning of their career?

Apart from being lucky and persistent, I’d say it helps to have children with someone, who insists on sharing all parental and domestic responsibilities equally. Then it’s also good to ignore all advice and listen to Fleetwood Mac or to try to think of a cool woman, whose career path you can copy. I copied from Monika Dörfler! Thanks Monika!

How do you manage with balancing family and work?

My first answer was: I would manage better if the Austrian school system was a little less based on the assumption, that after an exhausting morning of supervising the house-keeper, drinking prosecco and flirting with the mailman, Mama is looking forward to an afternoon of helping the little darlings with their homework. I thought the answer might be a bit strong, despite using the nice f-word. However, when I asked my office spouse to proof-read the answers for social acceptability, he was less offended by the answer than by the question. He said: I understand why they ask the question, but I have never seen a man being asked it. Somehow it transports the feeling, that family is a woman’s job. I think he has a point, so I’m changing my answer to: Oh, every father’s favourite question! I am doing ok – none of the two suffers too much. So in the working dad league I would probably score quite high. Also, thank you, Christian! I know you are going to be a high scorer as well.

## Vera Fischer

Vera Fischer obtained her MSc degree in 2001 from the University of Tübingen (Germany), then her PhD degree in 2008 from York University (Canada). Since March 2021, she is a fast track tenure track assistant professor in Mathematical Logic at University of Vienna. In February 2021, she became an editor of the Proceedings of the American Mathematical Society and in January 2022, editor of the Journal of Symbolic Logic. In 2018, she was awarded the Prize of the Austrian Mathematical Society and 2017 the FWF START Prize for her projects “Infinite Combinatorics and Definability”. She is a board member of the European Set Theory Society and the Austrian Mathematical Society. Her scientific interests are focused in set theory of the reals, infinitary combinatorics and forcing.

How did you decide to study mathematics?

I have always found mathematics to be really beautiful and interesting. Even as a child, mathematics was my favorite subject. I really enjoyed solving problems. I was going to mathematics competitions and later reading (well, more like taking a curious peek at) some higher level mathematics textbooks. I was very fortunate to grow up in an environment where mathematics was well respected and moreover my interests were nurtured and encouraged. Deciding to study mathematics was the most natural decision for me.

You work in a classical and fascinating mathematical field, namely Logic and Set Theory. Could you mention a few current challenges in this field? Where are your interests positioned?

My mathematical interests are in set theory of the real line and infinitary combinatorics. This is a very interesting and dynamically developing subject, focused on the properties of various sets of reals, sets which often emerge in other areas of mathematics, including analysis, algebra and topology. The set theoretic study of these objects gives an unique perspective, which greatly enriches our understanding of the real line.

You have received for your research a couple of important awards: the START and the Austrian Mathematical Society prize. How have they influenced your career?

The START program gives an amazing opportunity for scientists to make significant advances in their respective fields, by mapping out and realising a longterm scientific project. My START project attracted many brilliant scientists, with whom I am very thankful and glad to have worked. Moreover, I am happy to report that many of the original goals of the project are not only already achieved, but the obtained results brought to light many new interesting open questions and directions for further investigations.

The prize of the Austrian Mathematical Society is a great honor for me. It is an amazing recognition, which has made me even more aware of my role as a scientist and a member of the mathematical community. There are many leading mathematicians working in Austria. Aiming to maintain these high standards, engaging our students in our work and creating conditions where good mathematics can be done, is something we can all strive for.

You obtained your PhD in Canada. Could you mention a few traditions, rules or requirements on the PhD study there that you liked and you would recommend for Austria?

The most memorable experience I took with me from my doctoral studies years in Toronto is probably by far the enormous amount of mathematics that I was very lucky to witness first hand at the Fields Institute while being a visitor there: an impressive number of conferences, workshops, research seminars, meetings and scientists from every possible corner of the world, representing any imaginable area of mathematics.

Could you tell us about difficult moments in your career and how you overcame them?

If I have to summarize my experiences in difficult moments of my career and how I overcame them, I would simply say: focus, concentration, persistence and very importantly, one should not forget to smile, even when things seem rather gloomy.

In Canada you received an award for excellence in teaching. Can you share with us something about your teaching style, guidelines, and methods?

I try to share my enthusiasm about the subject and aim to present it in a way which makes it relevant, alive and intriguing. It is a story in which the students play a key role, as they are the ones who have to see a proof, provide a solution, give an example or simply understand a new concept.

How do you manage with balancing family and work?

The people and things we love make us better and stronger, and moreover they inadvertently call for the best in us. This is true for both our professional and personal lives. Not only, I greatly enjoy and value the time I spend with my family, but I am also happy and grateful for the many amazing professional experiences, which I can bring home and share with my loved ones, even if just in an informal way.

## Mihyun Kang

Mihyun Kang received a PhD degree in Mathematics from the Korea Advanced Institute of Science and Technology (KAIST) in 2001 and obtained a Habilitation in Theoretical Computer Science from the Humboldt-Universitat zu Berlin (HU Berlin) in 2007. As a Heisenberg fellow of the German Research Foundation (DFG) from 2008 to 2011 she conducted her research at the Free University Berlin, the New York University, and the University of Oxford. In 2012 she became Professor of Discrete Mathematics and Optimisation at the Graz University of Technology (TU Graz) and since then she leads the Combinatorics Group at TU Graz. She serves on the editorial board of several leading journals in her research field, including Random Structures and Algorithms. She received a Friedrich Wilhelm Bessel research award of the Alexander von Humboldt Foundation in 2019.

When and how did you realize that you wanted to become a mathematician? Did you have support from your family?

As far as I remember, the only subject that I really enjoyed in school and at the university was Mathematics. This naturally led me to become a mathematician. By and large my parents allowed me to decide the course of my life by myself. My mother provided me with warmth, comfort, and encouragement for any path I chose. My father gave me a very positive impression about the life as a professor, and one of his “hobbies” was to lecture me about his philosophy and life wisdom.

Your expertise lies in the field of Discrete Mathematics. Could you tell us more about your research in general and your current research topic in particular?

Discrete Mathematics is a vast area in Mathematics which deals with discrete objects. It has exciting and important connections to other areas of Mathematics, natural sciences, and computer science. My main research focus within Discrete Mathematics is random graph theory, which investigates very large graphs equipped with a certain probability distribution. Random graphs have been a source of fascination for decades not only as a theory of its own, but also due to their connection to other sciences, such as theoretical computer science, statistical physics, life sciences, to mention a few.

My current research topic concerns global and local properties of sparse random graphs and the interplay between them. The key questions are: What does a random graph globally and/or locally look like? How does a global structure affect its local structure? How much is a local structure of a random graph affected if we impose a global constraint on a random graph, such as being planar?

What scientific achievements are you most proud of?

About ten years ago, together with a colleague I studied a random graph that can be embedded in the plane without crossing edges, which we call a random planar graph. We discovered that phase transitions in random planar graphs differ significantly from the classical random graphs. We also studied other global properties of a random planar graph, such as the order and internal structure of the giant component. One of my PhD students at TU Graz extended and strengthened these results to random graphs that are embeddable on an orientable surface. Based on this work, another PhD student of mine determined the local structure of a random planar graph. I am proud of these scientific achievements of my PhD students.

Did you or do you have any role models?

It changes over time, but most of my colleagues, junior or senior, in the research field are my role models.

Before moving to TU Graz you have studied and worked at universities in several countries. In which way was this experience important for you?

First of all, I got the chance to work with world-leading experts and to expand my research network. Second, very active and diverse research environments and systems in those countries were invaluable. They broadened my horizons not only as a mathematician but also as a person.

In particular, collaborations that I have built up during my research stays in Germany and the UK continue until today. For example, I will visit the University Oxford during the winter break in 2023 as a visiting research fellow of Merton College and will work with some colleagues there, collaborations with whom go back to 2009 when I worked at the University of Oxford as a Heisenberg fellow. At the time of this Interview, I am visiting a colleague at TU Dortmund, whom I first met at HU Berlin back in 2001 and who is one of my frequent co-authors. Since 2018, we run a joint Austrian-German project and co-organise several workshops, e.g., at Banff and Oberwolfach.

In short, my work and research experience at universities in different countries have significantly affected my past and current research activities and outputs.

Have you come across obstacles on your career path as a mathematician? If yes, what motivated and helped you to pursue your plans?

At the beginning of my PhD studies, it was not easy to find the right subject for my PhD thesis. If I liked a certain subject, say A, then the subject A did not like me, in other words, I could not prove any new interesting results. Vice versa, if a certain subject, say B, liked me, then I did not enjoy it. It was quite a tough and discouraging time.

There was luckily a turning point during the second year of my PhD studies. My PhD superviser, who was visiting UC Berkeley for his sabbatical year, introduced me in an email to a problem involving shuffling cards that he heard about there. Fortunately, I liked the subject and could prove something in the end.

The search on related topics led me to a summer school on random graphs toward the end of my PhD studies, which changed the course of my academic path. I was more relaxed there after my PhD defence, and I liked random graph theory so much that I eventually found my way to Berlin. In October 2001 I arrived at the Adlershof science park which hosted a very strong research group working on random graphs. Since then, I mainly work in this field.

In short, the most important thing for me was to discover the research topics that I am fond of and good at.

The time after the PhD is sometimes considered difficult, if one wants or needs to go into new research directions. Did you face such a situation after graduating from the Korea Advanced Institute of Science and Technology?

As said above, a couple of months after my PhD defence at KAIST, I participated in a summer school where I first met random graphs. This strangely attractive topic led me to a postdoctoral position at a research group at HU Berlin where the world-leading experts were working on various topics in Discrete Mathematics, especially on random graphs. Back then, I had only a very basic knowledge about random graphs, while most of the other group members, including PhD students, knew way much more than I did. For the first half a year or so, it was quite tough to follow the talks at the weekly research seminars, but eventually I could have discussions with them and we could solve problems together. And now random graphs is my favourite research topic.

Do you have any special career advice for students and early career researchers in mathematics and especially for women?

I do not have any general advice, because each individual is different. Instead I could share my own experience and thoughts.

Stage 1 (during my PhD studies): First of all, I had to learn about myself by asking questions and seeking answers. What is most important for me? Which topics in Mathematics do I enjoy most and am I good at?

Stage 2 (after the PhD study and before Habilitation): For the first five to six years after my PhD studies, the most important thing for me was to write very good papers. During those years, a couple of colleagues at HU Berlin had obtained their Habilitation, which of course I had no idea about at the beginning. Gradually I realised that a Habilitation is one of many important qualifications necessary for a professorship in Germany. So, I did some research on what qualifications I would need if I would continue my academic career in Germany, apart from solving scientific problems and writing good papers.

Stage 3 (after Habilitation before Professorship): As a consequence of completing my Habilitation I became a Privatdozentin at HU Berlin, but this was not directly linked to a position. This meant I had to find out what possibilities there were for me to continue my academic career, and to enhance my chance of becoming a professor. The answer I found was a Heisenberg fellowship of DFG, which allowed me to conduct my research in Germany, UK, and USA.

After receiving a Heisenberg fellowship, further questions arose: How can I make my qualification more competitive for a full professorship? In which part of the world do I want to continue my academic career?

All these questions and experience in different career stages led me to what I am now. In conclusion, my only advice is to ask yourself questions of your own.

## Monika Ludwig

Monika Ludwig got her PhD from the Technische Universitat Wien in 1994. She worked as an Assistant Professor there until 1999 when she moved as an Erwin Schrödinger Fellow first to University College London and a year later to New York Polytechnic University. She became an Associate Professor at TU Wien in 2001 and was a visiting Professor at the University of Bern for one semester in 2002. In 2007, she moved as full Professor to the Polytechnic Institute of NYU and returned to TU Wien in 2010 as full Professor. She was the first woman who received the Hlawka-Prize of the Austrian Academy of Sciences and the Förderungspreis of the Austrian Mathematical Society. She became a Corresponding Member of the Austrian Academy of Sciences in 2011, a Fellow of the American Mathematical Society in 2012, and a Full Member of the Austrian Academy of Sciences in 2013. She was a plenary speaker at the European Congress of Mathematics in 2021.

Could you tell us about your research in general? What about your current research topic?

I work on questions in geometry and analysis. Presently, I am working on a project that aims at extending geometric valuation theory, that has been very successful within convex geometry, to function spaces including spaces of convex functions and Sobolev spaces. This can be seen as a part of the larger aim to geometrize analysis.

What are the results you are most proud of?

Let me mention two results, both within geometric valuation theory. About twenty years ago, I was able to give a simple characterization of, first, the classical notion of affine length and, a bit later together with Matthias Reitzner, of classical affine surface area in general dimensions. Much more recently, together with Andrea Colesanti and Fabian Mussnig, I established a version of the classical Hadwiger theorem for convex functions. This is part of an ongoing project.

You have worked at several universities abroad. Are there particular aspects that you liked at those universities and how important are such international experiences?

I enjoyed getting to know new things within mathematics and also in general. For me, it was very valuable to see that there are many different ways to do almost everything, including teaching and administration. It was also very inspiring to have colleagues and collaborators with very different backgrounds and ideas. More specifically, I liked the pragmatism at American universities and the commitment to excellence. I liked the egalitarian approach at Swiss universities and the fortitude and the wit of my British colleagues.

You have supervised quite a few PhD and MSc students. Did you experience any differences in working with female and male students?

There were many differences between my students but the different backgrounds had a much bigger impact than the difference between female and male students. I worked with male students from Austria and from the US and with female students from the US and China. I enjoyed to work with all of them, but, of course, it is easier to work with students who like mathematics a lot and want to make a significant contribution.

How important were mentors for you during your career?

Very important. I would recommend everyone to talk with their colleagues and professors about what it means to be a mathematician. This includes gossip about how other researchers were able to succeed and how they failed. In addition, it is important to get advice on how to do important things, in particular, how to find good research questions, how to establish a research program, how to write a grant proposal and how to publish in good journals. Let me add that it is not easy to be a good mentee. In the end, a good mentor will be demanding and, if necessary, he or she will also criticize your research program. He or she might remind you that you have to become independent in your research, that you have to write grant proposals, that you have to organize events, etc. All this is considered necessary by hiring committees and should not be neglected. But a good mentor should also encourage you and appreciate you and your scientific work.

Austrian universities and Research Institutions like IST Austria are attracting more and more young mathematicians with high scientific potential. Since the number of available academic positions in Austria is quite low, what would you advise them to do once they finished their PhD?

Don’t restrict your career options to Austria or to German speaking countries. Mathematics is very international, and working abroad can be a great experience. This is true within academia but also for the wide variety of jobs that a mathematician with a PhD can get nowadays.

Almost any career is facing ups and downs. Did you make such experiences and how did they affect you?

After my habilitation, I was applying for many positions as a professor for quite a few years. It was frustrating when often I was not even invited for an interview (by the way, I don’t think that this would happen that often nowadays). In the end, I realized that the restriction to German speaking countries was not wise and moved to New York City when I got an offer from there. I don’t think that I would have made this move if I had also got an offer from Germany or Austria. But in the end, my years in the US were very important and rewarding for me.

## Michaela Szölgyenyi

Michaela Szölgyenyi is a full-professor for Stochastic Processes at the Department of Statistics, University of Klagenfurt since 2018; in 2020 she became head of department. Michaela is mainly working on analysis and numerical methods for stochastic differential equations and stochastic optimal control. In 2020 the University of Klagenfurt was granted the FWF doc.funds doctoral school Modeling – Analysis – Optimization of discrete, continuous, and stochastic systems of which she is the coordinator. Michaela did her PhD in Mathematics at JKU Linz in 2015 and Post-docs at WU Vienna and at ETH Zurich.

How did you discover your attraction to Maths?

I think I just always liked it. Already as a four-year-old my grandfather played school with me, teaching me basic calculus.

Did you or do you have any role models?

During my career I met several great female mathematicians. At the moment I would call Barbara Kaltenbacher my role model. She is incredibly successful in research, extremely efficient, and still finds time for being very active in our departments’ life. I deeply admire her.

Did you have support (encouragement) from some mentor during your career?

I think the most important time in my career development was my time at WU Vienna. My mentor there was Rüdiger Frey, who was always very clear and honest with me in order to push me forward. For example, if you like the place where you are and your dear mentors tell you that you should apply to another great place abroad, then this might feel hard in the first place, but they are probably right. Besides a very good personal relationship we had, Rüdiger did a great deal in fostering me.

Why did you choose to work on stochastic differential equations and related topics?

I did my PhD on stochastic optimal control problems in insurance mathematics. While solving those problems, issues with existence and uniqueness of solutions to the underlying SDEs emerged. So I dived into those questions and soon became hooked also with numerics of SDEs and simulation methods.

What scientific achievements are you most proud of?

I am happy that nowadays several international research groups work on topics close to mine and also make use of methods from my papers. In addition, I am proud that we have been granted the first FWF doc.funds doctoral program at our university and that so many great young people came to Klagenfurt to work with us on this project.

You received a professorship only three years after the PhD graduation. What is the secret of your success?

I worked hard on my research papers, gave numerous talks at international conferences and in my departments’ seminars, asked for feedback from my peers and mentors, and applied for third party funding already at an early stage of my career. In addition, I was involved in a lot of teaching and in university management as a member of WU’s academic senate, where I learned a lot. I left JKU Linz shortly after my PhD defense, went on to WU Vienna and then after two and a half years to ETH Zurich, where I enjoyed a great research environment. So there are no secrets involved, just commitment, mobility, hard work, and great mentors.

What are the challenges of becoming a professor at such an early age stage of the career and how do you deal with them?

Independent of the age is the challenge that you suddenly have much more duties in teaching and university administration that reduces the time you can spend on your beloved research.

You are the leader of a prestigious FWF doc.funds doctoral school at the University of Klagenfurt. Could you tell us more about this achievement?

After being in Klagenfurt for only half a year, the faculty of the Departments of Statistics and Mathematics at University of Klagenfurt decided to apply for an FWF doc.funds project. As my field of research is well-connected to the other fields, I was asked if I would take over the role of the coordinator (project lead), to which I happily agreed. In February 2020, only days before the first lockdown, four female professors from Klagenfurt took part in the FWF hearing – my dear colleagues Barbara Kaltenbacher, Angelika Wiegele, our vice-rector for research Friederike Wall, and me. It was an awesome moment when the FWF president called me in March to tell me that we were successful! In the project we work on the proposed problems in a multi-perspective way, that is by joining different mathematical sub-disciplines. We do this together with 14 internationally hired PhD students, currently over 80 per cent female. It is extremely positive that so many fantastic young researchers fill up our departments with their spirits!

There are many ups and downs for young researchers, especially in Mathematics and especially for women. Do you have any special advice for students or postdocs in this regard?

It is hard to move all the time and once one is settled, move again. This also takes time – time that one would love to spend for research. Also it is hard to settle and it is hard for the relationships you have. But these issues are gender independent. Women suffer – more often than average – from the imposter syndrome. If you don’t know it, Google it! And then stop it!