On April 3, Artur Avila, professor at University of Zurich, also the winner of the highest international honor in the field of mathematics — the Fields Medal, officially accepted the appointment as a guest professor at Nankai University. On April 2, Prof. Avila was interviewed by NKU News Centre and several news medias at Chern Institute of Mathematics (CIM).
“I’m very hopeful for the development of Chinese community in mathematics”
Avila is an expert in the field of dynamical systems and spectral theory of Schrodinger operators. He has made deep contributions to dynamical systems theory. His work has "changed the face of the field". In August of 2014, he was awarded the Fields Medal, which is one of the most prestigious awards in mathematics and is often considered as the Nobel Prize of mathematics.
The Fields Medal is awarded every four years by the International Mathematical Union (IMU) on the occasion of the International Congress of Mathematicians (ICM) to mathematicians who have made outstanding contributions in the field of mathematics. At the age of 35, Avila became the first Latin American to receive the Medal, which is a full recognition of his significant achievements and contributions in mathematics. Avila's research work has been honored with numerous prizes, such as the 2006 Salem prize, the 2008 EMS Prize, the 2011 Michael Brin Prize, and the 2013 TWAS Prize in Mathematics.
Avila's academic experience was full of cross-cultural exchanges and integration. He moved to France to expand his vision after he finished all his education in Brazil. "I think that one thing that's very important is to change your environment from time to time...You should not become very comfortable at where you are. At some point you'll need to get outside of your initial field to see a little bit more of the diversity of math."
Coming to China and Nankai University, Avila spoke highly of the development of China's mathematics discipline. In his opinion, the quality of China's math education is excellent, and that makes China playing a increasingly important role in the international mathematics field. "At this moment in China I have access to great amount of very good students. I believe there is a lot of enthusiasm for math here. The students work very hard... I'm very hopeful for the development of Chinese community in Mathematics...I believe that the future is very good."
Avila has 5 Chinese PhD students, one of whom was from Nankai University. He mentioned that their concentration on research and their wide variety of research styles, which are exactly necessary for doing mathematical research, perfectly presented the vigour and potential of China's mathematics community. "Mathematics is international, so there's not one style of mathematics...probably you can develop very different cultures within China." said Avila, and he hopes to see different mathematical cultures in different countries as he believes that the integration and collision of mathematical cultures can stimulate more sparkling innovative ideas.
Connection with Nankai University: full of surprise
A photograph of Artur Avila (middle), Jiangong You (left) and Qi Zhou (right)
Prof.Avila's Chinese trip was a "reunion" with Prof. Jiangong You and Prof. Qi Zhou, who are the professors at Chern Institute of Mathematics at Nankai University. "(Speaking of) my first contact with Qi Zhou, he was my postdoc in France. He was visiting Paris in the period that I was still working there... I'm happy to finally have come here to see them at their workplace."
Prof. Avila met Prof. Zhou in Paris when Prof. Zhou was doing his postdoctoral research there. At that time, together with Professor You, they jointly started a challenging scientific research project. On a seemingly insurmountable project, Prof. Zhou came up with an idea that "surprised" him, providing new ideas for solving the problem. "Seeing such a new idea in a context that was unexpected to me, was really nice to give me more enthusiasm to keep collaborating. We have at work now on many other problems since then, and I am always now more ready to see that there will be good things coming up."
The cooperation with Prof. You and Prof. Zhou made Prof. Avila deeply aware of Nankai University's great strength in the field of mathematics. He said that currently, their research results are delightful, and their cooperation has made significant progress. The theories he previously proposed has been applied and extended under the international cooperation with the two professors, injecting new vitality into the development of mathematics.
Prof. Avila's impression of Nankai University gradually deepened from his in-depth cooperation and exchanges with Prof. You and Prof. Zhou. Looking ahead, Prof. Avila, who has become a guest professor of Nankai University, looks forward to more cooperation and exchanges with mathematicians at Nankai University to jointly promote the development of mathematics.
Fully impressed by the enthusiasm of Nankai students for mathematics
During his visit to Nankai, Prof. Avila not only had in-depth academic discussions with his "old friends", but also had extensive exchanges with the faculty members and students of Nankai University. He felt the love and pursuit of mathematics among people here, and also saw the unlimited potential and broad prospects of Nankai University in the field of mathematics.
This was Avila's first visit to China. As he stepped into Nankai University, the feeling of being a "newcomer" soon disappeared and he's very much impressed by the students' enthusiasm for mathematics. "We had this meeting on Sunday. And I found it very positive seeing the enthusiasm of the students... and they made very relevant questions. They are already thinking about how the future will go."
On March 31, at the "Dialogue with Fields Medal Winner" event held by Chern Institute of Mathematics, Prof. Avila shared his experience and understanding of mathematics research with the students on how to learn mathematics better through communication and cooperation.
The atmosphere at the event was warm and the interaction between the professor and students was relaxed and pleasant. From mathematical theories to research methods, from academic confusion to career planning, various problems were discussed. Prof. Avila listened patiently, answered every student's questions carefully, and took photos with the students one by one.
When talking about his feelings about communicating with students, Prof. Avila said, "I tried to answer and be helpful to the best of my abilities... I hope I could give appropriate answers to them. Anyway it was a very interesting experience for me, and I hope it was for them as well."
"Sometimes in a mathematical work, it can be very complex, and people can get lost. Sometimes it can be scary and can be even a little bit demotivating", said Prof. Avila. He emphasized the need to lay a solid foundation in mathematics teaching. "I try to teach my students now, at the university as a professor, in a way that try to give focus more on the ideas and the creative parts of the work, so that they can understand what is the fundamental discovery that enables the solution of a problem or getting development of a theory... The things that you lead them to be more enthusiastic, and eventually it would be more important in doing research, is really being able to locate where is the creative part happening."
Prof. Avila has high hopes for young people who are committed to learning and research in mathematics, and encourages them to be brave enough to ask questions and dare to challenge. "You need to make mistakes, and it's okay to make mistakes when you are trying to find something new."
The close communication with Prof. Avila has made many students more determined in their pursuit and dedication in the field of mathematics.
Duxiao Wang, a student in the 2020 Mathematics Boling Class, has always been curious about Prof. Avila's research. When he finally had the opportunity to communicate face-to-face with his "idol", he was extremely excited. "I once read a paper he published. I had a few doubts about it, so I asked a question that had long puzzled me. Regarding my questions, Prof. Avila clarified the key links in a few words, and then gave a concise explanation of my questions about the details of the proof, which helped me understand at once."
Yiyang Sun, a 2022 undergraduate student from the School of Mathematical Sciences, felt the new charm of the field of mathematics from this exchange with Prof. Avila. She said that she was deeply touched by the unknown and novelty of fields such as dynamical systems introduced by Prof. Avila, and also the charm of interdisciplinary research. "I very much hope to have further exchanges with Prof. Avila in the future and gain more inspiration and new insights from him."
(Resource: NKU News)
