Hometown: College Station, Texas
Current Position: Distinguished Professor of Mathematics, Texas A&M University (TAMU)
Professional Interests: Mathematics, Computer Science
Why did you decide to join the Shevchenko Scientific Society?
As I am a member of the Ukrainian branch of the Shevchenko Scientific Society, I found it natural to join NTShA after my move to the USA. I am proud to be a member of NTShA and try to serve the Society in the best possible way. When I became a member, I convinced several colleagues at TAMU to join the Society. Among them were Volodymyr Nekrashevych, Sergiy Butenko, Mariya Vorobets, and Yaroslav Vorobets.
In fact, the first US Ambassador to Ukraine Roman Popadiuk (1992-1993) influenced my decision to become a member. When I moved to the United States in 2002, accepting the position of Full Professor at Texas A&M University (by the way, the President of the University at that time was Robert Gates, former director of the Central Intelligence Agency), I was glad to hear that Amb. Roman Popadiuk was the Executive Director of the George H. W. Bush Presidential Library Foundation at TAMU. At that time, the Ukrainian Diaspora at TAMU was quite big and full of initiative, and Amb. Popadiuk took an active part in the Ukrainian events in our town.
When I came up with the idea to start a new competition “The best young mathematician in Ukraine” with the goal to support young talented mathematicians and stimulate academic research in Ukraine, Amb. Popadiuk suggested a way to find sponsors. With the active support of Roman Andrushkiw, chair of the Mathematics and Science section of NTShA, NTShA and the U.S.-Ukraine Foundation agreed to sponsor the competition. Now we regularly hold the competition. Among the competition’s winners is Olena Karlova who currently works in the Department of Mathematical Analysis at the Yuriy Fedkovych Chernivtsi National University. She is not only excellent mathematician but also a superb administrator of math summer camps for students in the Carpathian mountains. Chernivtsi is my favorite city in Ukraine, since I finished high school there, and my parents whom I visit every year continue to live there.
What do you value about membership in the Society?
The Society does important work in support of Ukrainian culture and science, making it more accessible for the general public in the USA, including Ukrainian diaspora. The Society afforded me an opportunity to get in touch with Professor Wolodymyr V. Petryshyn, a highly regarded professor of mathematics at Rutgers University. I also had a chance to meet Vasyl Lopukh, the Administrative Director of NTShA who, in my opinion, is doing excellent work for the Society. We realized that we are “zeml`iaky”: he is from a small picturesque town of Zalishchyky in Ternopil oblast, where I lived from the age of 2 to 6. My father Ivan F. Hrygorchuk worked as a teacher of mathematics and physics in a local school, and my mother Kateryna Murmylyuk was a doctor in hospital. Vasyl Lopukh and I discussed the idea of creating a photo album, documenting the history of the school, its teachers and alumni.
How did your interest in Ukrainian culture and society influence your career path?
I am a mathematician, and mathematics is international in its scope. But I was born in Vyshnivets (Ternopil oblast), a famous town not only in Ukrainian, but also in European history, and I was raised by my parents in the spirit of Ukrainian traditions. Though I lived only the first 17 years of my life in Ukraine, I keep in me the Ukrainian spirit as much as I can. I think in the Ukrainian language, I love Ukrainian culture and history, and I am proud to be Ukrainian. I cannot claim that this helped me in my career path. But it sustains me emotionally and ethically so it has some bearing on my research too.
What is your current research project?
It is almost impossible to explain to non-mathematicians what kind of research the mathematician is doing. In general, my research covers topics in algebra, dynamical systems, probability, geometry, topology, and computer science.
Specifically, I deal with such topics as “How can a group grow?”, spectral theory of groups and graphs, and in particular the question “Can one hear the shape of a group?” (which is a mimic of the famous question raised by Mark Kac “Can one hear the shape of a drum?”), applications of groups to fractals, chaos and renormalization, theory of finite automata and ergodic theory. Among groups invented by me is a famous group of intermediate growth that bears my name, the Basilica group, the Hanoi Tower group. My studies gave a better understanding of the phenomenon known as Banach-Tarski Paradox: the unit ball can be split in finitely many pieces uses which one can assemble a two identical disjoint copies (without holes inside) of the original ball. This is related to the work of John von Neumann. My students, colleagues, followers and I did and continue to do a lot of research around these and other fascinating topics.
What career advice would you give for new members of the Shevchenko Scientific Society?
Be active members, propose new ideas and try to implement them, do not forget to pay the membership fee.