It has been a cold winter in Ukraine, and a hard number of years since the full-scale invasion by Russia began in 2022. But life, and learning, go on. This January, some forty students and scientists gathered in Kyiv, united by their shared passion for mathematics.
“It was a really warming experience in such a cold winter,” one student expressed. “I learned a lot of interesting concepts, discovered career opportunities, and made a bunch of friends.”
The school, which ran from January 5 to 23, 2026, came about at the instigation of Mykola Semenyakin, a Perimeter Institute postdoctoral researcher, and Masha Vlasenko, Executive Director of the International Centre for Mathematics in Ukraine (ICMU).
Semenyakin, together with Lukas Mueller and Alex Turzillo – both Perimeter postdocs, though Turzillo has now moved to Cambridge University – proposed the three-week school to teach students about the mathematical foundations that underpin the study of quantum matter.
Quantum matter is a complex but exciting field, where experts try to understand the behaviours that emerge when many particles in highly entangled states interact. Mathematical tools like topological field theory and category theory can help scientists make sense of these complex systems.
“One of our main motivations for organizing this school was to connect students who have been relatively isolated from the international research community over the past few years with leading experts in an exciting and active area of research,” Mueller said.
Semenyakin, who is Ukrainian himself, explained that during his university years, the opportunity to learn from international researchers was a pivotal component of his higher education.
“During the war, it's way harder now to come to Ukraine and teach, so this component has been lost to students for several years, and I think them having this chance now is very important for their development as physicists,” he said.
The participants at the school had strong backgrounds in fundamental math and physics, but they’d had few previous opportunities to engage with the global research world. Given the chance, they engaged actively and enthusiastically. Many participants said they found the school rewarding both in the classroom and beyond.
Karolina Susol, a participant from Taras Shevchenko National University of Kyiv, explained: “As a mathematician, it was fascinating to see diverse areas of mathematics appearing in quantum physics. Although our days were very busy, the free time…provided a good balance. In particular, we visited an ice rink and a museum! It felt almost unbelievable that we were able to study, socialize, and enjoy some leisure activities during such difficult times in Kyiv.”
The organizers credit the students themselves for making it such a success, thanks to their enthusiastic commitment.
Vincentas Mulevicius, a researcher at the University of Vienna, travelled to Kyiv to teach participants about topological quantum field theory.
“We had these very intense practical sessions, and it was just an enormous joy just to go around talking with students, seeing what they find interesting. They would always have questions, and we would sometimes invent new tasks for students on the spot,” Mulevicius said.
Of course, there were challenges. The security situation in Kyiv continues to affect daily life. Some of the lectures had to be held in shelters, and some students found sleep was hard to come by due to unheated homes.
“There are ways to continue to teach, despite the circumstances. And the students are just intensely dedicated to showing up every morning and learning,” said Turzillo, who managed all on-site activities during the school.
With the winter school behind them, the organizers see the event as a hopeful beginning. There is more to come. The participants are staying connected via a Discord channel and online journal club that builds on what was learned in the school to explore research topics.
"The students, who come from a range of backgrounds across math and physics, have lots to learn from each other, and our hope is that they stay in touch throughout their careers,” said Turzillo.
The organizing team has also proposed sequel schools in 2026 and 2027, with one tentatively planned for the Carpathian mountains this summer, and back in Kyiv again next winter.
The team hopes to encourage more international participation wherever possible at these future events. The payoff, they say, makes it well worth doing.
“Several students said it was one of the most important opportunities they've had to interact with researchers outside of Ukraine. And we felt that implicitly from many more students. It seemed like it meant a lot.”
The ICMU winter school “Mathematics of Quantum Matter” was supported by the Kyiv School of Economics, Universiteit Leiden, Delta Institute for Theoretical Physics, Instituut Lorentz, TU Delft, and ICTP. Visit the ICMU’s website for more details.
About PI
Perimeter Institute is the world’s largest research hub devoted to theoretical physics. The independent Institute was founded in 1999 to foster breakthroughs in the fundamental understanding of our universe, from the smallest particles to the entire cosmos. Research at Perimeter is motivated by the understanding that fundamental science advances human knowledge and catalyzes innovation, and that today’s theoretical physics is tomorrow’s technology. Located in the Region of Waterloo, the not-for-profit Institute is a unique public-private endeavour, including the Governments of Ontario and Canada, that enables cutting-edge research, trains the next generation of scientific pioneers, and shares the power of physics through award-winning educational outreach and public engagement.
