When Sophia Breslavets first heard about Yulia's Dream, the MIT Department of Mathematics' Program for Research in Mathematics, Engineering, and Science (PRIMES) for Ukrainian students, Russia had just invaded her country, and she and her family lived in a town 20 miles from the Russian border.
Breslavets had attended a school that emphasized mathematics and physics, took math classes on weekends and during summer breaks, and competed in math Olympiads. "Math was really present in our lives," she says.
But the war shifted her studies to online. "It still wasn't like a fully functioning online school," she recalls. "You can't socialize."
So she was grateful to be accepted to the MIT program in 2022. "Yulia's Dream was a great thing to happen to me personally, because in the beginning, when the war was just starting, I didn't know what to do. This was just a great thing to take your mind off of what's going on outside your window, and you can just kind of get yourself into that and know that you have some work to do, and that was huge."
Second time around
Breslavets just finished up her second year in the online enrichment program, which offers small-group math instruction in their native language and in English to Ukrainian high schoolers by mentors from around the world. Students wrap up the program by presenting their papers at a conference; several of those papers are published on arXiv.org. This year's conference featured a guest talk by Professor Pavlo Pylyavskyy of the University of Minnesota Twin Cities, who discussed "Incidences and Tilings," a joint work with Professor Sergey Fomin of the University of Michigan.
The PRIMES program first organized Yulia's Dream in 2022, named in memory of Yulia Zdanovska, a talented mathematician and computer scientist who was a teacher with Teach for Ukraine. She was 21 when she was killed in 2022 during Russian shelling in her home city of Kharkiv.
The program fulfills one of PRIMES's goals, to expose students to the world community of research mathematics by connecting them with early-career mentors. Students must solve a challenging entrance problem set and are then referred by Ukrainian math teachers and leaders at math competitions and math camps.
Yulia's Dream is coordinated by Dmytro Matvieievskyi, a postdoc at the Kavli Institute in Tokyo, who graduated from School #27 of Kharkiv, and is a recipient of the Bronze medal at the 2012 International Math Olympiad (IMO) as part of the Ukraine Team.
In its first year, from 2022 to 2023, the program drew 48 students in Phase I (reading) and 33 students in Phase II (reading and research). "Our expectation for 2022-23 was that each of six research groups would produce a research paper, and they all did, and one group continued working and produced an extra paper a few months after, for a total of seven papers. Three papers are now on arXiv.org, which is a mark of quality. This went beyond our expectations."
This past year, the program provided guided reading and research supervision to 32 students. "We conduct thorough selection and provide opportunities to all Ukrainian students capable of doing advanced reading and/or research at the requisite level," says PRIMES's director Slava Gerovitch PhD '99.
MIT pipeline
Several students participated in both years, and at least two have been accepted to MIT.
One of those students is two-time Yulia's Dream participant Nazar Korniichuk, who had attended a high school in Kyiv that specialized in mathematics and physics when his education was disrupted by the war.
"I was confused and did not know which way I should go," he recalls. "But then I saw the program Yulia's Dream, and the desire to try real mathematical research ignited."
In his first year in the program, participation was a challenge. "On the one hand, it was very difficult, because in certain periods there was no electricity and no water. There was always stress and uncertainty about tomorrow. But on the other hand, because there was a war, it motivated me to do mathematics even more, especially during periods when there was no electricity or water."
He did complete his paper, with Kostiantyn Molokanov and Severyn Khomych, and with mentor Darij Grinberg PhD '16, a professor of mathematics at Drexel University: "The Pak-Postnikov and Naruse skew hook length formulas: A new proof" (2 Oct 2023; arXiv.org, 27 Oct 2023).
Korniichuk completed his second round from his new home in Newton, Massachusetts, to which his family had migrated last summer. At the recent conference, he presented his paper, with co-authors Kostiantyn Molokanov and Severyn Khomych, "Affine root systems via Lyndon words," that they worked on with mentor Professor Oleksandr Tsymbaliuk of Purdue University.
"Yulia's Dream was a very unique experience for me," says Korniichuk, who plans to study math and computer science at MIT. "I had the opportunity to work on a difficult topic for a long time and then take part in writing an article. Although these years have been difficult, this program encouraged me to go forward."
Real research
What makes the program work is providing a university level of instruction in mathematics research, to prepare high school students for top mathematics programs. In this case, it provides Ukrainian students an alternative route to reach their educational goals.
The core philosophy of the Yulia's Dream experience is to provide "the best possible approximation to real mathematical research," math professor and PRIMES chief research advisor Pavel Etingof told attendees at the 2024 conference. Etingof was born in Ukraine.
"In particular, all projects have to be real - i.e., of interest to professional research mathematicians - and the reading groups should be a bridge towards real mathematics as well. Also, the time frame of Yulia's Dream is closer to that of real mathematical research than it is in any other high school research program: the students work on their projects for a whole year!"
Other principles include an emphasis on writing and collaboration, with students working on teams with undergraduates, graduate students, postdocs, and faculty. There is also an emphasis on computer-assisted math, which "not only allows participation of high school students as equal members of our research teams, but also allows them to grasp abstract mathematical notions more easily," says Pavel. "If such notions (such as group, ring, module, etc.) have an incarnation in the familiar digital world, they are less scary."
Breslavets says that she especially appreciates the collaboration part of the program. Now 16, Breslavets just finished her second year with Yulia's Dream, and with Andrii Smutchak presented "Double groupoids," as mentored by University of Alberta professor Harshit Yadav. She says that they began working on the paper in October, and it took about three months to write.
This year's session was easier for her to participate in, because in summer 2022, her parents found her a host family in Connecticut so that she could transfer to St. Bernard's School. Even with her new school's great curriculum, she is grateful for the Yulia's Dream program.
"Our high school program is considered to be advanced, and we have a class that's called math research, but it's definitely not the same, because [with Yulia's Dream] you're working with people who actually do that for a living," she says. "I learned a lot from both of my mentors. It's so collaborative. They can give you feedback, and they can be honest about it."
She says she misses her Ukrainian math community, which drifted apart after the Covid-19 pandemic and because of the war, but reports finding a new one with Yulia's Dream. "I actually met a lot of new people," she says.
Group collaboration is a huge goal for PRIMES director Slava Gerovitch.
"Yulia's Dream reflects the international nature of the mathematical community, with the mentors coming from different countries and working together with the students to advance knowledge for the whole of humanity. Our hope is that our students grow and mature as scholars and help rebuild the intellectual potential of Ukraine after the devastating war," says Gerovitch.
Applications for next year's program are now open. Math graduate students and postdocs are also invited to apply to be a mentor. Weekly meetings begin in October, and culminate in a June 2025 conference to present papers.
