Dr. Chi Hoi (Kyle) Yip to receive the 2025 CMS Blair Spearman Doctoral Prize

Ottawa, ON – The Canadian Mathematical Society (CMS) is pleased to announce that Dr. Chi Hoi (Kyle) Yip (Georgia Institute of Technology) has been awarded the 2025 CMS Blair Spearman Doctoral Prize. This prize was inaugurated to recognize outstanding performance by a doctoral student who graduated from a Canadian university.

Dr. Yip earned his Ph.D. in Mathematics from the University of British Columbia (Vancouver) in 2024, under the supervision of Dr. Greg Martin, Dr. József Solymosi, and Dr. Joshua Zahl. His thesis, titled Topics in Arithmetic Combinatorics, explored various aspects of the field. Since 2021, he has (co-)authored close to 45 publications and preprints and has delivered nearly 30 talks. His contributions have been recognized with numerous awards, scholarships, and fellowships, including two NSERC fellowships and the 2023 Graduate Research Award from UBC’s Math Department. After gaining extensive teaching experience as a Teaching Assistant for multiple courses at UBC, Dr. Yip transitioned to the Georgia Institute of Technology, where he has been a Visiting Assistant Professor since 2024.

Dr. Yip’s Ph.D. research focused on problems in arithmetic combinatorics. His work primarily tackled variations of Sárközy’s conjecture, which relates to the way numbers interact when combined through multiplication and addition in a specific mathematical setting called finite fields. A stronger form of this conjecture, known as the Paley graph conjecture, predicts a certain kind of balancing effect when these operations are applied repeatedly. While these ideas are quite abstract, they have potential applications in number theory, particularly in studying special sets of numbers known as Diophantine tuples.

One major section of Dr. Yip’s thesis explores a completely different mathematical question known as the Erdős similarity problem. This problem asks whether every infinitely long sequence of numbers has a certain universal property, i.e. whether there are always ways to find copies of it hidden within large sets of real numbers. Dr. Yip made significant progress in understanding this question by developing a new condition for universality, using advanced techniques from probability and mathematical patterns. His work also applied earlier results from number theory to show that some sequences, particularly those involving powers of algebraic numbers, do not behave universally in this sense.

The core of Dr. Yip’s research, however, is dedicated to advancing methods that help solve Sárközy’s conjecture. He built upon an approach called the Stepanov polynomial method, originally developed by mathematicians Hanson and Petridis, to understand how sums of numbers behave inside multiplicative structures in finite fields. One of his key contributions was proving that for large enough finite fields, the set of quadratic residues (a specific type of number set) does not form a restricted sumset (a technical condition that had only been partially understood before). His result significantly improved on previous work by Shkredov, which relied on a different technique called Fourier analysis.

The final and most impressive part of Dr. Yip’s thesis applied his findings to a long-standing problem in number theory related to Diophantine tuples: special collections of numbers with unique properties. Using the Stepanov method, combined with a tool called Gallagher’s larger sieve, he achieved a major breakthrough in improving existing estimates on the number of such tuples. His work refined and extended prior results by Dixit, Kim, and Murty, leading to new discoveries that continue to inspire further research in the field.

Beyond his Ph.D. thesis, Dr. Yip has also been producing new results in arithmetic geometry, extremal combinatorics, finite fields, and a broadening scope of number-theoretical topics. To quote one of his nominators:

“The one thing that impressed me the most [about] Kyle is his mathematical versatility: he is a master of so many areas, from analytic number theory to combinatorics, from algebra to arithmetic geometry.”

In summary, Dr. Yip’s thesis and other contributions represent a significant step forward in multiple areas of mathematics, blending deep theoretical insights with innovative techniques that have the potential to influence future developments in fields such as arithmetic combinatorics and number theory. The CMS is proud to award Dr. Chi Hoi (Kyle) Yip with the 2025 CMS Blair Spearman Doctoral Prize.

About the CMS Blair Spearman Doctoral Prize
The CMS Blair Spearman Doctoral Prize recognizes outstanding performance by a doctoral student. The prize is awarded to one or two recipients of a Ph.D. from a Canadian university whose overall performance in graduate school is judged to be the most outstanding. Although the dissertation will be the most important criterion (the impact of the results, the creativity of the work, the quality of exposition, etc.) it will not be the only one. Other publications, activities in support of students and other accomplishments will also be considered.

For more information, visit the CMS Blair Spearman Doctoral Prize page.

About the Canadian Mathematical Society (CMS)
The Canadian Mathematical Society (CMS) is the main national organization whose goal is to promote and advance the discovery, learning and application of mathematics. The Society’s activities cover the whole spectrum of mathematics including meetings, research publications, and the promotion of excellence in mathematics competitions that recognize outstanding student achievements. The CMS is a registered non-profit, charitable organization and depends on grants, funding, and generous donations from sponsors, benefactors and community members to be able to carry out its activities.

For more information, please contact:

Dr. Maia Fraser (University of Ottawa) Chair, Doctoral Prize Selection Committee Canadian Mathematical Society mfrase8@uottawa.ca

or

Dr. Termeh Kousha Executive Director Canadian Mathematical Society tkousha@cms.math.ca