Dr. Ján Mináč to receive the 2025 Jeffery-Williams Prize

Ottawa, ON – The Canadian Mathematical Society (CMS) is pleased to announce Dr. Ján Mináč (Western University) as the recipient of the 2025 CMS Jeffery-Williams Prize, recognizing his significant contributions to mathematical research, particularly in the areas of Galois theory, cohomology of groups, number theory and related topics.

Dr. Mináč earned his B.Sc. and M.Sc. in Mathematics from Commenius University (Czechoslovakia) before completing his Ph.D. in Mathematics at Queen’s University in 1986. He then spent several years in California as a researcher at the Mathematical Sciences Research Institute and an NSF Postdoctoral Fellow in the Department of Mathematics at the University of California, Berkeley. Dr. Mináč later joined Western University, where he has held various positions from Assistant Professor to Associate Professor, and Professor of Mathematics (2003-present). He received a Distinguished Research Professorship in 2004-2005 and again in 2020-2021. He is also currently a cross-appointed Professor in the Computer Science Department.

Dr. Mináč is one of the international leaders in Galois theory and related topics in algebra and number theory. He has made foundational contributions to the study of absolute Galois groups of fields, a central topic in algebra and number theory with deep connections to arithmetic and geometry. His work has particularly advanced understanding of the profinite inverse Galois problem, which seeks to determine which profinite groups can arise as absolute Galois groups or as special quotients of them. His research, especially in the pro-p case (where p is a prime), has provided necessary conditions for groups to occur as absolute Galois groups of fields and demonstrated that certain specific groups cannot occur as absolute Galois groups of fields. A notable example is his paper in Mathematische Annalen with S. Chebolu and I. Efrat, which connects this problem to Galois cohomology. Additionally, he has shown that the presence of certain groups as subgroups of small quotients of absolute Galois groups carries structural implications for the underlying field itself.

In recent years, Dr. Mináč has explored the relationship between Galois theory and Massey products, with significant publications in journals such as the Journal of the European Mathematical Society, the Journal of the London Mathematical Society, Compositio Mathematica and Advances in Mathematics. His research into Galois embedding problems and Galois module structures with N. Lemire, A. Schultz and J. Swallow has further enriched the field. Some of this work has been published in Crelle’s Journal, Proceedings of the London Mathematical Society, and the Journal of the London Mathematical Society.

His work has also played an important role in ongoing research on Grothendieck’s anabelian conjecture, which seeks to characterize fields uniquely by their absolute Galois groups in important cases. Specifically, Dr. Mináč’s 2006 paper with L. Mahé and T. L. Smith provides a detailed analysis of the additive structure of the multiplicative groups of fields, shedding light on the intricate relationship between additive and multiplicative structures. This research has enabled further progress on Grothendieck’s conjecture.

Dr. Mináč’s more recent work has continued to push the boundaries of Massey products and unipotent Galois extensions, searching for the possibility of uncovering further information embedded in the Galois group that remains hidden from the perspective of Galois cohomology groups. A reviewer has described Dr. Mináč’s results on the vanishing of 3-fold Massey products as among the most intriguing recent developments in Galois theory. These insights have prompted significant follow-up research and have lead Dr. Mináč to further contributions on higher Massey products and the Koszulity of the Galois cohomology ring, with two recent papers expected to generate substantial activity in the field.

In 2016 and 2017, Dr. Mináč and N. D. Tân formulated the n-Massey vanishing conjecture for n greater than or equal to 3, now also called the Mináč-Tân conjecture. This conjecture, if true, implies a very interesting new and powerful restriction on possible absolute Galois groups. This conjecture has attracted considerable attention, and it has already led to some spectacular results.

One of Dr. Mináč’s most recognized contributions is the development of the W-group, which bridges quadratic forms and Galois theory. This group serves as the Galois group of a particular canonical field extension and exhibits a strong connection to the Witt ring of non-degenerate quadratic forms over the field. Dr. Mináč’s work has revealed profound interactions between W-groups and Witt rings, which then inspired further research in both areas and led to significant advances. This work was initiated with two significant joint papers authored by Dr. M. Spira and Dr. Mináč published in the Annals of Mathematics (1996) and in Mathematische Zeitschrift (1990).

In a different direction, Dr. Mináč has also contributed to the study of Freyd’s generating hypothesis, which concerns cohomology in relation to group algebras and has deep ties to stable homotopy theory. After a series of earlier papers coauthored with D. Benson, J. Carlson, D. Christensen and S. K. Chebolu on this problem, he, along with J. Carlson and S. K. Chebolu, published a complete solution in the Proceedings of the AMS in 2009.

From 2020 to the present, Dr. Mináč began with Dr. Lyle Muller and his team, some new and very productive interdisciplinary research in networks, dynamical systems and applications to neuroscience. In addition to Dr. Muller, several members of Muller’s lab have been actively collaborating with Dr. Mináč. They include: A. Busch, R. Budzinski and T. T. Nguyen. In 2024, Dr. Mináč together with members of Dr. Muller’s team and their collaborators, published two significant papers in Nature Communications and in Communication Physics. He also carried out some notable simultaneous research with M. Chudnovsky, M. Čižek, L. Crew, T. T. Nguyen, S. Spirkl, N. D. Tân, and others in number theory and combinatorics.

Dr. Mináč’s outstanding research contributions have resulted in over 115 publications in prestigious academic journals.

Beyond recognizing his important contributions to research, Dr. Mináč’s nominators strongly value his passion and enthusiasm for mathematics. To quote one of them:

“Learning about his insights and understanding of the structure of absolute Galois groups is a wonderful experience, both because of the depth of his knowledge and because of the flexibility of the approaches he uses to understand a problem. Watching Professor Mináč work is a little like watching a magician; what looks like an ordinary hat will suddenly turn into something unexpected and exciting.”

Moreover, Dr. Mináč has played an important role in mentoring both undergraduate and graduate students. He has supervised close to 25 graduate students, and has inspired many undergraduate students to pursue further studies in mathematics.

Dr. Mináč’s contributions have been recognized through numerous awards and prizes. In addition to the Distinguished Research Professorships awarded in 2004-05 and 2020-21 mentioned above, Dr. Mináč was a recurring recipient of Western University’s Teaching Honour Roll Awards of Excellence from 2007 to 2018 and received the CMS Excellence in Teaching Award in 2013. In recognition of his impact on the mathematical community, he was named a Fellow of the CMS in 2019 and a Fellow of the Western Academy for Advanced Research in 2022. Additionally, his research has been consistently supported by NSERC grants since 1989.

In conclusion, Dr. Jan Mináč is a remarkably versatile mathematician whose influential research encompasses some key areas of algebra, number theory and related parts of algebraic geometry and algebraic topology. Through his contagious energy, generosity in sharing ideas, and ability to engage and inspire others, Dr. Mináč has made profound contributions to the research community and Canadian mathematics. The CMS is proud to award him the 2025 Jeffery-Williams Prize.

About the Jeffery-Williams Prize

The Jeffery-Williams Prize was inaugurated to recognize mathematicians who have made outstanding contributions to mathematical research. The first award was presented in 1968 and is named after Ralph Jeffery and Lloyd Williams, who were two influential CMS Board members.

For more information, visit the Jeffery-Williams 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. Susan Cooper (uManitoba) Chair, CMS Research Committee Canadian Mathematical Society chair-resc@cms.math.ca

or

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