Notre Dame mathematicians' foundational work helps pave the way for a 2026 Fields Medalist
The Department of Mathematics celebrates the announcement that Jacob Tsimerman of the University of Toronto has been awarded a 2026 Fields Medal. Awarded every four years by the International Mathematical Union to no more than four mathematicians under the age of 40, the Fields Medal is one of the highest honors in mathematics, and recognizes both extraordinary research accomplishments and exceptional promise for future discoveries.
Tsimerman was recognized for a series of profound advances that helped recast the notion of o-minimality from mathematical logic and model theory as a fundamental method in arithmetic and complex algebraic geometry, and for his role in the proof of many central conjectures including Griffiths' conjecture on the algebraicity of images of the period maps, and the Andre-Oort conjecture for Siegel modular varieties.
An important part of this story concerns Notre Dame, at multiple stages in its development. The notion of o-minimality was defined and its theory developed in papers of Anand Pillay and Charles Steinhorn in the 1980's (inspired partly by work of van den Dries) , with Julia Knight contributing to the foundational series; Pillay is the William J. Hank Professor of Mathematics at Notre Dame, and Knight is Professor emerita here. The story continues with Sergei Starchenko, Professor of Mathematics at Notre Dame, and his longtime collaborator Ya'acov Peterzil. The citation for Tsimerman's award notes that "The development of o-minimal theory in the holomorphic setting was initiated by Peterzil and Starchenko, who established an affine version of Chow's algebraicity theorem. With Bakker and Brunebarbe, Tsimerman extended this theory ... Combining it with the earlier work of Bakker, Klingler and Tsimerman that placed period maps in the o-minimal domain, they proved Griffiths' conjecture on the algebraicity of images of the period maps, a long-standing problem in Hodge theory."
Starchenko's and Peterzil research, building on foundations laid by Pillay and co-authors, highlight the profound influence that the logic community at Notre Dame has had and continues to have on mathematics.