The Canadian Mathematical Society (CMS) is pleased to announce Daniel Litt as the recipient of the 2025 Cathleen Synge Morawetz Prize. This year’s prize recognizes contributions in algebra, number theory, and algebraic geometry.
Litt obtained his BA in Mathematics at Harvard University, before completing his Ph.D. in Mathematics at Stanford University. His first position was at Columbia University, where he was an NSF Postdoctoral Fellow. He then became a Member at the Institute for Advanced Study, and later an Assistant Professor at the University of Georgia. Litt is currently an Assistant Professor at the University of Toronto. Over the past 15 years, Litt has published nearly 30 articles, participated in various outreach activities, and delivered close to 150 invited talks.
Litt is receiving the 2025 Cathleen Synge Morawetz Prize for his recent series of three papers (joint with Landesman and Lam-Landesman) on the geometry and dynamics of local systems on Riemann surfaces:
Landesman, Aaron, and Daniel Litt. “Geometric local systems on very general curves and isomonodromy.” Journal of the American Mathematical Society 37.3 (2024): 683-729.
Landesman, Aaron, and Daniel Litt. “Canonical representations of surface groups.” Annals of Mathematics 199.2 (2024): 823-897.
Lam, Yeuk Hay Joshua, Aaron Landesma, and Daniel Litt. “Finite braid group orbits on SL2– character varieties.” arXiv preprint at arXiv:2308.01376 (2023).
This series of research papers explores deep mathematical structures related to differential equations, geometry, and symmetries. The authors use advanced techniques from algebra, geometry, and number theory to answer long-standing questions in these areas.
At the heart of Litt and his collaborators’ work is the study of “local systems,” which are mathematical objects that capture how solutions to differential equations behave when extended over different shapes (such as curved surfaces). A key question in algebraic geometry is understanding which of these local systems come from actual geometric structures, a question with broad implications for mathematics.
A breakthrough in this research was the discovery that certain expected patterns in these systems do not hold in general. Instead, Litt and his collaborators showed that for large and complex surfaces, the possible geometric structures are far more restricted than previously thought.
Another key part of Litt’s work involves the study of “isomonodromy”, a property that describes how solutions to differential equations change when the underlying space deforms. Litt and his collaborators connected this classical concept with modern mathematical theories, leading to new understanding of these systems.
Their findings also provide strong evidence for solving major open problems in geometry and mathematical physics. In particular, they classified all algebraic solutions to an important type of differential equation known as the rank 2 Schlesinger system, which governs how certain mathematical transformations evolve over time.
One nominator highlighted the significance of Litt’s work:
I think that Litt and his collaborators have really moved the field by demonstrating that you can make progress on old problems whose statement is purely topological (or even purely within the theory of discrete groups!) by bringing in real technique from Hodge theory. New theorems can be influential, but new ideas for what kinds of techniques can be applied to what kind of problems are even more influential, and I place Litt’s recent work in that latter category.
In summary, Litt’s research sheds new light on fundamental mathematical questions, whilst linking different areas of mathematics in unconventional ways and advancing our understanding of the interplay between geometry, algebra, and dynamics. The CMS is proud to award Daniel Litt with the 2025 Cathleen Synge Morawetz Prize.
About the Cathleen Synge Morawetz Prize
The Cathleen Synge Morawetz Prize was established in 2020 in honour of Cathleen Synge Morawetz (1923-2017), to reflect the remarkable breadth and influence of her research achievements in pure and applied mathematics. First awarded in 2021, this prize recognizes an author (or authors) of an outstanding research publication.
For more information, visit the Cathleen Synge Morawetz Prize page.