Research
Our expertise covers a broad spectrum of topics, including algebraic geometry, algebraic topology and homotopy theory, differential geometry and geometric analysis, history of mathematics, logic and proof formalisation, and number theory.
Research directions
Algebraic Geometry
Our research interests include algebraic number theory and arithmetic geometry, Diophantine geometry and arithmetic applications of birational geometry, enumerative geometry and moduli spaces of varieties and sheaves, modular forms, rational points over global fields, and toric varieties.
Algebraic Topology
Our research interests include algebraic K-theory, chromatic and telescopic homotopy theory, derived algebraic geometry, equivariant homotopy theory, functor calculus, higher category theory, homotopy type theory, ∞-operads and dendroidal sets, moduli of elliptic curves, spectral Lie algebras, topological modular forms, and unstable homotopy theory.
Differential Geometry
Our research interests include foliation theory, generalised geometry, geometry of PDEs, h-principle, Lie theory, Poisson geometry, and symplectic geometry and topology.
History of Mathematics
The Mathematical Institute in Utrecht has a long tradition of research in the history of mathematics that has operated continuously since the work of Henk Bos (1940-2024). We have broad interests in the history of mathematics from antiquity to the 19th century.
Mathematical Logic
Our research interests include category theory, topos theory, theory of (higher-type) computation, type theory, proof formalisation, and proof theory.
Number Theory
Our research interests include algebraic curves, algebraic and arithmetic dynamics, algorithmic number theory, analytic number theory, applications of number theory to spectral geometry, arithmetic geometry, arithmetic of linear differential equations, arithmetic statistics, Diophantine problems, geometry of numbers, hypergeometric functions, number theory in function fields of positive characteristic, undecidability and o-minimality.
The Utrecht Geometry Centre hosts an annual visiting professorship, named after T.A. Springer (1926 – 2011), who served as professor of mathematics at Utrecht University from 1959 to 1991. Professor Springer is well-known for his work in algebraic groups, Hecke algebras and complex reflection groups.