Anca Mustata

I am a lecturer in the School of Mathematical Sciences at the University College Cork, Ireland, since 2007. Before this worked at the University of Illinois, Urbana-Champaign and the University of British Columbia.

My research is in the area of algebraic geometry, with connections to topology and string theory. More precisely, I have studied algebraic and topological properties of parameter spaces of curves embedded in projective spaces.   Parameter spaces are sets whose elements share a number of common features. They have come to play a central role in Algebraic Geometry in recent years. For example, the geometry of parameter spaces of rational curves on a complex projective space is strongly related to such important properties of the space like rationality, unirationality or rational connectedness. In a distinct direction, counting rational curves, either via Gromov-Witten and Donaldson-Thomas invariant theories, was found by physicists working in string theory to describe observables in certain conformal quantum field theories.   In previous and current work, we explore the relation between the geometry of the parameter spaces of curves and that of the space where these curves live. For example, in joint work with Andrei Mustata, we have calculated the Chow and cohomology rings of a recently preeminent type of parameter spaces ¿ the moduli spaces of stable maps. These rings are algebraic structures encoding algebraic and topological invariants of the moduli spaces. We have shown a close, though intricate connection between the invariants of the moduli space of curves in a projective space and the invariants of the space itself. These cohomological data are generalising Gromov-Witten invariant calculations, a very active area of research in algebraic geometry. 

While at the University College Cork, I have taught modules in Introduction to Abstract Algebra Rings and Fields Modern Algebra Discrete Mathematics Euclidean Geometry Transformation Geometry Differential Equations Chaos and Experimentation Number Theory Introduction to Mathematical Studies In 2024 I have taught Algebraic Geometry as part of the UNIC Summer School in Mathematics