Berlin Mathematical School
Maria Donten-Bury defended her PhD thesis "Constructing algebraic varieties via finite group actions", supervised by Prof. Jarosław Wiśniewski, at the University of Warsaw in October 2013. Earlier she obtained MSc degrees in Mathematics (2008) and in Computer Science (2010), also at the University of Warsaw.
Research area: Algebraic Geometry. Research interests include Cox rings of algebraic varieties, hyperkaehler manifolds, resolutions of singularities, toric geometry, and also algebraic and geometric problems inspired by biology and statistics.
Maria Donten-Bury's current research project "Cox rings of resolutions of quotient singularities" concerns describing algebraic structures related to the birational geometry of algebraic varieties - the Cox rings - and applying them to constructing new resolutions of quotient singularities.
The main idea is that for certain classes of quotient singularities and their resolutions the structure of the Cox ring can be understood without having precise information o the geometry of the resolution.
Then the resolution can be reconstructed from the Cox ring by considering suitable torus actions and their quotients. This may lead to finding new resolutions of singularities, and also, by constructions involving smoothing quotients of compact spaces, to new examples of interesting classes of compact projective manifolds, e.g.
Phylogenetic invariants for Z_3 scheme-theoretically, preprint:
Cox rings of minimal resolutions of surface quotient singularities, to appear in Glasgow Mathematical Journal
Phylogenetic invariants of group based models (with Mateusz Michałek), Journal of Algebraic Statistics 3:44-63; 2012.
Cones of divisors of blow-ups of projective spaces (with Salvatore Cacciola, Olivia Dumitrescu, Alessio Lo Giudice and Jinhyung Park), Matematiche (Catania) 66:153-187; 2011.
On Kummer 3-folds, Revista Matematica Complutense 24:465-492; 2011
Isotropic models of evolution with symmetries (with Weronika Buczyńska and Jarosław A. Wiśniewski), Proceedings of the conference Interactions of Classical and Numerical Algebraic Geometry, Contemporary Mathematics 496:111-132; 2009.