Roland Púček

      I am a research fellow in the Algebra group led by Prof. Hendrik Süß at the Mathematical Institute of the University of Jena.
      Since 2023, I am a member of two working groups, Cartan Geometry and Representation Theory, and Integrable Systems and Supersymmetry, in the COST Action CaLISTA.
      I did my PhD under the the supervision of Prof. David M. J. Calderbank at the University of Bath, and defended my thesis, titled Extremal Kähler metrics and separable toric geometries, in February 2022.

Currently, I work on three projects.

• Toric separable geometries and extremal Käler metrics, where I systematically describe a construction of explicit toric Sasaki/Kähler geometries and study their extremal metrics. This approach unifies and recovers all known explicit extremal toric Kähler metrics, and provides new ones. The key notion in this construction is that of factorization structures, which led to
• Geometry of compatible polytopes, where Marie-Charlotte Brandenburg and I explicitly compute their Ehrhart polynomials, volumes, f-vectors and more. This class of polytopes vastly generalises cyclic polytopes and features a generalised Gale’s criterium.
• Hyperbolic integral formulae for solutions of constant coefficient 2nd order PDEs in even dimensions, where Miloslav Torda and I use differntial-geometric point of view on residue theory to obtain the formulae, and thus extend Green, Kirchhoff and Riesz’s formulae for Laplace and wave equations.

In summer semester 2023, I teach a course on toric varieties and supervise a student project on stacks and gerbes.