Carlo Scarpa - Oct 2020 pic

Carlo Scarpa's Home Page

Welcome! I am a postdoc at SISSA, working with the Geometry groups at SISSA and IGAP.

I wrote my PhD thesis under the supervision of professor Jacopo Stoppa.

My research focus is on Kähler geometry, particularly on the existence of Kähler metrics with special curvature properties, such as (in increasing generality) Kähler-Einstein metrics, cscK metrics or extremal Kähler metrics. For an introduction to these topics I recommend this book by Gábor Székelyhidi and two papers by Richard Thomas and Julius Ross and Ruadhaí Dervan.

My thesis studies a slight deformation of the cscK equation that we call the Hitchin-cscK (HcscK, for short) system. Essentially this system of equations can be interpreted as adding a Higgs term to the usual cscK equations. You can find an updated version here: HcscK.pdf

Preprints: arXiv

Some notes:

Brief CV

Recreational mathematics

Can you put 8 queens on a standard 8 by 8 chessboard in such a way that any two queens are not attacking each other? This is the classic "8 queens problem". It can be generalized to n queens on a p by q chessboard.

Here we propose a different question: can you put on a 8 by 8 chessboard two teams of 8 queens in such a way that any two queens from the same team do not attack each other? What about three simultaneously placed teams? The question was proposed initially by Boris Stupovski.

Thanks to Daan Van De Weem for proving that there are no solutions with 8 simultaneous teams. The current conjecture is that there are no solutions with 7 simultaneous teams, while we know some 6-teams solutions:

We think that these five 6-teams solutions actually describe all possible patterns of empty squares in a 6-teams solution; this would imply that there are no 7-teams solutions.