Speaker: Ludvig Svensson (Chalmers University of Technology)
Time: 14:30-15:30, Mar 19, 2026
Venue: room 1329, Building 1 (Section A), New Campus of USTC Shanghai Institute for Advanced Studies
I will talk about joint work with R.\ Andreasson and R.\ J.\ Berman on the extension of the probabilisitc framework for constructing Kähler--Einstein metrics, involving random point processes, due to Berman, to the case of (log) Fano manifolds with non-discrete automorphism group.
I will begin by giving an overview of the probabilistic approach. I will discuss the case of canonically polarized manifolds which has been settled, and go on to talk about Fano manifolds with discrete automorphism group, where the unique existence of a Kähler--Einstein metric is conjecturally equivalent to the (algebraic) notion of \textit{Gibbs stability}.
In a recent paper, we introduce the notion of \textit{Gibbs polystability}, and conjecture that it is equivalent to the existence of a Kähler--Einstein metric on a general Fano manifold. Furthermore, we conjecture that the unique such metric with vanishing moment emerges in the large $N$-limit when sampling $N$ points on $X$. This moment condition is defined with respect to a moment map induced by the action of a fixed maximal compact subgroup of the autromorphism group. This and other conjectures follow from an overarching conjectural large deviation principle for the large $N$-limit.
I will discuss the one-dimensional case, where we are able to prove many of the conjectures. Lastly, if time permits, I will comment on some applications of our results for log Fano curves.
For more information, please visit: https://vtmaths.github.io/imfp-igp-seminar/index.html
