Yanir Rubinstein (University of Maryland, USA) will speak in the geometry seminar on Monday 25 February, at 1.30pm in the Salle de Profs. Yanir’s title is *Differential, algebraic, and convex geometry arising from asymptotic positivity* and his abstract is below.

A general theme in geometry is the classification of algebraic/differential geometric structures which satisfy a positivity property. I will describe an “asymptotic” version of this theme based on joint work with Cheltsov, Martinez-Garcia, and Zhang. On the algebraic side, we introduce the class of asymptotically log Fano varieties and state a classification theorem in dimension 2, generalizing the classical efforts of the 19th century Italian school. The novelty here is the use of a convex optimization theorem that reduce the asymptotic positivity to determining intersection properties of high-dimensional convex bodies. On the differential side, I will give a conjectural picture for existence of singular Kahler-Einstein metrics and explain progress towards this conjecture making use of symmetry, log canonical thresholds, test configurations, and Fujita-Odaka’s basis type invariant. Time permitting, I will also touch on relations to singular Kahler-Ricci solitons, mention some conjectures and results about the `small angle limit’ when the angle tends to zero, and tie this picture to non-compact Calabi-Yau fibrations, steady Ricci solitons, and recent work of Liu on wall-crossings in moduli space.