Date: March 18 - 22

Time: 9:00 - 10:50

Speaker: Mingchen Xia（夏铭辰）, Sorbonne Université

Abstract: In this course, I will give an introduction to the series of works due to Darvas and me in the last few years. The goal is to provide a classification of reasonable singularities of quasi-plurisubharmonic functions on compact Kähler manifolds. The course consists of four lectures.

March 18, Monday

Lecture 1. Introduction and the toric situation

I will introduce the main results and main ideas involved in the theory. I will explain how everything works in the toric setting.

March 19, Tuesday

Lecture 2. Envelope operators and the singular Riemann—Roch type formulae

I will define the two important envelope operators and define the class of I-good singularities. We will prove various characterisations of I-good singularities, including one using Riemann—Roch type formulae.

March 20, Wednesday

No lecture today

March 21, Thursday

Lecture 3. The trace operator and restricted volumes

I will explain two general methods allowing us to make induction on the dimension while studying I-good singularities: the trace operator and the analytic Bertini theorem. As an application of the theory of trace operators, we prove a relative version of the Riemann—Roch type formulae studied in the previous lecture.

March 22, Friday

Lecture 4. Test curves and non-Archimedean applications

I will explain the theory of test curves. As an application, I will introduce the transcendental approach to non-Archimedean pluripotential theory, based on the techniques developed in the previous lectures.