Art Waeterschoot

Beware that the documents below likely contain mistakes -- so use with great care! Feel free to contact me with feedback, comments or questions.

expository notes and slides:

slides for an expository talk on Berkovich curves, skeleta and weight functions for YRANT 2021
notes on Kähler norms and notes on Temkin's metrization of differential forms. For a study group (spring 2022) on this paper.
notes on Néron models (my master thesis, 2019)

slides on introduction to the minimal model program (2023) for a study group on dual complexes of singularities
slides for a talk on Mazur's bounded torsion theorem for this study group (2020), following this course

Some more material from past study groups:

logarithmic geometry, hodge theory and degenerations (spring 2023)

We'll study logarithmic structures from scratch as well as two applications where they are used as a tool. One is steenbrink's algebraic construction of the limit mixed hodge structure, the second is log regular degenerations, see here for the outline and schedule.

april 11th (Nick): Introduction

april 18th (Art): log structures (notes)

apr 26th (Michael): log schemes (notes)

may 2nd (Ismaele): log smoothness (notes)

may 9th (Sasha): log analytic spaces

may 16th (Javier): hodge structures

may 23th (Irma): mixed hodge structures

may 30th (Art): limit MHS (notes)

June 6th (Nick): log regularity

June 13th (Art): log regular degenerations I

June 20th (Michael): log regular degenerations II

resolution of singularities (autumn 2021)

After studying some classical results we will work towards reading the following paper of Abramovich-Temkin-Wlodarczyk. A more detailed schedule with description of the contents can be found here.

oct 13th (Art): overview (slides)

oct 20th (Mathias): blowups and curves

oct 27th (Michael): surfaces and Jung's method (notes)

nov 3rd (Naud): resolution of toric varieties (notes)

nov 10th (Nick): local uniformisation of valuations (notes)

nov 17th (Floris): principalisation and maximal contact

nov 24th (Art): coefficient ideals and local invariant

dec 1st (Tim) : intro to stacks (notes)

dec 8th (Nick): weighted blowups and toric stacks (notes)

dec 15th (Tim): admissibility of centers (notes)

dec 22nd (Art): dream algorithm

unlikely intersections (autumn 2022): Following van den Dries and Masser-Zannier: website here