The Algebraic Geometry Pre-Seminar takes place on Wednesdays 3:00–3:25PM in STON 215. Graduate students are particularly encouraged to attend. Note that when there is no external speaker, we may schedule pre-print seminar at 3:00–4:30PM in the same location.
March 11: Marta Benozzo (Université Paris-Saclay)
Location: STON 215
Title: An introduction to F-singularities and F-splittings
Abstract: Even when trying to classify smooth varieties, it is natural to stumble upon singular ones. But what are “good” notions of singularities? In birational geometry there has been a lot of progress in the classification of varieties not only over the complex numbers, but also over fields of positive characteristics. This has been possible partly thanks to the introduction of new notions of singularities related to Frobenius splittings. In this talk, we will see their definition and some examples revolving around elliptic curves.
January 14: Alice Lin (Harvard)
Location: STONE 215
Title: What is the Mumford--Tate conjecture?
Abstract: In some sense, the Mumford--Tate conjecture relates the data of the singular cohomology and the etale cohomology of a smooth projective variety defined over a number field. I will explain this in more detail, and then discuss what is currently known about this conjecture as well as some variants of it.
January 21: Yujie Luo (National University of Singapore)
Location: Zoom (https://purdue-edu.zoom.us/j/99467898661?pwd=FOMrspNCAywfyh5VFOKDS80aWZLZuX.1)
Title: The dynamical Manin-Mumford conjecture
Abstract: We give a brief introduction to the dynamical Manin-Mumford conjecture.
February 4: Alexander Polishchuk (University of Oregon)
Location: Zoom (https://purdue-edu.zoom.us/j/99467898661?pwd=FOMrspNCAywfyh5VFOKDS80aWZLZuX.1)
Title: An analog of the Weierstrass form for higher genus
Abstract: I will explain a canonical way to present a curve of genus g with g marked by equations.
February 18: Ying Wang (University of Michigan)
Location: STON 215
Title: Berkovich Spaces
Abstract: Berkovich spaces were introduced in the 1990s to study analytic geometry over non-Archimedean fields. We will explain what they are, with a focus on concrete examples.
March 11: Marta Benozzo (Université Paris-Saclay)
Location: STON 215
Title: An introduction to F-singularities and F-splittings
Abstract: Even when trying to classify smooth varieties, it is natural to stumble upon singular ones. But what are “good” notions of singularities? In birational geometry there has been a lot of progress in the classification of varieties not only over the complex numbers, but also over fields of positive characteristics. This has been possible partly thanks to the introduction of new notions of singularities related to Frobenius splittings. In this talk, we will see their definition and some examples revolving around elliptic curves.