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.
September 2: Laurentiu Maxim (University of Wisconsin, Madison)
Location: STON 215
Title: The classical Hodge-index theorem and its generalizations
Abstract: I will introduce the signature and Hirzebruch genus for compact complex manifolds and explain the Hodge-index theorem in this context. I will then hint to possible generalizations (to be discussed in the seminar talk).
September 9: Hyunsuk Kim (Imperial College London)
Location: Zoom (https://purdue-edu.zoom.us/j/99467898661?pwd=FOMrspNCAywfyh5VFOKDS80aWZLZuX.1)
Title: Stanley's g-theorem
Abstract: For a simplicial polytope P, let f_i be the number of i-dimensional faces of P. What possible configuration of numbers can f_i be? For example, the famous Euler characteristic says that the alternating sum of these numbers should be 0 or 2. It turns out that there are many more relations of this sort. We will study Stanley's (and Billera–Lee's) g-theorem which completely characterizes the possible configurations of f_i's.
September 16: Daniil Serebrennikov (Johns Hopkins University)
Location: STON 215
Title: Kodaira dimension of algebraic varieties
Abstract: In this pretalk, I will introduce the Kodaira dimension, a fundamental birational invariant that helps extend the classification of smooth projective curves to higher dimensions. Even for surfaces, there are many distinct birational classes with the same Kodaira dimension. If time permits, I will briefly discuss why K3 surfaces are the most intriguing objects in the Enriques–Kodaira classification.
September 30 (Rescheduled for March 3, 2027): Nao Moriyama (Kyoto University)
Location: STON 215
Title: How to simplify a surface: An introduction to the Minimal Model Program
Abstract: From the early days of algebraic geometry, it has been understood that birationally equivalent varieties share many properties. It is therefore natural to look for a "simplest" representative within each birational equivalence class. The Minimal Model Program (MMP) aims to achieve this by simplifying a given variety into a nicely structured model. In this talk, we introduce the basic ideas of the MMP for surfaces.
October 21: Ze Yun (Stony Brook University)
Location: STON 215
Title:
Abstract: