The Algebraic Geometry Pre-Seminar takes place on Wednesdays 1:45–2:15PM in SC108. Graduate students are particularly encouraged to attend. Note that when there is no external speaker, we may schedule pre-print seminar at 1:30-3:30 in the same location.
Fall 2024
September 25: Haohua Deng (Duke)
Location: SC 108
Title: Hodge-theoretic versus geometric degenerations
Abstract: In this talk I will show by examples how Hodge-theoretic methods can be useful on studying degeneration of algebraic varieties. Necessary knowledges in Hodge theory will be reviewed.
October 2: Joe Waldron (Michigan State University)
Location: SC 108
Title: Introduction to the minimal model program
Abstract: This talk will provide an overview of the modern approach to the classification of higher dimensional varieties through Mori theory.
October 9: Sai-Kee Yeung (Purdue)
Location: SC 108
Title: Weil-Petersson geometry and moduli spaces of algebraic curves
Abstract: I will give a rudimentary introduction to moduli spaces of Riemann surfaces of fixed genus from Weil-Petersson perspective.
October 23: Lena Ji (University of Illinois Urbana-Champaign)
Location: SC 108
Title: Rationality of algebraic varieties
Abstract: An algebraic variety is said to be rational if it is birational to projective space, i.e., if it has a dense open subset admitting a 1-to-1 parametrization by an open subset of projective space. In this talk, we will see several examples of rational and non-rational varieties.
October 30: Benson Farb (University of Chicago)
Location: SC 108
Title: What is a rational variety?
Abstract: This pre-talk will be aimed at beginning graduate students. In this pre-talk I will explain what it means for a variety to be rational (a concept going back to Pythagoras). I will explain some beautiful classical constructions in algebraic geometry related to rationality.
Dec 4: Donu Arapura (Purdue)
Location: SC 108
Title: Introduction to mixed Hodge structures
Abstract: To motivate the story I will recall the equivalence between the category of complex abelian varieties and a certain category of linear algebra objects called pure Hodge structures (of a certain type). As the name suggests, these structures arise from the Hodge theorem. To extend this correspondence to semi-abelian varieties, we will be led naturally to mixed Hodge structures. Once we have the definition, I can state Deligne's generalization of the Hodge theorem for arbitrary complex algebraic varieties.