School of MathematicsSchool of Mathematicshttps://hdl.handle.net/20.500.12111/142022-09-27T14:25:45Z2022-09-27T14:25:45ZHodge theory: What is it? How can it be used in algebraic geometry?Griffiths, Philliphttps://hdl.handle.net/20.500.12111/80312022-08-04T20:00:14ZHodge theory: What is it? How can it be used in algebraic geometry?
Griffiths, Phillip
Lecture Slides
Extended Period MappingsGriffiths, Philliphttps://hdl.handle.net/20.500.12111/80302022-08-04T20:00:14ZExtended Period Mappings
Griffiths, Phillip
Clay Lecture at the INI, June 2022. The lecture is based on joint work with Mark Green and Colleen Robles. Theme of the lecture is global properties of period mappings with applications to the geometry of completions of moduli spaces.
Limits in Hodge TheoryGriffiths, Philliphttps://hdl.handle.net/20.500.12111/79802022-03-23T14:49:58ZLimits in Hodge Theory
Griffiths, Phillip
Almost all of the deep results in Hodge theory and its applications to algebraic geometry require understanding the limits in a family of Hodge structures. In the literature the proofs of these results frequently use the consequences of the analysis of the singularities acquired in a degenerating family of Hodge structures; that analysis itself is treated as a "black box." In these lectures an attempt will be made to give an informal introduction to the subject of limits of Hodge structures and to explain some of the essential ideas of the proofs. One additional topic not yet in the literature that we will discuss is the geometric interpretation of the extension data in limiting mixed Hodge structures and its use in moduli questions.
Lecture series at the University of Miami in Spring 2022.
Extended Period MappingsGriffiths, Philliphttps://hdl.handle.net/20.500.12111/79792022-03-23T14:50:35ZExtended Period Mappings
Griffiths, Phillip
This lecture will discuss the global structure of period mappings (variation of Hodge structure) defined over complete, 2-dimensional algebraic varieties. Some applications to moduli of general type algebraic surfaces will also be presented.
Clay Lecture at INI in June 2022. Based on joint work with Mark Green and Colleen Robles.