Haoming Ning (UW)
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PDL C-38
Pre-seminar Title: What are… Du Bois singularities?
Pre-seminar Abstract: In this pre-talk, we will introduce Du Bois singularities through a series of concrete examples. Along the way, we will discuss its Hodge theoretic origins and explore its profound applications towards MMP, vanishing theorems, and moduli theory.
Pre-seminar Abstract: In this pre-talk, we will introduce Du Bois singularities through a series of concrete examples. Along the way, we will discuss its Hodge theoretic origins and explore its profound applications towards MMP, vanishing theorems, and moduli theory.
Title: Higher Du Bois and Higher Rational Pairs
Abstract: Du Bois and rational singularities are among the most important singularities studied in algebraic geometry due to their nice cohomological behavior. Recently, motivated by developments in Hodge theoretic methods, there has been substantial interest in studying their higher analogs. This talk will survey recent literature on applications of these notions towards moduli problems and Hodge theory. I will also report on recent work (joint with Brian Nugent) extending the theory of higher Du Bois and higher rational singularities to pairs, following a guiding principle of the minimal model program. We generalize numerous results to these higher pairs, including “rational implies Du Bois”, Bertini type theorems and a Kovács—Schwede type injectivity theorem.
Abstract: Du Bois and rational singularities are among the most important singularities studied in algebraic geometry due to their nice cohomological behavior. Recently, motivated by developments in Hodge theoretic methods, there has been substantial interest in studying their higher analogs. This talk will survey recent literature on applications of these notions towards moduli problems and Hodge theory. I will also report on recent work (joint with Brian Nugent) extending the theory of higher Du Bois and higher rational singularities to pairs, following a guiding principle of the minimal model program. We generalize numerous results to these higher pairs, including “rational implies Du Bois”, Bertini type theorems and a Kovács—Schwede type injectivity theorem.