Wednesday, August 5, 2020

2020-08-12 / 14:00 ~ 15:00

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In this talk, I will give a brief survey on singularities and log pairs in birational geometry. Log terminal singularities, log canonical singularities, rational singularities, and Du Bois singularities naturally appear in many areas in algebraic geometry such as birational geometry, moduli theory, and Hodge theory.

2020-08-12 / 14:30 ~ 15:30

학과 세미나/콜로퀴엄 - 대수기하학: Brauer spaces of spectral algebraic stacks

by 조창연(IBS Center for Geometry and Physics)

Grothendieck posed a question of whether the natural map from the Brauer group of a scheme to its cohomological one is an isomorphism of abelian groups. It’s not true in general, but we have some positive results from Grothendieck and Gabber (and de Jong), among many others. After a brief review of Brauer groups in algebraic geometry, I’ll talk about some recent progress in the setting of derived and spectral algebraic geometry, where we can provide an affirmative answer for quasi-compact and quasi-separated (derived/spectral) schemes, and my work which extends the previous results to spectral algebraic stacks.

2020-08-05 / 14:30 ~ 15:30

학과 세미나/콜로퀴엄 - 대수기하학: An introduction to derived/spectral algebraic geometry II

by 조창연(IBS Center for Geometry and Physics)

Derived/spectral algebraic geometry is a relatively new area which features homotopy theory in algebraic geometry. I’ll take deformation theory and intersection theory to provide some flavor of these new fields. There are no prerequisites required other than ordinary algebraic geometry, so everyone is welcome to attend. (There are two lectures; I, II. This is the second of them.)

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