ARITHMETIC GEOMETRY LEARNING SEMINAR

Time: Wednesday, 11:30-1:30pm

Location: MATH 731

Speakers/Abstracts:

January 24 th: Feng Hao

Title: An algebraic introduction to Gauss-Manin connection (by Katz and Oda)
Abstract:
In this presentation, I will give a purely algebraic construction of Gauss-Manin connection arising from a smooth morphism $f: X \rightarrow Y$ between two smooth schemes over $k$, which is realized as a connection differential in the first page of certain spectral sequence. Then using Cech cohomology calculation, I will show that it is exactly the one Manin originally defined, as a connecting morphism in a long exact sequence of hyper-higher direct image sheaves of a certain short exact sequence De Rham complexes of the morphism $f$.

February 7: Pavel Coupek

Title: Existence of Lefschetz pencils
Abstract:
A Lefschetz pencil for a variety X is a tool that allows one to fibre X over the projective line (after a blowup) in a way that the non-smooth fibres have a unique quadratic singularity. In the presentation, I will discuss the proof of existence of Lefschetz pencils for smooth projective varieties in characteristic 0.

February 21st: Daxin Xu

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March 7th: Joe Knight

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March 21st:

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April 4th:

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April 18th: Donu Arapura

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