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Refined unramified cohomology

HARVARD-MIT ALGEBRAIC GEOMETRY

May 4, 2021      3:00 pm
Speaker: Stefan Schreieder - University of Hannover

We introduce refined unramified cohomology and prove some general comparison theorems to cycle groups. Our approach has several applications. For instance, it allows to construct the first example of a...
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Properness of the K-moduli space

HARVARD-MIT ALGEBRAIC GEOMETRY

April 27, 2021      3:00 pm
Speaker: Ziquan Zhuang - MIT

K-stability is an algebraic condition that characterizes the existence of K\"ahler-Einstein metrics on Fano varieties. Recently there has been a lot of work on the construction of the K-moduli space,...
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Hodge filtration on local cohomology and applications

HARVARD-MIT ALGEBRAIC GEOMETRY

March 30, 2021      3:00 pm
Speaker: Mihnea Popa - Harvard University

This describes joint work in progress with M. Mustata, in which we study the filtration on local cohomology sheaves induced by their natural mixed Hodge module structure. Special properties of...
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Lie algebras, deformations, and Galois theory in characteristic p.

HARVARD-MIT ALGEBRAIC GEOMETRY

March 16, 2021      4:30 pm
Speaker: Lukas Brantner

We introduce a derived version of Lie algebras in characteric p and describe two recent applications: first, we use them to classify infinitesimal deformations, generalising the Lurie-Pridham theorem in characteristic...
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On extension of pluricanonical forms for Kaehler families

HARVARD-MIT ALGEBRAIC GEOMETRY

March 9, 2021      3:00 pm
Speaker: Mihai Paun - University of Bayreuth

We will report on a recent joint work with Junyan Cao, cf. arXiv:2012.05063. The main topics we will discuss are revolving around the extension of pluricanonical forms defined on the...
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Decomposition theorem for semisimple local systems

HARVARD-MIT ALGEBRAIC GEOMETRY

March 2, 2021      3:00 pm
Speaker: Ruijie Yang - Stony Brook University

In complex algebraic geometry, the decomposition theorem asserts that semisimple geometric objects remain semisimple after taking direct images under proper algebraic maps. This was conjectured by Kashiwara and is proved...
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On the proportion of transverse-free curves

HARVARD-MIT ALGEBRAIC GEOMETRY

February 16, 2021      3:00 pm
Speaker: Shamil Asgarli

Given a smooth plane curve C defined over an arbitrary field k, we say that C is transverse-free if it has no transverse lines defined over k. If k is...
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