HARVARD-MIT ALGEBRAIC GEOMETRY
March 30, 2021 3:00 pmThis 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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HARVARD-MIT ALGEBRAIC GEOMETRY
March 16, 2021 4:30 pmWe 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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HARVARD-MIT ALGEBRAIC GEOMETRY
March 9, 2021 3:00 pmWe 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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HARVARD-MIT ALGEBRAIC GEOMETRY
March 2, 2021 3:00 pmIn 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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HARVARD-MIT ALGEBRAIC GEOMETRY
February 23, 2021 4:30 pmIn this talk, we study certain moduli spaces of semistable objects in the Kuznetsov component of a cubic fourfold. We show that they admit a symplectic resolution \tilde{M} which is...
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HARVARD-MIT ALGEBRAIC GEOMETRY
February 16, 2021 3:00 pmGiven 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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HARVARD-MIT ALGEBRAIC GEOMETRY
February 9, 2021 3:00 pmThe problem of determining the birational nature of the moduli space of curves of genus g has received constant attention in the last century and inspired a lot of development in moduli...
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HARVARD-MIT ALGEBRAIC GEOMETRY
December 8, 2020 3:00 pmModuli spaces of curves admit finite covers by moduli spaces which parametrize curves together with so-called level structures. In my talk, I will discuss how the cohomology of these spaces...
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HARVARD-MIT ALGEBRAIC GEOMETRY
December 1, 2020 3:00 pmPositroid varieties are subvarieties of the Grassmannian obtained by intersecting cyclic rotations of Schubert varieties. We show that the "top open positroid variety" has mixed Hodge polynomial given by the...
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HARVARD-MIT ALGEBRAIC GEOMETRY
November 17, 2020 3:00 pmI will discuss recent work on computing the top weight cohomology of A_g for g up to 7. We use combinatorial methods coming from the relationship between the top weight...
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