HARVARD-MIT ALGEBRAIC GEOMETRY
October 27, 2020 3:00 pmThe generic vanishing theorem of Green-Lazarsfeld says that for general elements in the Picard variety of a projective manifold, their cohomology groups vanish in all degrees. Moreover, the cohomological jumping...
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HARVARD-MIT ALGEBRAIC GEOMETRY
October 20, 2020 3:00 pmStringy Hodge numbers are certain generalizations, to the singular setting, of Hodge numbers. Unlike usual Hodge numbers, stringy Hodge numbers are not defined as dimensions of cohomology groups. Nonetheless, an...
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HARVARD-MIT ALGEBRAIC GEOMETRY
October 13, 2020 3:00 pmUsing recent advances in the Minimal Model Program for moduli spaces of sheaves on the projective plane, we compute the cohomology of the tensor product of general semistable bundles on...
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HARVARD-MIT ALGEBRAIC GEOMETRY
September 29, 2020 3:00 pmIf a complex, integral, projective curve C has only planar singularities, then its Jacobian admits a natural compactification with interesting topology. Work of Oblomkov, Shende, and others suggests the existence...
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HARVARD-MIT ALGEBRAIC GEOMETRY
September 22, 2020 3:00 pmRecently there has been tremendous progress on constructing (projective) moduli spaces of Fano varieties using K-stability. In this talk, we will show that the K-moduli space of cubic fourfolds coincide...
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HARVARD-MIT ALGEBRAIC GEOMETRY
September 8, 2020 3:00 pmThis talk is an invitation to derived methods in algebraic geometry. We will use derived algebraic geometry to give a solution to the problem of descending "bases" (semiorthogonal decompositions) on...
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HARVARD-MIT ALGEBRAIC GEOMETRY
March 3, 2020 3:00 pmIn a series of papers, Aluffi and Faber computed the degree of the GL3 orbit closure of an arbitrary plane curve. We attempt to generalize this to the equivariant setting...
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HARVARD-MIT ALGEBRAIC GEOMETRY
February 25, 2020 3:00 pmIt is well known that, for pointed nodal curves, considering flat and proper families of pairs (X,D) leads to a proper moduli space. Still, while the notion of stable pairs...
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HARVARD-MIT ALGEBRAIC GEOMETRY
February 11, 2020 3:00 pmThe talk will revolve around combinatorial aspects Prym varieties, a class of Abelian varieties that occurs in the presence of double covers. Pryms have deep connections with torsion points of...
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HARVARD-MIT ALGEBRAIC GEOMETRY
February 4, 2020 3:00 pmI will construct LG mirrors for the Johnson-Kollár series of anticanonical del Pezzo surfaces in weighted projective 3-spaces. The main feature of these surfaces is that their anticanonical linear system...
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