SEMINARS, HARVARD-MIT ALGEBRAIC GEOMETRY
March 7, 2023 3:00 pmSyzygies of algebraic varieties have long been a topic of intense interest among algebraists and geometers alike. Starting with the pioneering work of Mark Green on curves, numerous attempts have...
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SEMINARS, HARVARD-MIT ALGEBRAIC GEOMETRY
February 28, 2023 3:00 pmBrill-Noether theory answers the question of whether a general curve of genus $g$ admits $g^r_d$, a linear system of rank $r$ and degree $d$. A refined Brill-Noether theory hopes to...
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SEMINARS, HARVARD-MIT ALGEBRAIC GEOMETRY
February 28, 2023 3:00 pmBrill-Noether theory answers the question of whether a general curve of genus $g$ admits $g^r_d$, a linear system of rank $r$ and degree $d$. A refined Brill-Noether theory hopes to...
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SEMINARS, HARVARD-MIT ALGEBRAIC GEOMETRY
February 21, 2023 3:00 pmThe period-index problem is a longstanding question about the complexity of Brauer classes over a field. I will discuss some Hodge-theoretic aspects of the problem for complex function fields, and...
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SEMINARS, HARVARD-MIT ALGEBRAIC GEOMETRY
February 14, 2023 3:00 pmThe purpose of this talk is to discuss Newton-Okounkov bodies, a convex geometric construction associated to divisors on projective varieties. We will touch on their relationship with local positivity, multiplicative...
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SEMINARS, HARVARD-MIT ALGEBRAIC GEOMETRY
February 7, 2023 3:00 pmIn this talk, I will discuss the behavior of positivity, hyperbolicity, and Kodaira dimension under smooth morphisms of complex quasi-projective manifolds. This includes a vast generalization of a classical result:...
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SEMINARS, HARVARD-MIT ALGEBRAIC GEOMETRY
January 31, 2023 3:00 pmA conjecture of Orlov predicts the invariance of the Hodge numbers of a smooth projective complex variety under derived equivalence. For instance this has been verified in the case of...
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SEMINARS, HARVARD-MIT ALGEBRAIC GEOMETRY
December 12, 2022 3:00 pmThe intersection theory of the moduli space of K3 surfaces polarized by a lattice is a subject of recent interest because of its deep connections with a wide variety of...
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SEMINARS, HARVARD-MIT ALGEBRAIC GEOMETRY
December 6, 2022 3:00 pmI will discuss various aspects of the geometry of Quot schemes of torsion quotients on a smooth projective curve. I will describe in particular results on the cohomology of tautological...
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SEMINARS, HARVARD-MIT ALGEBRAIC GEOMETRY
November 29, 2022 3:00 pmI will discuss recent work calculating the top weight cohomology of the moduli space A_g of principally polarized abelian varieties of dimension g for small values of g. The key...
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