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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SEMINARS, HARVARD-MIT ALGEBRAIC GEOMETRY
November 15, 2022 3:00 pmGiven integers g, m, and n, the heavy/light moduli space Mbar_{g, m|n} is a compactification of the moduli space of smooth (m+n)-marked curves of genus g. These spaces are particular...
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SEMINARS, HARVARD-MIT ALGEBRAIC GEOMETRY
November 8, 2022 3:00 pmI’ll discuss a number of interactions between algebraic geometry, low-dimensional topology, and arithmetic, arising from the study of local systems on moduli spaces of curves. I’ll explain how, in joint...
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SEMINARS, HARVARD-MIT ALGEBRAIC GEOMETRY
October 25, 2022 3:00 pmCohomology groups of moduli spaces of curves are fruitfully studied from several mathematical perspectives, including geometric group theory, stably homotopy theory, and quantum algebra. Algebraic geometry endows these cohomology groups...
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SEMINARS, HARVARD-MIT ALGEBRAIC GEOMETRY
October 18, 2022 3:00 pmI will explain how to reinterpret invariant distributions on p-adic GL_n and its Lie algebra using symmetric functions. This reinterpretation, combined with some old results of Waldspurger, allows us to...
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SEMINARS, HARVARD-MIT ALGEBRAIC GEOMETRY
October 11, 2022 3:00 pmThe minimal model program is an ambitious program that aims to understand the geometry of complex projective varieties (eg. manifolds defined by polynomial equations). In this talk we will discuss...
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HARVARD-MIT ALGEBRAIC GEOMETRY
October 4, 2022 3:00 pmI will discuss my ongoing effort to comprehend, from a geometric viewpoint, the motivic monodromy conjecture for a "generic" complex multivariate polynomial f, namely any polynomial f that is non-degenerate...
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SEMINARS, HARVARD-MIT ALGEBRAIC GEOMETRY
September 27, 2022 3:00 pmArithmetic quotients of Type IV Hermitian symmetric domains have cohomology-valued modular forms whose coefficients are special cycles, by work of Borcherds. These can be interpreted as non-compact period spaces for...
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SEMINARS, HARVARD-MIT ALGEBRAIC GEOMETRY
September 20, 2022 3:00 pmWe prove that the categories of coherent (or, equivalently, of quasi-coherent) sheaves over two noetherian non-commutative schemes X and Y are equivalent if and only if there centers C(X) and...
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