Seminar
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Location: | UCB, Evans Hall, Rm 748 |
Elizabeth Pratt: "The Chow-Lam Form": The classical Chow form encodes any projective variety by a single equation. In this talk, I will introduce the Chow-Lam form, which is a generalization of the Chow form to subvarieties of arbitrary Grassmannians. Like the Chow form, it has useful computational properties: for example, it gives us universal formulas for certain linear projections between Grassmannians. Such formulas were pioneered by Thomas Lam for positroid varieties in the study of amplituhedra. This is joint work with Bernd Sturmfels.
Hannah Kerner Larson: "Cohomology of moduli spaces of curves": The moduli space of genus g curves (or Riemann surfaces) is a central object of study in algebraic geometry. Its cohomology is important in many fields. For example, the cohomology of is the same as the cohomology of the mapping class group, and is also related to spaces of modular forms. Using its properties as a moduli space, Mumford defined a distinguished subring of the cohomology of called the tautological ring. The definition of the tautological ring was later extended to the compactification and the moduli spaces with marked points . While the full cohomology ring of is quite mysterious, the tautological subring is relatively well understood, and conjecturally completely understood. In this talk, I'll ask the question: which cohomology groups are tautological? And when they are not, how can we better understand them? This is joint work with Samir Canning and Sam Payne.
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