SFU Number Theory and Algebraic Geometry Seminar: Carl Lian

Abstract: The geometric Tevelev degrees of projective space enumerate general, pointed curves with fixed complex structure interpolating through the maximal number of points in $\mathbb{P}^r$. The study of the corresponding virtual invariants goes back to the beginning of Gromov-Witten theory in the 1990s, whereas the closely related problem of enumerating linear series on general curves goes back even earlier, to the 19th century. We explain a complete calculation of the geometric Tevelev degrees of projective space in terms of Schubert calculus, which interpolates between both of these worlds. The final answer involves torus orbit closures on Grassmannians, which are fundamental objects in matroid theory. Recent work with Saskia Solotko expresses the invariants alternatively in terms of combinatorics of words, via the RSK correspondence.