Advisor: Dr. Maria Gillespie

Committee: Dr. Alexander Hulpke, Dr. Mark Shoemaker, Dr. Sudipto Ghosh

Title: Generalized RSK for enumerating projective maps from $n$-pointed curves

A recent result of Farkas and Lian in enumerative geometry arose in the study of linear series on curves. The theory of Schubert calculus leads to a natural combinatorial interpretation of their identity in terms of Young tableaux.

In this talk, we define the combinatorial and geometric objects involved, such as Young tableaux, the RSK correspondence, the Grassmannian and projective spaces, and Schubert cells. Then, we describe how Schubert calculus and the Littlewood-Richardson rule allow us to turn problems of intersecting geometric spaces into ones of counting Young tableaux with particular characteristics. Finally, we reinterpret Farkas and Lian’s results in purely combinatorial terms, and present new combinatorial proofs which generalize the RSK bijection on words.

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Meeting ID: 935 3200 1559

Passcode: 518283