Sigma Function on Curves with Non-symmetric Semigroup

Watch a 37-minute lecture from Harvard CMSA's Workshop on Nonlinear Algebra and Combinatorics from Physics where Emma Previato from Boston University explores the sigma function on curves with non-symmetric semigroup. Delve into the relationship between spectral curves and commutative rings of differential operators, integrable hierarchies of non-linear PDEs, and Jacobian vector fields. Learn how operator coefficients can be explicitly written using the Kleinian sigma function - a generalization of Weierstrass' sigma function for genus greater than one that serves as a crucial tool in integrability. Examine the construction of a curve with non-symmetric Weierstrass semigroup (or Young tableau) and its sigma function through collaborative research, with discussions on potential applications to commutative rings of differential operators. The presentation covers topics including differential algebra, trans settings, elliptical curves, higher genus curves, differential resultants, and operator analysis.