Seminar in Algebraic Geometry and Number Theory

Abstract: In this talk, I will discuss the determinant of cohomology and its (conjectural) relationship to certain curve-counting on Calabi—Yau manifolds. The case in which the Calabi— Yau manifolds are elliptic curves will be discussed in detail, and other examples will be considered. If time permits, I will discuss ongoing work (w. Gerard Freixas) on these topics, surrounding the Grothendieck—Riemann—Roch theorem and geometric properties possibly expected from mirror symmetry considerations.