Colloquium in Algebraic Geometry and Arithmetic Geometry

Abstract: It has been a long history, since Schwarz, that one of ways to search for a complex hyperbolic lattice is closely related to understanding the monodromy group of a hypergeometric system. In this talk, I will review the work of Schwarz and Klein on the classical Euler-Gauss hypergeometric functions, as well as the Deligne-Mostow theory on Lauricella hypergeometric functions. Then I will discuss a recent progress on this direction, inspired by the root system hypergeometric functions constructed by Heckman-Opdam.
 

Abstract: Let X be a surface of degree n, which is considered as a branch cover of CP^2 with respect to a generic projection. The surface X has a natural Galois cover with Galois group S_n. In this talk, we will use Moishezon-Teicher’s method to compute the fundamental group of the Galois cover of certain algebraic surfaces that can degenerate to a union of n projective planes such that no three planes meet in a line. This is joint work with M. Amram, C. Gong, M. Teicher and S.-L. Tan.
 

Abstract: In this talk, we will present some conjectural relations between scrollar syzygy resolution of algebraic curves and the classical theory of resolvents for solving algebraic equations. We will give a Galois theoretic perspective of the syzygy theory. If time permits, some possible number theory applications will also be discussed. This is a joint work with Wouter Castryck.
 

Abstract: The notion of generalized polarized pairs was introduced by Birkar and Zhang to deal with the effectivity of Iitaka fibration. Its prototype already appeared in the treatment of the canonical bundle formula for elliptic fibrations. The notion has since found more and more applications in solving problems for usual pairs.
  In the other direction, efforts have been made by several authors to extend results about pairs to the generalized setting. In this talk, after introducing the basic definitions of generalized polarized pairs, I will report on a recent joint work with HAN Jingjun on the (numerical) nonvanishing conjecture for generalized log canonical pairs.