Seminar on Complex Analysis and Complex Geometry - Spring 2012

Wednesday, January 25, 2012, 11am, PGH 646

Title: Modular forms and special cubic fourfolds

Speaker: Zhiyuan Li, Rice University

Abstract: We study the degree of the special cubic fourfolds in the moduli space of cubic fourfolds via a computation of the generating series of Heegner divisors of even lattice of signature (20,2).

Friday-Sunday, February 17-19, 2012

Texas Geometry and Topology Conference (see TGTC Spring 2012)

Wednesday, March 28, 2012, 11am, PGH 646

Title: On the Demailly-Semple jet bundles of hypersurfaces in the 3-dimensional complex projective space

Speaker: Jingzhou Sun, Johns Hopkins University

Abstract: Let $X$ be a smooth hypersurface of degree $d$ in the 3-dimensional complex projective space. By totally algebraic calculations, we prove that on the third Demailly-Semple jet bundle $X_3$ of $X$, the Demailly-Semple line bundle is big for $d\geq 11$, and that on the fourth Demailly-Semple jet bundle $X_4$ of $X$, the Demailly-Semple line bundle is big for $d\geq 10$, improving a recent result of Diverio.

Wednesday, April 4, 2012, 11am, PGH 646

Title: Duality for the movable cone

Speaker: Brian Lehmann, Rice University

Abstract: Cones of divisors play an important role in describing the geometry of a smooth complex projective variety. Their main feature is the duality with cones of curves. I will describe a birational form of duality for the cone of movable divisors.

Wednesday, April 25, 2012, 11am, PGH 646

Title: On algebraic geometric codes

Speaker: Angelynn Alvarez, UH

Abstract: Whenever data is transmitted across a channel, errors are likely to occur and the received message may not be identical to the original message sent. An error-correcting code is an algorithm for expressing a sequence of elements such that any errors formed during transmission can be detected (and possibly corrected). These codes have multiple applications in, for example, cell-phones, credit cards, mp3 players, CDs, high-speed modems, and ISBN numbers. In 1977, V.D. Goppa applied algebraic geometry to Coding Theory to create improved codes, called algebraic geometric codes. In this talk, I will discuss the basic construction of algebraic geometric codes, and a strategy for producing efficient ones.