Recent Developments in Higher Dimensional Algebraic Geometry Conference

Johns Hopkins University, Baltimore MD

Investigators

Abstract

The Johns Hopkins University Department of Mathematics, together with the Japan-U.S. Mathematics Institute (JAMI), will hold a conference and workshop in March 2006 under the title "Recent developments in higher dimensional algebraic geometry". The main focus of the proposed activity will be birational geometry. Finding good birational models of algebraic varieties and understanding the way these appear is the main achievement of the minimal model program. The activity will cover related topics of interest: derived categories, Fano varieties, Mori-Fano fiber spaces, explicit 3-fold geometry, minimal log discrepancies, singularities, rational curves and connectivity. Geometry is one of the oldest mathematical subjects. The Greeks were describing geometrical objects using congruence (of segments, angles, ...) and incidences (collinearity, tangency, ...). Congruence evolved into the modern-day differential geometry. Incidences evolved into algebraic geometry simply by replacing geometrical shapes by the equations defining them. The objects of study of algebraic geometry are called algebraic varieties. Understanding the structure of algebraic varieties is of fundamental importance from both the standpoint of algebraic geometry alone, and from that of the related disciplines and areas of application - mathematical physics, computational geometry, number theory, and others. Knowledge of algebraic varieties is also important in applied fields, such as optimization, control, statistics, economics and bioinformatics, coding, complexity and communications.