Higher Dimensional Geometry

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McKernan The area of the planned research is in higher dimensional algebraic geometry, more especially the minimal model program and Mori theory. Building on previous work, some questions centered around the log category (projective varieties with boundaries), especially work on log del Pezzo surfaces and deformation theory. Some more general problems in higher dimensional algebraic geometry are also proposed. This is research in the field of algebraic geometry. Algebraic geometry is one of the oldest parts of modern mathematics, but one which has had a revolutionary flowering in the past quarter-century. In its origin, it treated figures that could be defined in the plane by the simplest equations, namely polynomials. Nowadays the field makes use of methods not only from algebra, but from analysis and topology, and conversely is finding application in those fields as well as in physics, theoretical computer science, and robotics.