Mathematical Sciences: "Ascending/Descending Chain Conditions for Varieties with Log Canonical Singularities"

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Professor Alexeev will study varieties with log canonical singularities. In particular he intends to work on boundedness theorems in the 3-dimensional case in an attempt to generalize work of Kawamata and Mori on boundedness of Fano varieties. This is research in the field of algebraic geometry. Algebraic geometry itself 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.