Mathematical Sciences: Geometry and Topology

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The investigator will pursue research on various questions concerned with topological properties of algebraic spaces. He intends to study the topology of algebraic varieties, especially invariants of families of plane algebraic curves, invariants of smooth structure on algebraic varieties, and the behavior of complex polynomials near infinity. Relating algebraic to topological structure of spaces is a source of some of the most basic and important questions in mathematics. It calls upon a wide variety of techniques and has challenged major figures in topology and algebra both here and abroad.