Mathematical Sciences: Diophantine Equations, Diophantine Approximation and Geometry

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This research will study various problems in diophantine approximations and analytic number theory. One of the main themes will be the study of solutions of certain diophantine equations which are known to have nontrivial solutions and therefore must have solutions of small height. This Principal Investigator is an expert in the area of number theory which uses sophisticated analytic tools to answer questions about the integers and the rational approximations of real numbers. He will carry forward these investigations in the current research. It is important in many problems to know that it is possible to obtain solutions to certain equations for which one has precise measures on how big the solutions are. This will be a major theme of the current research, although there are many others in this broadly based research. Much of great interest will result from this program.