Professor Beckmann will work on the arithmetic of branched coverings of curves. She hopes to describe arithmetic coverings of the projective line defined over number fields in terms of branch cycle descriptions of the coverings. In particular, she hopes to describe the ramification properties of field extensions derived from these coverings. This project falls into the general area of arithmetic geometry -a subject that blends two of the oldest areas of mathematics: number theory and geometry. This combination has proved extraordinarily fruitful - having recently solved problems that withstood generations. Among its many consequences are new error correcting codes. Such codes are essential for both modern computers (hard disks) and compact disks.
