The National Science Foundation has named the University of Utah the lead institution in a five-school Mathematical Sciences Regional Geometry Institute.

C. Herbert Clemens, U. professor of mathematics, will direct the institute under a 2 1/2-year, $1.4 million NSF grant. Other participating schools are the University of Texas at Austin, Rice University, the University of Illinois at Chicago and the University of Washington at Seattle.The U. will host summer institutes in 1991 and 1992, says Clemens, an algebraic geometrist and author of an innovative new textbook for high school geometry teachers. The text is used at the U. and at several other universities in the nation.

The institute's goals are to improve the understanding of elementary geometry, advance research in geometry and increase the number of talented students who pursue careers in mathematics, science and engineering.

The institute, says Clemens, will consist of academic-year programs at the five member schools and two summer institutes at the U., the first scheduled June 22-July 20, 1991, in Park City, Utah.

One hundred invited undergraduate and graduate students and high school geometry teachers will participate in the summer institute, which will also have a research component, led by 30 invited research mathematicians.

Because of its strong programs in geometry, the U. was named "home" institution for the NSF-funded program. The U.'s mathematics department is strong in geometric research, has ample course offerings in geometry, a good library in geometry and related subjects and outstanding computer facilities.

Over the past 16 years, the U. has emerged as a major national center for algebraic geometry. The mathematics department ranks among the highest in the nation in that specialty.

Clemens and James A. Carlson, also professor of mathematics, will teach courses at the summer institute, along with faculty from the other participating schools.

"NSF is concerned because the United States is simply not producing enough mathematicians to keep abreast of its national needs," says Clemens.

Clemens cites several national reports that indicate foreign nationals now make up the majority of students studying for doctorates and other advanced degrees in pure mathematics in the United States.

A special committee will select 100 fully funded participants for the summer institutes, including 30 outstanding high school geometry teachers from cities where the five participating universities are located. The institutes are also open to other high school geometry teachers who can pay their own registration and travel expenses.

Institute directors also hope to attract postgraduate fellows, outstanding upper division undergraduate students and graduate students in mathematics who are interested in doing research and pursuing doctoral degrees in geometry-related fields of study.